Simple and Compound Interest, Stock

PrepBank · পাতা ২ / ৯ · ১০১–২০০ / ৮৫৮

১০১.

A man's investment doubles in every 5 years. If he invested Tk. 5,000 in each of the years 2010, 2015, 2020 then what will be the amount received by him in 2025?

ক
Tk. 50000
খ
Tk. 70000
গ
Tk. 110000
ঘ
Tk. 120000

সঠিক উত্তর: খ

Tk. 70000

উত্তর

সঠিক উত্তর: খ

Tk. 70000

খ

ব্যাখ্যা

Question: A man's investment doubles in every 5 years. If he invested Tk. 5,000 in each of the years 2010, 2015, 2020 then what will be the amount received by him in 2025?

Solution:
২০১০ এ বিনিয়োগ করা ৫০০০ টাকার ক্ষেত্রে,
২০২৫ সালে পাওয়া যাবে = ৫০০০ × ২^৩
= ৪০০০০ টাকা

২০১৫ এ বিনিয়োগ করা ৫০০০ টাকার ক্ষেত্রে,
২০২৫ সালে পাওয়া যাবে = ৫০০০ × ২^২
= ২০০০০ টাকা

২০২০ এ বিনিয়োগ করা ৫০০০ টাকার ক্ষেত্রে,
২০২৫ সালে পাওয়া যাবে = ৫০০০ × ২^১
= ১০০০০ টাকা

মোট = ৪০০০০ + ২০০০০ + ১০০০০
= ৭০০০০ টাকা

১০২.

A certain sum of money triples itself in 8 years at simple interest. What is the rate of interest per annum?

ক
25%
খ
20%
গ
12.5%
ঘ
15%

সঠিক উত্তর: ক

25%

উত্তর

সঠিক উত্তর: ক

25%

ক

ব্যাখ্যা

Question: A certain sum of money triples itself in 8 years at simple interest. What is the rate of interest per annum?

Solution:
Let,
Principal = P
Interest, I = 3P - P = 2P
Time, n = 8 years
rate = r

r = I/(Pn)
= (2P)/(P × 8)
= (1/4) × 100%
= 25%

১০৩.

Tk. 8000 becomes Tk. 9600 in 2 years at a certain rate of simple interest. If the rate becomes double, what will be the total amount in 5 years on the same principal?

ক
Tk. 13200
খ
Tk. 18500
গ
Tk. 12000
ঘ
Tk. 16000

সঠিক উত্তর: ঘ

Tk. 16000

উত্তর

সঠিক উত্তর: ঘ

Tk. 16000

ঘ

ব্যাখ্যা

Question: Tk. 8000 becomes Tk. 9600 in 2 years at a certain rate of simple interest. If the rate becomes double, what will be the total amount in 5 years on the same principal?

Solution:
Principal = Tk. 8000
Amount after 2 years = Tk. 9600
∴ Interest in 2 years = 9600 - 8000 = Tk. 1600
∴Interest per year = 1600/2 = Tk. 800

Since the interest rate doubles, the yearly interest also doubles,
∴ Interest per year = 800 × 2 = Tk. 1600
⇒ Interest for 5 years = 1600 × 5 = Tk. 8000
⇒ New total amount = 8000 + 8000 = Tk. 16000

১০৪.

How much must 1 pay for Tk. 1365 stock at 104? (brokerage 1%)

ক
Tk 1514.75
খ
Tk 1435.50
গ
Tk 1433.25
ঘ
None of these

সঠিক উত্তর: গ

Tk 1433.25

উত্তর

সঠিক উত্তর: গ

Tk 1433.25

গ

ব্যাখ্যা

Question: How much must 1 pay for Tk. 1365 stock at 104? (brokerage 1%)

Solution:
Required answer = Tk. 1365 × (104 + 1)/100
= Tk. (1365 × 105)/100
= Tk. 1433.25

১০৫.

What sum of money will amount to Tk. 2,500 in 4 years and to Tk. 2,900 in 6 years at simple interest?

ক
Tk. 1,700
খ
Tk. 1,900
গ
Tk. 2,100
ঘ
Tk. 2,300

সঠিক উত্তর: ক

Tk. 1,700

উত্তর

সঠিক উত্তর: ক

Tk. 1,700

ক

ব্যাখ্যা

Question: What sum of money will amount to Tk. 2,500 in 4 years and to Tk. 2,900 in 6 years at simple interest?

Solution:
Increase in 2 years = 2,900 - 2,500
= Tk. 400

∴ Simple interest for 2 years = Tk. 400
∴ Simple interest for 4 years = Tk. (400 × 4/2)
= Tk. 800

Principal, P = 2,500 - 800
= Tk. 1,700

১০৬.

A sum of money at compound interest doubles itself in 15 years. It will become four times of itself in-

ক
ক) 20years
খ
খ) 25 years
গ
গ) 30 years
ঘ
ঘ) 45 years

সঠিক উত্তর: গ

গ) 30 years

উত্তর

সঠিক উত্তর: গ

গ) 30 years

গ

ব্যাখ্যা

Question: A sum of money at compound interest doubles itself in 15 years. It will become four times of itself in-

Solution:
let the sum P

2P = P (1 + r)¹⁵
⇒ (1 + r)¹⁵ = 2

let, sum will 4 times in n years
4P = P(1 + r)ⁿ
⇒ 4 = (1 + r)ⁿ
⇒ 2² = (1 + r)ⁿ
⇒ ((1 + r)¹⁵)² = (1 + r)ⁿ
⇒ (1 + r)³⁰ = (1 + r)ⁿ
∴ n = 30 years

১০৭.

A man sells Tk. 5000, 12 % stock at 156 and invests the proceeds parity in 8 % stock at 90 and 9 % stock at 108. He hereby increases his income by Tk. 70. How much of the proceeds were invested in each stock?

ক
ক) Tk. 4000
খ
খ) Tk. 4200
গ
গ) Tk. 4002
ঘ
ঘ) Tk. 4020

সঠিক উত্তর: খ

খ) Tk. 4200

উত্তর

সঠিক উত্তর: খ

খ) Tk. 4200

খ

ব্যাখ্যা

S.P of Tk. 5000 stock = {(156/100) × 5000}
= Tk. 7800

Income from this stock = tk. {(12/100) × 5000}
= Tk. 600

Let investment in 8 % stock be x and that in 9 % stock = (7800 - x).

Therefore,
x × (8/90) + (7800 - x) × 9/108 = 600 + 70
⇒ 4x/45 + {(7800 - x)/12} = 670
⇒ 16x + 117000 - 15x = 670 × 180
⇒ x = 3600

Money invested in 8% stock at 90 = Tk. 3600
Money invested in 9% at 108 = Tk. (7800 - 3600)
= Tk. 4200.

১০৮.

Find the compound interest on Tk. 10,000 in 2 years at 4% per annum, the interest being compounded half-yearly.

ক
832.24
খ
824.32
গ
823.23
ঘ
438.31
ঙ
428.32

সঠিক উত্তর: খ

824.32

উত্তর

সঠিক উত্তর: খ

824.32

খ

ব্যাখ্যা

Principal = Tk. 10000;
Rate = 2% per half-year;
Time = 2 years = 4 half-years.
Amount= [10000 × (1+2/100)⁴]
=[10000 × 51/50 × 51/50 × 51/50 × 51/50]
= 10824.32.
C.I. = (10824.32 - 10000) = 824.32.

১০৯.

A sum of money amounts to Tk.6690 after 3 year and to Tk.10,035 after 6 year on compound interest.find the sum.

ক
ক) 4360
খ
খ) 4460
গ
গ) 4560
ঘ
ঘ) 4660

সঠিক উত্তর: খ

খ) 4460

উত্তর

সঠিক উত্তর: খ

খ) 4460

খ

ব্যাখ্যা

Let the sum be Tk.P.then
P(1+R/100)³=6690…(i) and
P(1+R/100)⁶=10035…(ii)
On dividing,we get (1+R/100)³=10025/6690=3/2.
Substituting this value in (i),we get:
P×(3/2)=6690 or
P=(6690× 2/3)=4460
Hence,the sum is Tk.4460.

১১০.

A sum of Tk. 10,000 amounts to Tk. 12,000 in 4 years at the rate of simple interest. What is the rate of interest?

ক
ক) 3%
খ
খ) 4%
গ
গ) 5%
ঘ
ঘ) 6%

সঠিক উত্তর: গ

গ) 5%

উত্তর

সঠিক উত্তর: গ

গ) 5%

গ

ব্যাখ্যা

Question: A sum of Tk. 10,000 amounts to Tk. 12,000 in 4 years at the rate of simple interest. What is the rate of interest?

Solution:
সুদ = ১২০০০ - ১০০০০ টাকা
= ২০০০ টাকা

ধরি, সুদের হার r%

I = pnr
⇒ 2000 = 10000 × 4 × r/100
⇒ r = 5

সুদের হার ৫%

১১১.

Some principal becomes Tk. 1,560 as profit-principal in 3 years and Tk. 1,920 as profit-principal in 6 years. Find the rate of profit.

ক
13.5%
খ
12%
গ
10%
ঘ
10.5%

সঠিক উত্তর: গ

10%

উত্তর

সঠিক উত্তর: গ

10%

গ

ব্যাখ্যা

Question: Some principal becomes Tk. 1,560 as profit-principal in 3 years and Tk. 1,920 as profit-principal in 6 years. Find the rate of profit.

Solution:
Given,
Principal + Profit for 3 years = 1560
Principal + Profit for 6 years = 1920

So the profit of 3 years I = Tk. (1920 - 1560)
= Tk. 360

So the principal P = Tk. (1560 - 360)
= Tk. 1200

∴ The rate of profit r = (I × 100)/(P × n)
= (360 × 100)/(1200 × 3)
= 10

১১২.

Mr. Rahim deposited a certain amount of money in a bank. Upon maturity, he received a total of Tk. 72,000, where the ratio of interest to principal was 1 : 5. If the simple interest rate was 4%, for how many years was the money invested?

ক
3 years
খ
5 years
গ
6 years
ঘ
8 years
ঙ
4 years

সঠিক উত্তর: খ

5 years

উত্তর

সঠিক উত্তর: খ

5 years

খ

ব্যাখ্যা

Question: Mr. Rahim deposited a certain amount of money in a bank. Upon maturity, he received a total of Tk. 72,000, where the ratio of interest to principal was 1 : 5. If the simple interest rate was 4%, for how many years was the money invested?

Solution:
প্রদত্ত তথ্য অনুযায়ী, আসল (P) এবং সুদের (I) অনুপাত = 5 : 1
মোট প্রাপ্ত টাকা (সুদ-আসল) = 72,000 টাকা
অনুপাতের যোগফল = 5 + 1 = 6

আসল (P) = 72,000 এর (5/6) অংশ = 60,000 টাকা
সুদ (I) = 72,000 এর (1/6) অংশ = 12,000 টাকা

এখানে,
I = 12,000 টাকা
P = 60,000 টাকা
R = 4%
T = ?

আমরা জানি, SI = (P × R × T)/100
⇒ 12,000 = (60,000 × 4 × T)/100
⇒ 12,000 = 600 × 4 × T
⇒ 12,000 = 2,400 × T
⇒ T = 12,000/2,400
⇒ T = 5

∴ টাকাটি 5 বছরের জন্য বিনিয়োগ করা হয়েছিল।

১১৩.

In January, the value of a stock increased by 50%; and in February, it decreased by 20%. In March, it increased by 25%; and in April, it decreased by 10%. If a person invested Tk. 200 in the stock on January 1 and sold it at the end of April, what was the percentage change in the price of the stock?

ক
5%
খ
15%
গ
20%
ঘ
35%

সঠিক উত্তর: ঘ

35%

উত্তর

সঠিক উত্তর: ঘ

35%

ঘ

ব্যাখ্যা

Question: In January, the value of a stock increased by 50%; and in February, it decreased by 20%. In March, it increased by 25%; and in April, it decreased by 10%. If a person invested Tk. 200 in the stock on January 1 and sold it at the end of April, what was the percentage change in the price of the stock?

Solution:
At the end of January,
The value of the stock is = Tk. 200 + 50% of (Tk. 200)
= Tk. 200 + Tk. 100 = Tk. 300.

At the end of February,
The value of the stock is = Tk. 300 - 20% of (Tk. 300)
= Tk. 300 - Tk. 60 = Tk. 240.

At the end of March,
The value of the stock is = Tk. 240 + 25% of (Tk. 240)
= Tk. 240 + Tk. 60 = Tk. 300.

At the end of April,
The value of the stock is = Tk. 300 - 10% of (Tk. 300)
= Tk. 300 - Tk. 30 = Tk. 270.

Now, the percentage change in price is,
= (Change in price/Original price) × 100%
= (270 - 200)/200 × 100%
= (70/200) × 100%
= 35%

১১৪.

Simple interest on a certain sum at a certain annual rate of interest is 1/9 of the sum. If the numbers representing rate percent and time in years be equal, then the rate of interest is -

ক
ক) (8/3)%
খ
খ) (7/3)%
গ
গ) (5/3)%
ঘ
ঘ) (10/3)%

সঠিক উত্তর: ঘ

ঘ) (10/3)%

উত্তর

সঠিক উত্তর: ঘ

ঘ) (10/3)%

ঘ

ব্যাখ্যা

Let sum=x Then, S.I.=x/9.
Let rate=R% and time= R years.
Now
(x × R × R)/100 = x/9
R²/100 = 1/9
R² = 100/9
R = 10/3

Rate=(10/3)%

১১৫.

A person borrows Tk. 5,000 for 2 years at 4% p.a. simple interest. He immediately lends it to another person at 25/4 % per annum for 2 years. Find his gain in the transaction per year.

ক
ক) Tk. 120.4
খ
খ) Tk. 115.7
গ
গ) Tk. 112.50
ঘ
ঘ) Tk. 108

সঠিক উত্তর: গ

গ) Tk. 112.50

উত্তর

সঠিক উত্তর: গ

গ) Tk. 112.50

গ

ব্যাখ্যা

Gain in 2 years = (5000 × 25/4 × 2/100) - (5000 × 4 × 2/100) = Tk. 225
Gain in 1 year = Tk. 225/2 = Tk. 112.5

১১৬.

In how many years the simple interest on Tk. 6000 at 10% rate of interest S.I will become Tk. 1800?

ক
3 years
খ
3.5 years
গ
4 years
ঘ
4.5 years

সঠিক উত্তর: ক

3 years

উত্তর

সঠিক উত্তর: ক

3 years

ক

ব্যাখ্যা

Question: In how many years the simple interest on Tk. 6000 at 10% rate of interest S.I will become Tk. 1800?

Solution:
Principal, P = 6000
Simple Interest, I = 1800
Rate of interest = 10%
Number of time = n year

n = I/Pr
= (1800 × 100)/(6000 × 10)
= 3

১১৭.

Soma borrowed Tk. 50,000 for 3 years at the rate of 3.5% per annum. Find the interest accumulated at the end of 3 years.

ক
ক) Tk. 4750
খ
খ) Tk. 5000
গ
গ) Tk. 5250
ঘ
ঘ) Tk. 5580

সঠিক উত্তর: গ

গ) Tk. 5250

উত্তর

সঠিক উত্তর: গ

গ) Tk. 5250

গ

ব্যাখ্যা

Given that,
P = Rs 50,000
R = 3.5%
T = 3 years

S.I.
= (P × R × T)/100
= (50,000 × 3.5 × 3)/100
= Tk. 5250.

১১৮.

A man purchased a cow for Tk. 3000 and sold it the same day for Tk. 3600, allowing the buyer a credit of 2 years. If the rate of interest be 10% per annum, then the man has a gain of -

ক
5%
খ
7%
গ
3%
ঘ
0%
ঙ
2%

সঠিক উত্তর: ঘ

উত্তর

সঠিক উত্তর: ঘ

ঘ

ব্যাখ্যা

Cost price = Tk 3000
Selling price = [{3600 × 100}/{100 + (10 × 2)}]
= Tk. 3000
Gain = 0%

১১৯.

A man borrowed some money for six months. He paid Tk. 500 at an interest rate of 10% per annum. What was the amount he borrowed?

ক
Tk. 8000
খ
Tk. 10000
গ
Tk. 12500
ঘ
Tk. 15000

সঠিক উত্তর: খ

Tk. 10000

উত্তর

সঠিক উত্তর: খ

Tk. 10000

খ

ব্যাখ্যা

Question: A man borrowed some money for six months. He paid Tk. 500 at an interest rate of 10% per annum. What was the amount he borrowed?

Solution:
এখানে,
সরল সুদ (SI) = Tk. 500
সুদের হার, r = 10%
সময়, n = 6 মাস = 6/12 = 1/2 বছর
আসল (Principal), P = ?

আমরা জানি,
I = Pnr/100
⇒ 500 = (P × 1/2 ×10)/100
⇒ 500 = 5P/100
⇒ 500 = P/20
⇒ P = 20 × 500
∴ P = 10000

অতএব, তিনি মোট Tk. 10,000 ধার নেন।

১২০.

A certain sum of money is invested at an interest rate of 5% per annum and a second sum twice as large as the first is invested at 5.5% p. a. The total amount of interest earned from two investments together is Tk. 1000 per year and the interest is withdrawn every year. The first sum invested is:

ক
Tk. 6750
খ
Tk. 6250
গ
Tk. 6220
ঘ
Tk. 6520

সঠিক উত্তর: খ

Tk. 6250

উত্তর

সঠিক উত্তর: খ

Tk. 6250

খ

ব্যাখ্যা

Question: A certain sum of money is invested at an interest rate of 5% per annum and a second sum twice as large as the first is invested at 5.5% p. a. The total amount of interest earned from two investments together is Tk. 1000 per year and the interest is withdrawn every year. The first sum invested is:

Solution:
Let
Two sums Tk. x and Tk. 2x

Now
{(x × 5 × 1)/100} + {(2x × 5.5× 1)/100} = 1000
5x + 11x = 100000
16x = 100000
x = 6250

The first sum = Tk. 6250

১২১.

Kabir paid Tk. 9,600 as interest on a loan he took 5 years ago at the rate of 16% simple interest per annum. What was the principal amount (the original loan amount) he borrowed?

ক
Tk. 12000
খ
Tk. 16400
গ
Tk. 18000
ঘ
Tk. 12500

সঠিক উত্তর: ক

Tk. 12000

উত্তর

সঠিক উত্তর: ক

Tk. 12000

ক

ব্যাখ্যা

Question: Kabir paid Tk. 9,600 as interest on a loan he took 5 years ago at the rate of 16% simple interest per annum. What was the principal amount (the original loan amount) he borrowed?

Solution:
SI = Interest paid = Tk. 9600
R = Rate of interest = 16% per annum
T = Time = 5 years
P = Principal (the amount we need to find)

We know,
SI = (P × R × T)/100
⇒ 9600 = (P × 16 × 5)/100
⇒ 9600 = (P × 80)/100
⇒ P = 96000/8
∴ P = 12000

∴ Kabir took a loan of Tk. 12000.

১২২.

The difference in taka between simple and compound Interest at 5% annually on a sum of Tk 2000 after 2 year is –

ক
ক) 5
খ
খ) 50
গ
গ) 20
ঘ
ঘ) 200

সঠিক উত্তর: ক

ক) 5

উত্তর

সঠিক উত্তর: ক

ক) 5

ক

ব্যাখ্যা

5% হার সুদে 2000 টাকার 2 বছরের সরল সুদ = (5 × 2000 × 2) / 100 = 200 টাকা
5% হার সুদে 2000 টাকার 2 বছরের চক্রবৃদ্ধি সুদ = [2000(1 + 5/100)² - 2000]
= 2205 - 2000 = 205 টাকা
সুতরাং, সরল সুদ এবং চক্রবৃদ্ধি সুদের পার্থক্য = 205 - 200 = 5 টাকা

১২৩.

At what rate per annum will Tk. 32000 yield a compound interest of Tk. 5044 in 9 months interest being compounded quarterly?

ক
20%
খ
26%
গ
32%
ঘ
40%

সঠিক উত্তর: ক

20%

উত্তর

সঠিক উত্তর: ক

20%

ক

ব্যাখ্যা

Question: At what rate per annum will Tk. 32000 yield a compound interest of Tk. 5044 in 9 months interest being compounded quarterly?

Solution:
Let, the rate of CI be R per cent per annum
CI = P[{1 + (R/100)}^T - 1]
5044 = 32000[{1 + (R/400)}³ - 1]

Since, Interest is compounded quarterly
(5044/32000) = {1 + (R/400)}³ - 1
⇒ {1 + (R/400)}³ - 1 = 1261/8000
⇒ {1 + (R/400)}³ = 1 + (1261/8000)
⇒ {1 + (R/400)}³ = 9261/8000
⇒ {1 + (R/400)}³ = (21/20)³
⇒ 1 + (R/400) = 21/20
⇒ R/400 = (21/20) - 1
⇒ R/400 = 1/20
⇒ r = 400/20
∴ r = 20%

১২৪.

What will be the difference between simple and compound interest at 10% on a sum of Tk. 5000 after 3 years?

ক
Tk. 50
খ
Tk. 120
গ
Tk. 155
ঘ
Tk. 180
ঙ
Tk. 32

সঠিক উত্তর: গ

Tk. 155

উত্তর

সঠিক উত্তর: গ

Tk. 155

গ

ব্যাখ্যা

Question: What will be the difference between simple and compound interest at 10% on a sum of Tk. 5000 after 3 years?

Solution:
Given that,
Principal, P = Tk. 5000
Rate of interest, r = 10%
Time, n = 3 years

Simple Interest (SI):
SI = (P × r × n) / 100
⇒ SI = (5000 × 10 × 3) / 100
⇒ SI = 150000 / 100
⇒ SI = Tk. 1500

Compound Interest (CI):
CI = P × (1 + r/100)ⁿ
= 5000 × (1 + 10/100)³= 5000 × (1.10)³= 5000 × 1.331
= 6655

CI = A - P
= 6655 - 5000 = Tk. 1655

∴ Difference between CI and SI:
= CI - SI
= 1655 - 1500
= Tk. 155

১২৫.

Find compound interest on Tk. 8000 at 15% per annum for 2 year 4 months, compounded annually

ক
ক) 2109
খ
খ) 3109
গ
গ) 4109
ঘ
ঘ) 5109

সঠিক উত্তর: খ

খ) 3109

উত্তর

সঠিক উত্তর: খ

খ) 3109

খ

ব্যাখ্যা

Time = 2 year 4 months = 2(4/12) year = 2(1/3) year.
Amount = Tk'. [8000 X (1+(15/100))² X (1+((1/3)×15)/100)]
=Tk. [8000 ×(23/20) × (23/20) ×(21/20)]
= Tk. 11109.
:. C.I. = Tk. (11109 - 8000)
= Tk. 3109.

১২৬.

The difference between the simple interest received from two different sources on Tk.1500 for 3 year is Tk.13.50. The difference between their rates of interest is

ক
ক) 0.1%
খ
খ) 0.2%
গ
গ) 0.3%
ঘ
ঘ) 0.4%

সঠিক উত্তর: গ

গ) 0.3%

উত্তর

সঠিক উত্তর: গ

গ) 0.3%

গ

ব্যাখ্যা

(1500 x R1 x 3)/100
=> 4500 (R1-R2) = 1350
=> (R1-R2)= 1350/4500 = 0.3 %

১২৭.

Find the amount if Tk. 20000 is invested at 10% compound interest p.a. for 3 years.

ক
Tk. 26600
খ
Tk. 26680
গ
Tk. 26620
ঘ
Tk. 26660

সঠিক উত্তর: গ

Tk. 26620

উত্তর

সঠিক উত্তর: গ

Tk. 26620

গ

ব্যাখ্যা

Question: Find the amount if Tk. 20000 is invested at 10% compound interest p.a. for 3 years.

Solution:
Using the formula:
C = P [1 + R/100]ⁿ
C = 20000 [1 + (10/100)]³
= 20000 × 1.1 × 1.1× 1.1
= 26620

১২৮.

To produce an annual income of Tk. 1200 from a 12% stock at 90, the amount of stock required is-

ক
Tk. 10800
খ
Tk. 10000
গ
Tk. 14400
ঘ
Tk. 16000

সঠিক উত্তর: খ

Tk. 10000

উত্তর

সঠিক উত্তর: খ

Tk. 10000

খ

ব্যাখ্যা

Question: To produce an annual income of Tk. 1200 from a 12% stock at 90, the amount of stock required is-

Solution:
12% stock at 90 mean,
Stock face value 100 and market value 90

12 Taka can be produced from Tk. 100
1 Taka can be produced from Tk. 100/12
1200 Taka can be produced from Tk. (100 × 1200)/12 = Tk. 10000

১২৯.

A sum becomes Tk 13,310 in 3 years at 10% per annum compound interest. Find the principal amount.

ক
9513 tk
খ
9831 tk
গ
10000 tk
ঘ
11234 tk

সঠিক উত্তর: গ

10000 tk

উত্তর

সঠিক উত্তর: গ

10000 tk

গ

ব্যাখ্যা

Question: A sum becomes Tk 13,310 in 3 years at 10% per annum compound interest. Find the principal amount.

Solution:
Let the sum be Tk p
∴ 13310 = p{1 + (10/100)³
⇒ 13310 = p{1 + (1/10)³
⇒ 13310 = p(11/10)³
⇒ p = (13310 × 10 × 10 × 10) / (11 × 11 × 11)
⇒ p = 10000 tk

১৩০.

A sum of money at simple interest amounts to Tk. 815 in 3 years and to Tk. 854 in 4 years. The sum is-

ক
Tk. 500
খ
Tk.525
গ
Tk. 612
ঘ
Tk. 698

সঠিক উত্তর: ঘ

Tk. 698

উত্তর

সঠিক উত্তর: ঘ

Tk. 698

ঘ

ব্যাখ্যা

Question: A sum of money at simple interest amounts to Tk. 815 in 3 years and to Tk. 854 in 4 years. The sum is-

Solution:
Simple interest for 1 year = Tk. (854 - 815)
= Tk. 39

∴ Simple interest for 3 years = Tk.(39 × 3)
= Tk. 117

∴ Sum = (815 - 117)
= Tk. 698

১৩১.

A sum of money at simple interest amounts to Tk 815 in 3 years and to Tk 854 in 4 years. The sum is _______

ক
ক) Tk. 650
খ
খ) Tk. 690
গ
গ) Tk. 700
ঘ
ঘ) Tk. 698

সঠিক উত্তর: ঘ

ঘ) Tk. 698

উত্তর

সঠিক উত্তর: ঘ

ঘ) Tk. 698

ঘ

ব্যাখ্যা

Question: A sum of money at simple interest amounts to Tk 815 in 3 years and to Tk 854 in 4 years. The sum is _______

Solution:
Simple interest for 1 years = Tk. (854 - 815)
= Tk. 39

∴ Simple interest for 3 years = Tk.(39 × 3)
= Tk. 117

∴ Sum = (815 - 117)
= Tk. 698

১৩২.

A sum of money at simple interest doubles in 7 years. It will becomes four times in -

ক
14 years
খ
21 years
গ
28 years
ঘ
35 years

সঠিক উত্তর: খ

21 years

উত্তর

সঠিক উত্তর: খ

21 years

খ

ব্যাখ্যা

Question: A sum of money at simple interest doubles in 7 years. It will becomes four times in -

Solution:
Let,
Principal be, P = x
Amount after 7 years = 2x
Simple interest, I = 2x - x = x

we know that,
I = Pnr
x = 7xr/100
∴r = 100/7 %

again
Amount, P = 4x
Interest, I = 4x - x = 3x

I = Pnr
n = I/Pr
= 3x/{x(100/7%)}
= 21

∴ in 21 years it will be four times.

১৩৩.

Find the difference between compound and simple interest for Tk. 8,000 invested at 10% per annum for 3 years.

ক
Tk. 248
খ
Tk. 325
গ
Tk. 284
ঘ
Tk. 240

সঠিক উত্তর: ক

Tk. 248

উত্তর

সঠিক উত্তর: ক

Tk. 248

ক

ব্যাখ্যা

Question: Find the difference between compound and simple interest for Tk. 8,000 invested at 10% per annum for 3 years.

Solution:
Given that,
Principal, P = Tk. 8,000
Rate, r = 10% = 10/100 = 0.1
Time, n = 3 years

We know that,
Simple Interest = Prn/100
= (8000 × 10 × 3)/100
= 2400
And
Compound Interest = P(1 + r)ⁿ - P
= 8000(1 + 0.1)³ - 8000
= 8000(1.1)³ - 8000
= 10648 - 8000
= 2648

∴ Difference = 2648 - 2400 = 248
The difference between compound and simple profit is Tk. 248

১৩৪.

Find the amount on Tk. 5000 at the rate of 20% per annum for 18 months when interest is compounded half yearly.

ক
6644
খ
6666
গ
6000
ঘ
6655

সঠিক উত্তর: ঘ

6655

উত্তর

সঠিক উত্তর: ঘ

6655

ঘ

ব্যাখ্যা

Question: Find the amount on Tk. 5000 at the rate of 20% per annum for 18 months when interest is compounded half yearly.

Solution:
n = 18/12 = 3/2
A = P (1 + R/200)²ⁿ = 5000 (1 + 20/200)²ⁿ
= 5000(1 + 1/10)^{2 × (3/2)}
= 5000 (1.1)³
= 6655

১৩৫.

What will be the difference between simple and compound interest at 6% on a sum of Tk. 15000 after 2 years?

ক
Tk. 24
খ
Tk. 42.5
গ
Tk. 54
ঘ
Tk. 64

সঠিক উত্তর: গ

Tk. 54

উত্তর

সঠিক উত্তর: গ

Tk. 54

গ

ব্যাখ্যা

Question: What will be the difference between simple and compound interest at 6% on a sum of Tk. 15000 after 2 years?

Solution:
দেওয়া আছে, Principal, P = 15000 টাকা
Rate of interest, r = 6%
Time, n = 2 বছর

Simple Interest (SI):
SI = (P × r × n) / 100
= (15000 × 6 × 2) / 100
= 180000 / 100
= 1800 টাকা

Compound Interest (CI):
CI = P × (1 + r/100)ⁿ - P
= 15000 × (1 + 6/100)² - 15000
= 15000 × (1.06)² - 15000
= 15000 × 1.1236 - 15000
= 16854 - 15000
= 1854 টাকা

∴ Difference between CI and SI:
= 1854 - 1800
= 54 টাকা

১৩৬.

Find compound amount and compound interest for Tk. 10000 at 3% interest per annum in 2 years.

ক
Tk. 10609, Tk. 609
খ
Tk. 10509, Tk. 509
গ
Tk. 10409, Tk. 409
ঘ
Tk. 10309, Tk. 309

সঠিক উত্তর: ক

Tk. 10609, Tk. 609

উত্তর

সঠিক উত্তর: ক

Tk. 10609, Tk. 609

ক

ব্যাখ্যা

Question: Find compound amount and compound interest for Tk. 10000 at 3% interest per annum in 2 years.

Solution:
Principal (P) = Tk. 10000
Rate (R) = 3%
Time (n) = 2 years

A = P[1+(R/100)]ⁿ
A = 10000(1 + 3/100)²
= 10000 × 1.03 × 1.03
= 10609

Compound Amount (A) = Tk. 10609

Compound Interest (CI) = A - P
⇒ CI = 10609 - 10000
⇒ CI = 609

১৩৭.

A 2-year certificate of deposit is purchased for Tk. K. If the certificate earns interest at an annual rate of 6 percent compound quarterly, which of the following represents the value, in Tk., of the certificate at the end of 2 years?

ক
k(1.06)⁶
খ
k(1.06)⁸
গ
k(1.015)⁸
ঘ
k(1.015)²
ঙ
k(1.06)²

সঠিক উত্তর: গ

k(1.015)⁸

উত্তর

সঠিক উত্তর: গ

k(1.015)⁸

গ

ব্যাখ্যা

Question: A 2-year certificate of deposit is purchased for Tk. K. If the certificate earns interest at an annual rate of 6 percent compound quarterly, which of the following represents the value, in Tk., of the certificate at the end of 2 years?

Solution:
Annual Rate of interest= 6%
∴ Quaterly rate of interest= (6/4)% = 1.5% = 1.5/100 = 0.015

Now, periods of compounding in 2 years= 8 (8 quarters)

value of k at the end of 2 years, if compounded quaterly = k(1 + r)ⁿ
= k(1 + 0.015)⁸
= k(1.015)⁸

১৩৮.

বার্ষিক ৫% মুনাফায় ১৬,০০০ টাকার ২ বছরের সরল ও চক্রবৃদ্ধি মুনাফার পার্থক্য কত হবে?

ক
৫০ টাকা
খ
৬০ টাকা
গ
৭০ টাকা
ঘ
৪০ টাকা
ঙ
৮০ টাকা

সঠিক উত্তর: ঘ

৪০ টাকা

উত্তর

সঠিক উত্তর: ঘ

৪০ টাকা

ঘ

ব্যাখ্যা

প্রশ্ন: বার্ষিক ৫% মুনাফায় ১৬,০০০ টাকার ২ বছরের সরল ও চক্রবৃদ্ধি মুনাফার পার্থক্য কত হবে?

সমাধান:
এখানে,
মূলধন, P = ১৬০০০ টাকা
সুদের হার, R = ৫%
সময়, T = ২ বছর

সরল মুনাফা, I = (PRT)/১০০
= (১৬০০০ × ৫ × ২)/১০০
= ১৬০০০০/১০০
= ১৬০০ টাকা

চক্রবৃদ্ধি মুনাফার ক্ষেত্রে,
A = P × {১ + (R/১০০)}^T
= ১৬০০০ × {১ + (৫/১০০)}^২
= ১৬০০০ × (১.০৫)^২
= ১৬০০০ × ১.১০২৫
= ১৭৬৪০ টাকা

∴ চক্রবৃদ্ধি মুনাফা, CI = A − P
= ১৭৬৪০ − ১৬০০০
= ১৬৪০ টাকা

∴ পার্থক্য = ১৬৪০ − ১৬০০ = ৪০ টাকা

১৩৯.

If Tk. P is invested at an annual interest rate of 5 percent, which of the following gives the amount of simple interest, in Tk., earned after n months?

ক
0.05P + n
খ
0.05P + (n/12)
গ
0.05P × n
ঘ
(0.05P)/(12n)
ঙ
0.05P × (n/12)

সঠিক উত্তর: ঙ

0.05P × (n/12)

উত্তর

সঠিক উত্তর: ঙ

0.05P × (n/12)

ঙ

ব্যাখ্যা

Question: If Tk. P is invested at an annual interest rate of 5 percent, which of the following gives the amount of simple interest, in Tk., earned after n months?

Solution:
Simple Interest, I = (Pnr)/100
= (P) × (5/100) × (n/12)
= 0.05P × (n/12)

১৪০.

If the compound interest in the third year at 8% per annum on a certain sum is Tk 3600, then what is the difference between the compound interest in the 4th and 5th year?

ক
ক) 210.05
খ
খ) 315.07
গ
গ) 421.07
ঘ
ঘ) 375.07
ঙ
ঙ) 311.04

সঠিক উত্তর: ঙ

ঙ) 311.04

উত্তর

সঠিক উত্তর: ঙ

ঙ) 311.04

ঙ

ব্যাখ্যা

Compound interest for the 4th year = 3600 + (3600 × 8 × 1)/100.
= 3600 + 288.
= Tk. 3888.

Compound interest for the 5th year = 3888 + (3888 × 8 × 1)/100.
= 3888 + 311.04.
= Tk. 4199.04.

Difference between the compound interest in the 4th and 5th year = 4199.04 - 3888.
= Tk. 311.04.

১৪১.

Rasel obtained an amount of Tk. 8376 as simple interest on a certain amount at 8 p.c.p.a. after 6 years. What is the amount invested by Rasel?

ক
16450 Tk.
খ
18470 Tk.
গ
17450 Tk.
ঘ
19472 Tk.
ঙ
None

সঠিক উত্তর: গ

17450 Tk.

উত্তর

সঠিক উত্তর: গ

17450 Tk.

গ

ব্যাখ্যা

Question: Rasel obtained an amount of Tk. 8376 as simple interest on a certain amount at 8 p.c.p.a. after 6 years. What is the amount invested by Rasel?

Solution:
Here,
Simple interest, I = Tk. 8376
Rate of interest, r = 8%
Time, n = 6 years

We know,
I = Pn(r/100)
Or, P = 100I/nr
= (8376 × 100)/(6 × 8)
∴ P = 17450 Tk.

১৪২.

একজন ব্যক্তি ৯০০০ টাকার উপরে ৩০% হারে খাজনা ১২টি সমান কিস্তিতে পরিশোধ করে। প্রতি কিস্তির পরিমাণ কত?

ক
ক) ২২৫ টাকা
খ
খ) ২.৫০ টাকা
গ
গ) ২.২৫ টাকা
ঘ
ঘ) ২৫০ টাকা

সঠিক উত্তর: ক

ক) ২২৫ টাকা

উত্তর

সঠিক উত্তর: ক

ক) ২২৫ টাকা

ক

ব্যাখ্যা

প্রশ্ন: একজন ব্যক্তি ৯০০০ টাকার উপরে ৩০% হারে খাজনা ১২টি সমান কিস্তিতে পরিশোধ করে। প্রতি কিস্তির পরিমাণ কত?

সমাধান:
১০০ টাকার খাজনা ৩০ টাকা
∴ ৯০০০ টাকার খাজনা (৩০ × ৯০০০)/১০০ টাকা
= ২৭০০ টাকা

প্রতি কিস্তির পরিমাণ (২৭০০ ÷ ১২) টাকা
= ২২৫ টাকা

১৪৩.

A stock increases in value by 20%. By what percent must the stock decrease to reach back to its former value?

ক
16.66%
খ
26%
গ
15%
ঘ
26.66%

সঠিক উত্তর: ক

16.66%

উত্তর

সঠিক উত্তর: ক

16.66%

ক

ব্যাখ্যা

Question: A stock increases in value by 20%. By what percent must the stock decrease to reach back to its former value?

Solution:
এখানে,
20% বৃদ্ধিতে মূল্য = (100 + 20) = 120 টাকা

120 টাকায় মূল্য কমাতে হবে 20 টাকা
∴ 1 টাকায় মূল্য কমাতে হবে 20/120
∴ 100 টাকায় মূল্য কমাতে হবে (20 × 100)/120
= 16.66 টাকা

১৪৪.

A 12% stock yielding 10% is quoted at:

ক
ক) 105
খ
খ) 95
গ
গ) 110
ঘ
ঘ) 120
ঙ
ঙ) 115

সঠিক উত্তর: ঘ

ঘ) 120

উত্তর

সঠিক উত্তর: ঘ

ঘ) 120

ঘ

ব্যাখ্যা

To earn Tk. 10, money invested = Tk. 100.
To earn Tk. 12, money invested = Tk (100/10 × 12)
= Tk. 120.
Market value of Tk.100 stock = Tk. 120.

১৪৫.

How much time will it take for an amount of Tk. 450 to yield Tk. 90 as interest at 2% per annum of simple interest?

ক
ক) 5 years
খ
খ) 8 years
গ
গ) 10 years
ঘ
ঘ) 12 years

সঠিক উত্তর: গ

গ) 10 years

উত্তর

সঠিক উত্তর: গ

গ) 10 years

গ

ব্যাখ্যা

Question: How much time will it take for an amount of Tk. 450 to yield Tk. 90 as interest at 2% per annum of simple interest?

Solution:
Given that
Principal = Tk. 450,
Rate of interest = 2% and
simple interest = Tk. 90

Time = (100 × 90)/(450 × 2)
= 10 years.

১৪৬.

A sum of money amounts to Tk 9800 after 5 years and Tk. 12005. after 8 years at the same rate of simple interest. The rate of interest per annum is -

ক
ক) 5%
খ
খ) 8%
গ
গ) 12%
ঘ
ঘ) 15%

সঠিক উত্তর: গ

গ) 12%

উত্তর

সঠিক উত্তর: গ

গ) 12%

গ

ব্যাখ্যা

Simple interest for 3 years
= 12005 - 9800 = 2205
Simple interest for 5 years
= (2205/3) × 5 = 3675

Some of money = 9800 - 3675 = 6125

∴ Rate of interest = (100 × 2205)/(6125 × 3)
= 12%

১৪৭.

A sum of money at compound interest doubles itself in 15 years. It will become eight times of itself in-

ক
ক) 30 years
খ
খ) 38 years
গ
গ) 45 years
ঘ
ঘ) 49 years

সঠিক উত্তর: গ

গ) 45 years

উত্তর

সঠিক উত্তর: গ

গ) 45 years

গ

ব্যাখ্যা

Question: A sum of money at compound interest doubles itself in 15 years. It will become eight times of itself in-

Solution:
let the sum P

2P = P (1 + r)¹⁵
⇒ (1 + r)¹⁵ = 2

let, sum will 8 times in n years
8P = P(1 + r)ⁿ
⇒ 8 = (1 + r)ⁿ
⇒ 2³ = (1 + r)ⁿ
⇒ ((1 + r)¹⁵)³ = (1 + r)ⁿ
⇒ (1 + r)⁴⁵ = (1 + r)ⁿ
∴ n = 45 years

১৪৮.

Find the compound interest on Tk 8000 at 15% interest per annum for 2 years, compounded annually-

ক
ক) 9800 Tk
খ
খ) 10580 Tk
গ
গ) 11200 Tk
ঘ
ঘ) 11560 Tk

সঠিক উত্তর: খ

খ) 10580 Tk

উত্তর

সঠিক উত্তর: খ

খ) 10580 Tk

খ

ব্যাখ্যা

Question: Find the compound interest on Tk 8000 at 15% interest per annum for 2 years, compounded annually-

Solution:
Compound Principal for 2 years = 8000(1 + 15/100)²
= 8000(115/100)²
= (8000 × 115 × 115)/(100 × 100)
= 10580

১৪৯.

The compound interest on 300 tk. at 7% per annum is 21 taka. The period is:

ক
1 year
খ
2 years
গ
3 years
ঘ
4 years

সঠিক উত্তর: ক

1 year

উত্তর

সঠিক উত্তর: ক

1 year

ক

ব্যাখ্যা

Question: The compound interest on 300 tk. at 7% per annum is 21 taka. The period is:

Solution:
চক্রবৃদ্ধি সুদাসল = P (1 + r)ⁿ
= 300 + 21
= 321 tk.

প্রশ্নমতে,
321 = 300 × (1 + 7/100)ⁿ
⇒ (1 + 7/100)ⁿ = 321/300
⇒ (107/100)ⁿ = 107/100
⇒ (107/100)ⁿ = (107/100)¹
∴ n = 1 year

১৫০.

A 9% stock yields 8%. The market value of the stock is-

ক
Tk. 72
খ
Tk. 116.50
গ
Tk. 90
ঘ
Tk. 112.50

সঠিক উত্তর: ঘ

Tk. 112.50

উত্তর

সঠিক উত্তর: ঘ

Tk. 112.50

ঘ

ব্যাখ্যা

Question: A 9% stock yields 8%. The market value of the stock is-

Solution:
Earn Tk. 8 when market value Tk. 100
Earn Tk. 1 when market value Tk. 100/8
Earn Tk. 9 when market value Tk. (100 × 9)/8
= Tk. 112.5

১৫১.

There is 60% increase in an amount in 6 years at simple interest. What will be the compound interest of 12,000 after 3 years at the same rate?

ক
Tk. 3500
খ
Tk. 3812
গ
Tk. 3972
ঘ
Tk. 4100

সঠিক উত্তর: গ

Tk. 3972

উত্তর

সঠিক উত্তর: গ

Tk. 3972

গ

ব্যাখ্যা

Question: There is 60% increase in an amount in 6 years at simple interest. What will be the compound interest of 12,000 after 3 years at the same rate?

Solution: let simple interest r%

I = pnr/100
⇒ I/p = nr/100
⇒ 0.6 = 6r/100
⇒ r = 10%

The compound interest = 12000 (1.1)³ - 12000
= 12 × 1331 - 12000
= 15972 - 12000
= Tk. 3972

১৫২.

A sum of Tk. 20,000 yields a compound interest of Tk. 4200 when invested at 10% per annum. What is the investment period in years?

ক
2 years
খ
3 years
গ
3.5 years
ঘ
4 years

সঠিক উত্তর: ক

2 years

উত্তর

সঠিক উত্তর: ক

2 years

ক

ব্যাখ্যা

Question: A sum of Tk. 20,000 yields a compound interest of Tk. 4200 when invested at 10% per annum. What is the investment period in years?

Solution:
দেওয়া আছে,
আসল, P = 20000 টাকা
সুদের হার, r = 10% বার্ষিক
চক্রবৃদ্ধি সুদ, CI = 4200 টাকা

আমরা জানি,
চক্রবৃদ্ধি মূল, A = P + CI
= 20000 + 4200 = 24200 টাকা

চক্রবৃদ্ধি মূলের সূত্র ব্যবহার করে পাই,
A = P × (1 + r/100)ⁿ
⇒ 24200 = 20000 × (1 + 10/100)ⁿ
⇒ 24200 = 20000 × (110/100)ⁿ
⇒ (110/100)ⁿ = 24200/20000
⇒ (1.10)ⁿ = 1.21
⇒ (1.10)ⁿ = (1.10)²
∴ n = 2

∴ বিনিয়োগের সময়কাল 2 বছর।

১৫৩.

The compound interest on a certain sum for 2 years at 12% per annum is Tk. 795. The simple interest on the same sum for double the time at half the rate percent per annum is-

ক
Tk. 650
খ
Tk. 680
গ
Tk. 720
ঘ
Tk. 750

সঠিক উত্তর: ঘ

Tk. 750

উত্তর

সঠিক উত্তর: ঘ

Tk. 750

ঘ

ব্যাখ্যা

Question: The compound interest on a certain sum for 2 years at 12% per annum is Tk. 795. The simple interest on the same sum for double the time at half the rate percent per annum is-

Solution:
Let
The sum be Tk. P

ATQ,
P{1 + (12/100)}² - P = 795
⇒ P[{1 + (3/25)}² - 1] = 795
⇒ P{(28/25)² - 1} = 795
⇒ P{(784/625) - 1} = 795
⇒ P(159/625) = 795
⇒ P = (795 × 625)/159
∴ P = 3125

So The simple interest on the same sum for double the time at half the rate percent per annum is-
SI = 3125 × 4 × 6%
= 3125 × 4 × 6/100
= 750

১৫৪.

Find the compound interest after 2 years on Tk. 14000 at the rate of interest 5% per annum.

ক
1445
খ
1440
গ
1455
ঘ
1435

সঠিক উত্তর: ঘ

1435

উত্তর

সঠিক উত্তর: ঘ

1435

ঘ

ব্যাখ্যা

Question: Find the compound interest after 2 years on Tk. 14000 at the rate of interest 5% per annum.

Solution:
Let the sum P = 14000.
Rate of interest = 5%
Period = 2 years

Hence, compound interest = 14000(1 + 5/100)² - 14000
= 14000(1.05)² - 14000
= 14000 × 1.05 × 1.05 - 14000
= 15435 - 14000
= 1435

১৫৫.

At what annual rate of interest will a sum of money be thrice in 10 years?

ক
10%
খ
12%
গ
15%
ঘ
20%

সঠিক উত্তর: ঘ

20%

উত্তর

সঠিক উত্তর: ঘ

20%

ঘ

ব্যাখ্যা

Question: At what annual rate of interest will a sum of money be thrice in 10 years?

Solution:
Amount = Principal + SI
If the sum of money would be thrice the principal after 10 years, the SI would be twice the principal.
⇒ SI = 2 × P
⇒ (P × R × T / 100) = 2 × P
⇒ R × T / 100 = 2
⇒ R × T = 200
⇒ R × 10 = 200
⇒ R = 20%
Thus, the required rate of interest is 20%

১৫৬.

A lends Tk. 2500 to B and a certain sum to C at the same time at 7% p.a. simple interest. If after 4 years, A altogether receives Tk. 1120 as interest from B and C, then the sum lent to C is -

ক
Tk. 1000
খ
Tk. 1200
গ
Tk. 1500
ঘ
Tk. 1600

সঠিক উত্তর: গ

Tk. 1500

উত্তর

সঠিক উত্তর: গ

Tk. 1500

গ

ব্যাখ্যা

Question: A lends Tk. 2500 to B and a certain sum to C at the same time at 7% p.a. simple interest. If after 4 years, A altogether receives Tk. 1120 as interest from B and C, then the sum lent to C is -

Solution:
ধরি,
C এর মুলধন x টাকা

প্রশ্নমতে,
(2500 × 7 × 4)/100) + (x × 7 × 4/100) = 1120
⇒ 7x/25 = (1120 - 700)
⇒ x = (420 × 25)/7
∴ x = 1500

C এর মুলধন 1500 টাকা।

১৫৭.

A man invested a sum of money at compound interest. It amounted to Tk 2420 in 2 years and to Tk 2662 in 3 years. Find the sum.

ক
1800
খ
1900
গ
2000
ঘ
2100
ঙ
None

সঠিক উত্তর: গ

2000

উত্তর

সঠিক উত্তর: গ

2000

গ

ব্যাখ্যা

Question: A man invested a sum of money at compound interest. It amounted to Tk 2420 in 2 years and to Tk 2662 in 3 years. Find the sum.

Solution:

১৫৮.

The compound interest on Tk. 2600 for 18 months at 10% per annum is-

ক
Tk. 403
খ
Tk. 395
গ
Tk. 465
ঘ
Tk. 420

সঠিক উত্তর: ক

Tk. 403

উত্তর

সঠিক উত্তর: ক

Tk. 403

ক

ব্যাখ্যা

Question: The compound interest on Tk. 2600 for 18 months at 10% per annum is-

Solution:
Interest after 1 year or 12 month = 2600 × 1 × (10/100)
= 260
New principal = 2600 + 260
= 2860

6 months = 1/2 year

Now,
I = Pnr
= 2860 × (1/2) × (10/100)
= 143

∴ Total interest = 260 + 143 = Tk. 403

১৫৯.

কোনো আসল ৩ বছরে মুনাফাসহ ৫৫০০ টাকা হয় । মুনাফা আসলের ৩/৮ অংশ হলে মুনাফার হার কত?

ক
ক) ১২.৪০%
খ
খ) ১২.৫০%
গ
গ) ১২%
ঘ
ঘ) ১০%

সঠিক উত্তর: খ

খ) ১২.৫০%

উত্তর

সঠিক উত্তর: খ

খ) ১২.৫০%

খ

ব্যাখ্যা

প্রশ্ন: কোনো আসল ৩ বছরে মুনাফাসহ ৫৫০০ টাকা হয় । মুনাফা আসলের ৩/৮ অংশ হলে মুনাফার হার কত?

সমাধান:
ধরি,
আসল, P টাকা
∴ মুনাফা, I = (৩P)/৮ টাকা
মুনাফার হার, r
সময়, n = ৩ বছর

শর্তমতে,
P + (৩P)/৮ = ৫৫০০
বা, ৮P + ৩P = ৫৫০০ × ৮
বা, ১১P = ৫৫০০ × ৮
বা, P = ৫০০ × ৮
∴ P = ৪০০০

আসল ৪০০০ টাকা

মুনাফা (৩ × ৪০০০)/৮ টাকা
= ১৫০০ টাকা

মুনাফার হার, r = I/(Pn) = ১৫০০/(৪০০০ × ৩)
= (১/৮) × ১০০ %
= ১২.৫০%

১৬০.

Akash lends a part of Tk. 20000 at 8% simple interest and remaining at (4/3)% simple interest. His total income after a year was Tk. 800. Find the sum lent at 8%.

ক
Tk. 5000
খ
Tk. 8000
গ
Tk.10000
ঘ
Tk. 12000

সঠিক উত্তর: খ

Tk. 8000

উত্তর

সঠিক উত্তর: খ

Tk. 8000

খ

ব্যাখ্যা

Question: Akash lends a part of Tk. 20000 at 8% simple interest and remaining at (4/3)% simple interest. His total income after a year was Tk. 800. Find the sum lent at 8%.

Solution:
Amount lent at 8% rate of interest = Tk. x
Amount lent at 4/3 % rate of interest = Tk. (20000 - x)

∴ S.I. = (Principal × Rate × Time)/100
{(x × 8 × 1)/100} + [{(20000 - x) × (4/3) × 1}/100] = 800
⇒ (2x/25) + {(20000 - x)/75} = 800
⇒ (6x + 20000 - x)/75 = 800
⇒ 5x + 20,000 = 75 × 800 = 60000
⇒ 5x = 60,000 - 20000 = 4000
⇒ x = 40000/5
∴ x = Tk. 8000

১৬১.

If a sum triples in 15 years at simple interest, how much will it be in 10 years?

ক
1/3 times
খ
2/3 times
গ
5/3 times
ঘ
7/3 times

সঠিক উত্তর: ঘ

7/3 times

উত্তর

সঠিক উত্তর: ঘ

7/3 times

ঘ

ব্যাখ্যা

Question: If a sum triples in 15 years at simple interest, how much will it be in 10 years?

Solution:
Let, Principal = P

If the sum triples in 15 years,
Amount after 15 years = 3P

∴ Simple interest for 15 years = 3P - P
= 2P

So, Simple interest for 1 year = 2P/15

∴ Simple interest for 10 years = (2P/15) × 10
= 20P/15
= 4P/3

Amount after 10 years = P + 4P/3
= 7P/3

Hence, the sum will be = 7/3 times the principal.

১৬২.

The difference in Taka between simple and compound interest at 10% annually on a sum of Tk. 8,000 after 2 years is:

ক
Tk. 12.5
খ
Tk. 34
গ
Tk. 54
ঘ
Tk. 80

সঠিক উত্তর: ঘ

Tk. 80

উত্তর

সঠিক উত্তর: ঘ

Tk. 80

ঘ

ব্যাখ্যা

Question: The difference in Taka between simple and compound interest at 10% annually on a sum of Tk. 8,000 after 2 years is:

Solution:
Given that,
Principal, P = Tk. 8,000
Rate, r = 10%
Time, n = 2 years

We know that,
Simple Interest = Pnr/100
= (8000 × 2 × 10)/100
= 1600 Tk.

And Compound Interest = P(1 + r/100)ⁿ - P
= 8000(1 + 10/100)² - 8000
= 8000(11/10)² - 8000
= 8000(1.21) - 8000
= 9680 - 8000
= 1680 Tk.

∴ Difference = 1680 - 1600 = 80 Tk.
The difference between compound and simple interest is Tk. 80.

১৬৩.

A certain amount of money earning simple interest becomes 7/5th of the initial amount in 4 years. What is the interest rate?

ক
ক) 4%
খ
খ) 6%
গ
গ) 8%
ঘ
ঘ) 10%

সঠিক উত্তর: ঘ

ঘ) 10%

উত্তর

সঠিক উত্তর: ঘ

ঘ) 10%

ঘ

ব্যাখ্যা

Questtion: A certain amount of money earning simple interest becomes 7/5th of the initial amount in 4 years. What is the interest rate?

Solution:
মনেকরি
আসল P = 100 টাকা
মুনফা- আসল A = 100 এর 7/5 = 140 টাকা
মুনাফা I = 140 - 100 = 40 টাকা
সময় n = 4 বছর
মুনাফার হার r = ?

আমরাজানি
I = Pnr
r = I/Pn
= (40 × 100)/(100 × 4)
= 10%

১৬৪.

There is 60% increase in an amount in 6 years at simple interest. What will be the compound interest of 12,000 after 3 years at the same rate?

ক
Tk. 4250
খ
Tk. 3972
গ
Tk. 3886
ঘ
Tk. 3735

সঠিক উত্তর: খ

Tk. 3972

উত্তর

সঠিক উত্তর: খ

Tk. 3972

খ

ব্যাখ্যা

Question: There is 60% increase in an amount in 6 years at simple interest. What will be the compound interest of 12,000 after 3 years at the same rate?

Solution:
Let,
the simple interest rate = r%

Given,
60% increase in an amount in 6 years at simple interest
∴ If P = Tk. 100, then I = Tk. 60

Then,
I = Pnr/100
⇒ I/P = nr/100
⇒ 60/100 = 6r/100
⇒ 0.6 = 6r/100
⇒ r = 10%

Now,
P = Tk. 12000
n = 3 years
r = 10%

We know,
The compound interest = P(1 + r)ⁿ - P
= 12000 (1.1)³ - 12000
= 12 × 1331 - 12000
= 15972 - 12000
= Tk. 3972

১৬৫.

A money lender borrows money at 4% per annum and pays the interest at the end of the year. He lends it at 6% per annum compound interest compounded half yearly and receives the interest at the end of the year. In this way, he gains Tk. 104.50, a year. The amount of money be borrows, is?

ক
Tk. 4000
খ
Tk. 5000
গ
Tk. 6000
ঘ
Tk.7000
ঙ
Tk. 6500

সঠিক উত্তর: খ

Tk. 5000

উত্তর

সঠিক উত্তর: খ

Tk. 5000

খ

ব্যাখ্যা

Question: A money lender borrows money at 4% per annum and pays the interest at the end of the year. He lends it at 6% per annum compound interest compounded half yearly and receives the interest at the end of the year. In this way, he gains Tk. 104.50, a year. The amount of money be borrows, is?

Solution:
Let, the sum Tk. x

Then,
C.I. when compounded half yearly = Tk. [x × {1 + (3/100)}²- x]
= Tk. {(10609x/10000) - x}
= Tk. {(10609x - 10000x)/10000}
= Tk. (609x/10000)

C.I. when compounded yearly = Tk. [x × {1 + (4/100)} - x]
= Tk. {(26x/25) - x}
= Tk. x/25

∴ (609x/10000) - (x/25) = 104.50
⇒ (609x - 400x)/10000 = 104.50
⇒ 209x/10000 = 104.50
⇒ x = {104.50 × (10000/209)}
⇒ x = 5000

১৬৬.

On a sum of money, the simple interest for 2 years is Tk. 660, while the compound interest is Tk. 696.30, the rate of interest being the same in both cases. The rate of interest is -

ক
10%
খ
10.5%
গ
11%
ঘ
11.5%

সঠিক উত্তর: গ

11%

উত্তর

সঠিক উত্তর: গ

11%

গ

ব্যাখ্যা

Question: On a sum of money, the simple interest for 2 years is Tk. 660, while the compound interest is Tk. 696.30, the rate of interest being the same in both cases. The rate of interest is -

Solution:
Difference of Compound interest and Simple interest for 2 years = Tk. (696.30 - 660) = Tk. 36.30
Simple interest for 1 years = 660/2 = Tk. 330

Simple interest on 330 for 1 year = 36.30
Interst rate = {(36.30 × 100)/330}% = 11%

১৬৭.

A sum of money amounts to Tk. 735 in 3 years and Tk. 815 in 4 year. What's the sum?

ক
ক) Tk. 575
খ
খ) Tk. 520
গ
গ) Tk. 495
ঘ
ঘ) Tk. 480

সঠিক উত্তর: গ

গ) Tk. 495

উত্তর

সঠিক উত্তর: গ

গ) Tk. 495

গ

ব্যাখ্যা

Question: A sum of money amounts to Tk. 735 in 3 years and Tk. 815 in 4 year. What's the sum?

Solution:
Simple interest for 1 years = Tk. (815 - 735)
= Tk. 80
∴ Simple interest for 3 years = Tk.(80 × 3)
= Tk. 240

∴ Sum = (735 - 240)
= Tk. 495

১৬৮.

A company issued 25000 shares of par value tk. 15 each. If the company has decided to give the dividend tk. 30000, what is the rate of dividend paid by the company?

ক
ক) 5%
খ
খ) 7%
গ
গ) 8%
ঘ
ঘ) 10%
ঙ
ঙ) 12%

সঠিক উত্তর: গ

গ) 8%

উত্তর

সঠিক উত্তর: গ

গ) 8%

গ

ব্যাখ্যা

Number of shares = 25000
Face value of each share = Tk. 15
Let R be the rate of interest.

Dividend per share = 15 × R/100
Total dividend = 25000 × 15 × R/100
As per the question: 25000 × 15 × R/100
= 30000
R = 30000/3750 = 8

So, the dividend is 8%.

১৬৯.

In how many years will Tk. 20,000 amount to Tk. 28,800 at 20% per annum compound interest?

ক
2 years
খ
3 years
গ
4 years
ঘ
5 years

সঠিক উত্তর: ক

2 years

উত্তর

সঠিক উত্তর: ক

2 years

ক

ব্যাখ্যা

Question: In how many years will Tk. 20,000 amount to Tk. 28,800 at 20% per annum compound interest?

Solution:
Given that,
Principal, P = Tk. 20,000
Amount, C = Tk. 28,800
Rate, r = 20%

We know,
C = P(1 + r)ⁿ⇒ 28,800 = 20,000 × {(1 + (20/100)}ⁿ
⇒ 28,800 = 20,000 × (6/5)ⁿ⇒ 28,800/20,000 = (6/5)ⁿ
⇒ 36/25 = (6/5)ⁿ⇒ (6/5)²= (6/5)ⁿ

∴ n = 2 years

১৭০.

In order to obtain an income of Tk. 600 from 10% stock at Tk. 120, one must make an investment of-

ক
Tk. 8000
খ
Tk. 7200
গ
Tk. 6200
ঘ
Tk. 8400

সঠিক উত্তর: খ

Tk. 7200

উত্তর

সঠিক উত্তর: খ

Tk. 7200

খ

ব্যাখ্যা

Question: In order to obtain an income of Tk. 600 from 10% stock at Tk. 120, one must make an investment of-

Solution:
To obtain Tk. 10,
investment = Tk. 120
To obtain Tk. 600
investment = Tk. (120/10) × 600
= Tk. 7200

১৭১.

What will be the total worth if 135 Tk. is kept for 2 years at simple interest rate 5%?

ক
ক) 13.5 Tk.
খ
খ) 148.5 Tk.
গ
গ) 140.5 Tk.
ঘ
ঘ) 17.5 Tk.

সঠিক উত্তর: খ

খ) 148.5 Tk.

উত্তর

সঠিক উত্তর: খ

খ) 148.5 Tk.

খ

ব্যাখ্যা

Question: What will be the total worth if 135 Tk. is kept for 2 years at simple interest rate 5%?

Solution:
Here,
P = 135,
n = 2,
R = 5%
I = ?

I = Pnr
= 135 × 2 × 5%
= 270 × 5/100
= 13.5

total worth = 135 + 13.5 = 148.5 Tk.

১৭২.

A 4% stock yields 5%. The market value of the stock of face value Tk. 100 is-

ক
Tk. 75
খ
Tk. 133
গ
Tk. 120
ঘ
Tk. 80

সঠিক উত্তর: ঘ

Tk. 80

উত্তর

সঠিক উত্তর: ঘ

Tk. 80

ঘ

ব্যাখ্যা

Question: A 4% stock yields 5%. The market value of the stock of face value Tk. 100 is-

Solution:
For an income of tk. 5, investment = tk. 100.
For an income of tk. 4, investment = tk. (100/5) × 4 = tk. 80.
Market value of tk. 100 stock = tk. 80.

১৭৩.

Amin took a loan of Tk.1400 with simple interest for as many years as the rate of interest. If he paid Tk.686 as interest at the end of the loan period, what was the rate of interest?

ক
ক) 6%
খ
খ) 8%
গ
গ) 7%
ঘ
ঘ) 4%

সঠিক উত্তর: গ

গ) 7%

উত্তর

সঠিক উত্তর: গ

গ) 7%

গ

ব্যাখ্যা

Given that T = R
S.I = (P × R × T)/100
⇒ 686 = (1400 × R × R)/100
⇒ 686 = 14R²
⇒ R² = 49
⇒ R = 7.

১৭৪.

A lends Tk. 1500 to B and a certain sum to C at the same time at 8% per annum. If A receives Tk. 1400 as simple interest from B and C after 4 years, then the sum lent to C is -

ক
ক) Tk. 1885
খ
খ) Tk. 2245
গ
গ) Tk. 2875
ঘ
ঘ) Tk. 2615

সঠিক উত্তর: গ

গ) Tk. 2875

উত্তর

সঠিক উত্তর: গ

গ) Tk. 2875

গ

ব্যাখ্যা

Let the sum lent to C be x
Simple interest on Tk. 1500 at 8% for 4 years + simple interest on x at 8%for 4 years.
= Tk. 1400
(1500 × 8 × 4)/100 + (x × 8 × 4)/100 = 1400
⇒ {8 × 4(1500 + x)}/100 = 1400
⇒ 1500 + x = 4375
⇒ x = 4375 - 1500
⇒ x = 2875.

১৭৫.

The population of a village decreases at the rate of 25% per annum. If its population 2 years ago was 24000, the present population is =?

ক
Tk. 13000
খ
Tk. 13500
গ
Tk. 12000
ঘ
Tk. 14000

সঠিক উত্তর: খ

Tk. 13500

উত্তর

সঠিক উত্তর: খ

Tk. 13500

খ

ব্যাখ্যা

Question: The population of a village decreases at the rate of 25% per annum. If its population 2 years ago was 24000, the present population is =?

Solution:
Given that,
The population of a village 2 years ago = 24000
Rate of growth = 25% p.a.
Time period = 2 years

Present population = P{(1 - (r/100)}ⁿ
= 24000 × {1 - (25/100)}²
= 24000 × {1 - (1/4)}²
= 24000 × (3/4)²
= 24000 × (9/16)
= 13500

১৭৬.

A certain sum of money becomes 2.5 times itself in 5 years at simple interest. What is the rate of interest per annum?

ক
10%
খ
25%
গ
30%
ঘ
11%

সঠিক উত্তর: গ

30%

উত্তর

সঠিক উত্তর: গ

30%

গ

ব্যাখ্যা

Question: A certain sum of money becomes 2.5 times itself in 5 years at simple interest. What is the rate of interest per annum?

Solution:
Let the principal amount be P.
The sum becomes 2.5 times itself in 5 years.

So, A = 2.5P
∴ Simple Interest, I = 2.5P - P = 1.5 P

We know, I = Pnr/100
⇒ 1.5 P = (P × 5 × r)/100
⇒ 5r = 150
∴ r = 30%

১৭৭.

A sum of money at simple interest amount to tk. 4400 in 2 years and to tk. 4700 in 5 years at a rate of:

ক
2.5%
খ
3.3%
গ
3.2%
ঘ
2.3%

সঠিক উত্তর: ঘ

2.3%

উত্তর

সঠিক উত্তর: ঘ

2.3%

ঘ

ব্যাখ্যা

Question: A sum of money at simple interest amount to tk. 4400 in 2 years and to tk. 4700 in 5 years at a rate of:

Solution:
Simple interest for 3 years = (4700 - 4400) Tk.
= Tk. 300
Now, Simple Interest for 3 years = Tk. 300
∴ Simple Interest for 5 years = Tk. 300 × (5/3)
= Tk. 500

∴ Principal = 4700 - 500 = Tk. 4200

We know,
I = Pnr
⇒ r = I/Pn
⇒ r = (500 × 100)/(4200 × 5)
∴ r = 2.3%

১৭৮.

Robi invested Tk. ‘x’ in a scheme offering 15% p.a. simple interest for three years while Shami invested same amount in another scheme offering 10% p.a. compound interest for three years, compounded annually. Find the value of ‘x’ if the difference between the interests earned by them after three is Tk. 1428.

ক
Tk. 9000
খ
Tk. 10000
গ
Tk. 11000
ঘ
Tk. 12000

সঠিক উত্তর: ঘ

Tk. 12000

উত্তর

সঠিক উত্তর: ঘ

Tk. 12000

ঘ

ব্যাখ্যা

Question: Robi invested Tk. ‘x’ in a scheme offering 15% p.a. simple interest for three years while Shami invested same amount in another scheme offering 10% p.a. compound interest for three years, compounded annually. Find the value of ‘x’ if the difference between the interests earned by them after three is Tk. 1428.

Solution:
Robi invested Tk. ‘x’ in a scheme offering 15% p.a. simple interest for three years
∴ Simple interest = x × 3 × (15/100) = 9x/20 = 0.45x

Shami invested Tk. x in another scheme offering 10% p.a. compound interest for three years
∴ Compound interest = x(1 + 10/100)³ - x
= x × 1.1 × 1.1 × 1.1 - x
= 1.331x - x
= 0.331x

ATQ,
0.45x - 0.331x = 1428
⇒ 0.119x = 1428
⇒ x = 1428/0.119
∴ x = 12000

১৭৯.

The sum for 4 years given a compound interest of Tk. 5992.05 at 15% rate. Then the sum is ?

ক
Tk. 8000
খ
Tk. 10000
গ
Tk. 7000
ঘ
Tk. 7500

সঠিক উত্তর: ক

Tk. 8000

উত্তর

সঠিক উত্তর: ক

Tk. 8000

ক

ব্যাখ্যা

Question : The sum for 4 years given a compound interest of Tk. 5992.05 at 15% rate. Then the sum is ?

Solution :
Given,
Compound interest = Tk. 5992.05
Time n = 4 years
Interest rate r = 15%
= 15/100
= 0.15

We know,
Compound interest = P(1 + r)ⁿ - P
⇒ 5992.05 = P{(1 + 0.15)⁴ - 1}
⇒ 5992.05 = P{(1.15)⁴ - 1}
⇒ 5992.05 = P(1.749 - 1)
⇒ 5992.05 = P × 0.749
⇒ P = 5992.05 ÷ 0.749
∴ P = 8000

১৮০.

A certain amount of money becomes 3 times in 12 years. What is the interest rate?

ক
12.5%
খ
15.56%
গ
16.67%
ঘ
20%

সঠিক উত্তর: গ

16.67%

উত্তর

সঠিক উত্তর: গ

16.67%

গ

ব্যাখ্যা

Question: A certain amount of money becomes 3 times in 12 years. What is the interest rate?

Solution:
let the principle amount it X.
so, the Interest = 3X -X = 2X
time, n = 12 years
let,
rate = r%

As we know,
I = Pnr/100
r = (I × 100)/Pn
= (2X × 100)/ 12X
= 16.67%

১৮১.

Asif obtained an amount of Tk. 8376 as simple interest on a certain amount at 8 p.c.p.a. after 6 years. What is the amount invested by Asif?

ক
Tk. 17550
খ
Tk. 16450
গ
Tk. 17450
ঘ
Tk. 17455

সঠিক উত্তর: গ

Tk. 17450

উত্তর

সঠিক উত্তর: গ

Tk. 17450

গ

ব্যাখ্যা

Question: Asif obtained an amount of Tk. 8376 as simple interest on a certain amount at 8 p.c.p.a. after 6 years. What is the amount invested by Asif?

Solution:
Simple interest, I = Tk. 8376
Rate of interest, r = 8%
Time, n = 6 years

We know,
I = Pnr
Or, P = I/nr
= (8376 × 100)/(6 × 8)
∴ P = 17450 Tk.

১৮২.

A man borrowed some money for 6 months. He asked the banker for the money and the banker charged Tk. 720 as interest at 6% per annum. What was the amount he borrowed?

ক
Tk. 18000
খ
Tk. 20000
গ
Tk. 24000
ঘ
Tk. 23000

সঠিক উত্তর: গ

Tk. 24000

উত্তর

সঠিক উত্তর: গ

Tk. 24000

গ

ব্যাখ্যা

Question: A man borrowed some money for 6 months. He asked the banker for the money and the banker charged Tk. 720 as interest at 6% per annum. What was the amount he borrowed?

Solution:
এখানে
সময় n = 6 মাস
= 6/12 বছর
= 1/2 বছর

মুনাফা I = 720 টাকা
মুনাফার হার r = 6% = 6/100 = 3/50
আসল P = ?

আমরা জানি,
I = Pnr
⇒ Pnr = I
⇒ P = I/nr
= 720/{(1/2) × (3/50)}
= 720/(3/100)
= (720 × 100)/3
= 24000 টাকা

১৮৩.

If the ratio of simple interest and principal is 8 : 25/2 and rate of interest is equal to the time invested then find the time of investment?

ক
ক) 12 years
খ
খ) 8 years
গ
গ) 10 years
ঘ
ঘ) 16 years

সঠিক উত্তর: খ

খ) 8 years

উত্তর

সঠিক উত্তর: খ

খ) 8 years

খ

ব্যাখ্যা

সরল সুদ ও আসলের অনুপাত 8 : 25/2
ধরি
n বছরের জন্য বিনিয়োগ করা হয়েছিল

আমরা জানি
সরল সুদ I = prn/100
⇒ (25 × n × n)/(2×100 ) = 8
⇒ n²= (8 ×2×100)/25
⇒ n² = 64
⇒ n = √64
∴ n = 8

১৮৪.

A sum of money invested at simple interest becomes 23/10 of itself in 2 years and 6 months. What is the rate of interest per annum?

ক
52%
খ
50%
গ
38%
ঘ
28%

সঠিক উত্তর: ক

52%

উত্তর

সঠিক উত্তর: ক

52%

ক

ব্যাখ্যা

Question: A sum of money invested at simple interest becomes 23/10 of itself in 2 years and 6 months. What is the rate of interest per annum?

Solution:
let,
principle = P
interest, I = (23P/10 - P)
= 13P/10
time, n = 2 years 6 months
= 2.5 years
we know,
I = Pnr/100
r = (100 × I)/Pn
= (100 × 13P/10) /P × 2.5
= 52%

১৮৫.

The compound interest on Tk.30000 at 7% per annum is Tk.4347. The period is

ক
ক) 2 year
খ
খ) 2.5 year
গ
গ) 3 year
ঘ
ঘ) 4 year

সঠিক উত্তর: ক

ক) 2 year

উত্তর

সঠিক উত্তর: ক

ক) 2 year

ক

ব্যাখ্যা

Amount = Tk.(30000+4347) = Tk.34347
let the time be n year
Then,
30000(1+7/100)ⁿ = 34347
(107/100)ⁿ = 34347/30000 = 11449/10000 = (107/100)²
n = 2year

১৮৬.

In order to obtain an income of Tk. 650 from 10% stock at Tk. 97, one must make an investment of-

ক
Tk. 3110
খ
Tk. 6305
গ
Tk. 6500
ঘ
Tk. 9700

সঠিক উত্তর: খ

Tk. 6305

উত্তর

সঠিক উত্তর: খ

Tk. 6305

খ

ব্যাখ্যা

Question: In order to obtain an income of Tk. 650 from 10% stock at Tk. 97, one must make an investment of-

Solution:
To obtain Tk. 10, investment = Tk. 97.
To obtain Tk. 650

investment = Tk. (97/10) × 650
= Tk. 6305

১৮৭.

An investor purchased 100 shares of stock X at tk per share and sold them all a year later at 24 tk per share. If the investor paid a 2 percent brokerage fee on both the total purchase price and the total selling price, which of the following is closest to the investor's percent gain on this investment?

ক
92%
খ
240%
গ
280%
ঘ
300%

সঠিক উত্তর: গ

280%

উত্তর

সঠিক উত্তর: গ

280%

গ

ব্যাখ্যা

Question: An investor purchased 100 shares of stock X at tk per share and sold them all a year later at 24 tk per share. If the investor paid a 2 percent brokerage fee on both the total purchase price and the total selling price, which of the following is closest to the investor's percent gain on this investment?

Solution:
buying price = price os total shares + brokerage charges on buy price
=100 × (49/8) + 2% of {100 × (49/8)}
= 624.75 tk

similarly selling price = (24 × 100) - 2% of 2400
= 2352 tk

So, Profit = SP - CP
= 2352 - 624.75
= 1727.25 tk

% = (1727.25/624.75) × 100%
= 276 ~ 280%

১৮৮.

4200 Taka is lent at compound interest of 10% per annum for 2 years. Find the amount after two years.

ক
Tk. 5028
খ
Tk. 6068
গ
Tk. 2520
ঘ
Tk. 5082

সঠিক উত্তর: ঘ

Tk. 5082

উত্তর

সঠিক উত্তর: ঘ

Tk. 5082

ঘ

ব্যাখ্যা

Question: 4200 Taka is lent at compound interest of 10% per annum for 2 years. Find the amount after two years.

Solution:
Compound amount = P (1 + r)ⁿ
= 4200 {1 + (10/100)}²
= 4200 × (110/100) × (110/100)
= 42 × 11 × 11
= 5082

১৮৯.

What would be the compound interest accrued on an amount of Tk. 5000 at the rate of 20% per annum in 2 years?

ক
ক) Tk. 2200
খ
খ) Tk. 2400
গ
গ) Tk. 2600
ঘ
ঘ) Tk. 2800

সঠিক উত্তর: ক

ক) Tk. 2200

উত্তর

সঠিক উত্তর: ক

ক) Tk. 2200

ক

ব্যাখ্যা

Question: What would be the compound interest accrued on an amount of Tk. 5000 at the rate of 20% per annum in 2 years?

Solution:
Here,
Principal = Tk. 5000
Rate = 20%
Time = 2 years

Amount = 5000 × {1 + (20/100)}²
= 5000 × (120/100) × (120/100)
= 7200

∴ Compound interest = Tk. (7200 - 5000) = Tk. 2200

১৯০.

In how many years will a sum of money double itself at 12.5% simple interest per annum?

ক
5 years
খ
7 years
গ
8 years
ঘ
12 years

সঠিক উত্তর: গ

8 years

উত্তর

সঠিক উত্তর: গ

8 years

গ

ব্যাখ্যা

Question: In how many years will a sum of money double itself at 12.5% simple interest per annum?

Solution:
let,
principal = P
interest, I = P
rate, r = 12.5%
time, n = ?

we know,
I = Pnr
n = I/Pr
= P/(P × 12.5%)
= 100/12.5
= 8 years.

১৯১.

Which is better investment: 11% stock at 143 or (39/4)% stock at 117?

ক
11% stock at 143
খ
(39/4)% stock at 117
গ
Both are equally good
ঘ
Cannot be compared, as the total amount of investment is not given.

সঠিক উত্তর: খ

(39/4)% stock at 117

উত্তর

সঠিক উত্তর: খ

(39/4)% stock at 117

খ

ব্যাখ্যা

Question: Which is better investment: 11% stock at 143 or (39/4)% stock at 117?

Solution:
Let investment in each case beTk. (143 × 117)
Income in 1st case = {(11/143) × 143 × 117}
= Tk 1287

Income in 2nd case = [{39/(4 × 117)} × 143 × 117]
= Tk 1394.25

Clearly (39/4)% stock at 117 is better.

১৯২.

A sum becomes Tk.13520 in 2 years at 4% per annum compound interest. Then the original sum is-

ক
Tk. 12250
খ
Tk. 12700
গ
Tk. 12450
ঘ
Tk. 12500

সঠিক উত্তর: ঘ

Tk. 12500

উত্তর

সঠিক উত্তর: ঘ

Tk. 12500

ঘ

ব্যাখ্যা

Question: A sum becomes Tk.13520 in 2 years at 4% per annum compound interest. Then the original sum is-

Solution:
Let the sum be Tk x

∴ 13520 = x(1 + 4/100)²
⇒ 13520 = x(1 + 1/25)²
⇒ 13520 = x(26/25)²
⇒ x = (13520 × 25 × 25) / (26 × 26)
⇒ x = 12500

১৯৩.

Shejan deposited Tk. 10000 for 4 year at a rate of 6% p.a. Find the amount Shejan got after 4 years.

ক
Tk. 12600
খ
Tk. 12350
গ
Tk. 12000
ঘ
Tk. 12400

সঠিক উত্তর: ঘ

Tk. 12400

উত্তর

সঠিক উত্তর: ঘ

Tk. 12400

ঘ

ব্যাখ্যা

Question: Shejan deposited Tk. 10000 for 4 year at a rate of 6% p.a. Find the amount Shejan got after 4 years.

Solution:
Principal (P) = 10000,
Time (n) = 4 years,
Rate (r) = 6% p.a.

Simple Interest (SI) = {Principal (P) × Rate (r) × Time (n)}/100
= (10000 × 6 × 4)/100
= 2400

Amount (A) = Principal (P) + Interest (I)
= 10000 + 2400
= 12400

১৯৪.

At what rate percent per annum will the simple interest on a sum of money 3/5 of the amount in 5 years?

ক
12%
খ
10%
গ
14%
ঘ
8%

সঠিক উত্তর: ক

12%

উত্তর

সঠিক উত্তর: ক

12%

ক

ব্যাখ্যা

Question: At what rate percent per annum will the simple interest on a sum of money 3/5 of the amount in 5 years?

Solution:
Let the principal be p Tk
So, interest = 3p/5 Tk
Time = 5 years
rate of interest, r =?

Now,
I = pnr
r = I/pn
= (3p/5)/(p × 5)
= (3/25) × 100%
= 12%

১৯৫.

The difference in taka between simple and compound interest at 5% annually on a sum of Tk. 5000 after 2 years is –

ক
ক) 12.5
খ
খ) 25
গ
গ) 50
ঘ
ঘ) 500

সঠিক উত্তর: ক

ক) 12.5

উত্তর

সঠিক উত্তর: ক

ক) 12.5

ক

ব্যাখ্যা

SI = 500 × 2 × 5/100 = 500
CI = 5000(1 + 5/100)² – 5000= 512.5
Difference = 512.5 - 500 = 12.5

১৯৬.

There is 50% increase in an amount in 5 years at simple interest. What will be the compound interest of Tk.1600 after 2 years at the same rate?

ক
ক) Tk. 363
খ
খ) Tk. 366
গ
গ) Tk. 336
ঘ
ঘ) Tk. 636

সঠিক উত্তর: গ

গ) Tk. 336

উত্তর

সঠিক উত্তর: গ

গ) Tk. 336

গ

ব্যাখ্যা

Let P = Tk. 100.
Then, S.I. Tk. 50 and T = 5 years
Rate =(100 × 50)/(100 × 5) = 10%

Now, P = Tk.. 1600.
T = 2 years and R = 10% p.a.

C.I. =1600(1 + 10/100)² - 1600
= 1600(1.1)² - 1600
= 1936 - 1600
= 336

১৯৭.

In 4 years the simple interest on certain sum of money is 9/25 of the principal. The annual rate of interest is-

ক
6%
খ
9%
গ
12%
ঘ
8.5%

সঠিক উত্তর: খ

উত্তর

সঠিক উত্তর: খ

খ

ব্যাখ্যা

Question: In 4 years the simple interest on certain sum of money is 9/25 of the principal. The annual rate of interest is-

Solution:
Given that,
In 4 years, Simple Interest (SI) = 9/25 of Principal (P)

We know,
SI = (P × r × n)/100
⇒ 9P/25 = (P × r × 4)/100
⇒ 9/25 = r/25
∴ r = 9

∴ Annual rate of interest = 9%

১৯৮.

What is the interest for 2 years on 600 tk at a simple interest rate of 9.5%?

ক
108 tk
খ
114 tk
গ
118 tk
ঘ
122 tk

সঠিক উত্তর: খ

114 tk

উত্তর

সঠিক উত্তর: খ

114 tk

খ

ব্যাখ্যা

Question: What is the interest for 2 years on 600 tk at a simple interest rate of 9.5%?

Solution:
Interest rate, r = 9.5% = 9.5/100 = 95/1000
Principal amount, p = 600 tk
Time, n = 2 years

We know,
Simple Interest, I = Pnr
= 600 × 2 × (95/1000)
= 114 tk

১৯৯.

What is the difference between the simple interest and the compound interest on a sum of Tk. 8000 for 2 years at the rate of 10% per annum when the interest is compounded yearly?

ক
Tk. 70
খ
Tk. 85
গ
Tk. 75
ঘ
Tk. 80

সঠিক উত্তর: ঘ

Tk. 80

উত্তর

সঠিক উত্তর: ঘ

Tk. 80

ঘ

ব্যাখ্যা

Question: What is the difference between the simple interest and the compound interest on a sum of Tk. 8000 for 2 years at the rate of 10% per annum when the interest is compounded yearly?

Solution:
Given that,
Principal, P = Tk. 8000
Rate, r = 10% per annum
Time, n = 2 years

Wee know,
SI = (P × r × n)/100
= (8000 × 10 × 2)/100
= 160000/100
= Tk. 1600

And,
Compound Interest (CI) – compounded annually
= P(1 + r)ⁿ- P
= P × (1 + 10/100)² - 8000
= 8000 × (1 + 1/10)² - 8000
= 8000 × (1.1)² - 8000
= 8000 × 1.21
= 9680 - 8000
= Tk. 1680

Difference between CI and SI
= 1680 - 1600
= Tk. 80

২০০.

A sum of money amounts to Tk. 9800after 5 years and Tk. 12005 after 8 years at the same rate of simple interest. The rate of interest per annum is -

ক
15%
খ
5%
গ
12%
ঘ
8%

সঠিক উত্তর: গ

12%

উত্তর

সঠিক উত্তর: গ

12%

গ

ব্যাখ্যা

Simple interest for 3 years
= 12005 - 9800
= 2205
Simple interest for 5 years
= (2205/3) × 5
= 3675
Some of money = 9800 - 3675
= 6125
R = (100 × 2205)/(6125 × 3)
= 12%