Simple and Compound Interest, Stock

PrepBank · পাতা ৯ / ৯ · ৮০১–৮৫৬ / ৮৫৮

৮০১.

A sum of money doubles itself in 4 years at a certain rate of simple interest. In how many years will it become four times itself at the same rate of interest?

ক
10 years
খ
12 years
গ
16 years
ঘ
20 years

ব্যাখ্যা

Question: A sum of money doubles itself in 4 years at a certain rate of simple interest. In how many years will it become four times itself at the same rate of interest?

Solution:
মনে করি, আসল (P) = 100 টাকা
4 বছরে এটি দ্বিগুণ হয়ে হয় (A) = 200 টাকা
∴ 4 বছরের সুদ (I) = 200 - 100 = 100 টাকা

অর্থাৎ, 100 টাকা সুদ হতে সময় লাগে 4 বছর।

এখন, আসল চারগুণ হলে সবৃদ্ধিমূল (A) হবে = 400 টাকা
∴ তখন প্রয়োজনীয় মোট সুদ (I) = 400 - 100 = 300 টাকা

এখন,
100 টাকা সুদ হতে সময় লাগে 4 বছর
1 টাকা সুদ হতে সময় লাগে 4/100 বছর
300 টাকা সুদ হতে সময় লাগে (4 × 300)/100 বছর
= 12 বছর

∴ আসল বা মূলধন 12 বছরে চারগুণ হবে।

৮০২.

Rakib obtained an amount of Tk. 8300 as simple interst on a certain amount at 8 p.c.p.a. after 5 years. What is the amount invested by Rakib?

ক
ক) Tk. 20750
খ
খ) Tk. 20700
গ
গ) Tk. 20720
ঘ
ঘ) Tk. 20760

ব্যাখ্যা

Question: Rakib obtained an amount of Tk. 8300 as simple interest on a certain amount at 8 p.c.p.a. after 5 years. What is the amount invested by Rakib?

Solution:
Suppose, Principal = Tk. 100
Then interest for 5 years at 8% = 5 × 8 = Tk. 40.

Now,
If interest is 40 taka then Principal = 100
∴ If interest is Tk. 8300 then Principal = (8300 × 100)/40 Tk.
= 20750 Tk.

৮০৩.

1000 tk. is being charged at 50% per annum. what is the interest for 2nd year at compound interest?

ক
ক) 1250 tk.
খ
খ) 1000 tk.
গ
গ) 750 tk.
ঘ
ঘ) 425 tk.

ব্যাখ্যা

Question: 1000 tk. is being charged at 50% per annum. what is the interest for 2nd year at compound interest?

solution:
১মবছরে চক্রবৃদ্ধি সুদাসল = 1000 (1 + 50/100)1
= 1000 (1 + 1/2)¹
= 1000 (3/2)¹
= 1500 টাকা

২য় বছরে চক্রবৃদ্ধি সুদাসল = 1000 (1 + 50/100)2
= 1000 (1 + 1/2)²
= 1000 (3/2)²
= 2250 টাকা

২য় বছরের জন্য সুদ = 2250 - 1500 টাকা
= 750 টাকা

৮০৪.

A man buys Tk. 20 shares paying 9% dividend. The man wants to have an interest of 12% on his money. The market value of each share is-

ক
Tk. 12
খ
Tk. 15
গ
Tk. 18
ঘ
Tk. 21

ব্যাখ্যা

Question: A man buys Tk. 20 shares paying 9% dividend. The man wants to have an interest of 12% on his money. The market value of each share is-

Solution:
Dividend on Tk. 20 = Tk. (9/100) × 20 = Tk. 9/5

Tk. 12 is an income on Tk. 100.
∴ Tk. 9/5 is an income on = Tk. (100 × 9)/(12 × 5)
= Tk.15

৮০৫.

A certain amount of money at simple interest turns into Tk. 1110 in 4 years and into Tk. 1200 in 5 years. The amount of money is:

ক
Tk. 750
খ
Tk. 840
গ
Tk. 660
ঘ
Tk. 800

ব্যাখ্যা

Question: A certain amount of money at simple interest turns into Tk. 1110 in 4 years and into Tk. 1200 in 5 years. The amount of money is:

Solution:
Simple interest for 1 years = Tk. (1200 - 1110)
= Tk. 90

∴ Simple interest for 4 years = Tk. (90 × 4)
= Tk. 360

∴ The amount of money is = Tk. (1110 - 360)
= Tk. 750

৮০৬.

A certain sum of money becomes three times of itself in 20 years at simple interest. In how many years does it become double of itself at the same rate of simple interest?

ক
ক) 5 years
খ
খ) 10 years
গ
গ) 12 years
ঘ
ঘ) 15 years

ব্যাখ্যা

Question: A certain sum of money becomes three times of itself in 20 years at simple interest. In how many years does it become double of itself at the same rate of simple interest?

Solution:
Let,
the principal be P.
After 20 years, Amount = 3P
Simple interest, I = 3P - P = 2P

We know that,
SI = PRT/100
⇒ 2P = (P × R × 20)/100
⇒ R = 10%

Now,
Amount = 2P
SI = Amount - Principal
= 2P - P
= P

∴ SI = PRT/100
⇒ P = (P × 10 × T)/100
∴ T = 10 years

৮০৭.

A sum of money at simple interest amounts to Tk. 1665 in 3 years and to Tk. 1782 in 4 years. The sum is :

ক
1414
খ
1352
গ
1374
ঘ
1314

ব্যাখ্যা

Question: A sum of money at simple interest amounts to Tk. 1665 in 3 years and to Tk. 1782 in 4 years. The sum is :

Solution:
interest in one year = (1782 - 1665 ) = 117
in three years = ( 117 × 3 ) = 351

∴ the sum of the money = ( 1665 - 351 )
= 1314

৮০৮.

The difference between simple and compound interests compounded annually on a certain sum of money for 2 years at 4% per annum is Tk. 1. The sum is:

ক
ক) 650
খ
খ) 640
গ
গ) 635
ঘ
ঘ) 625

ব্যাখ্যা

Question: The difference between simple and compound interests compounded annually on a certain sum of money for 2 years at 4% per annum is Tk. 1. The sum is:

Solution:
Let the sum be Tk. x.

Compound interest = x{1 + (4/100)}² - x
= x{1 + (1/25)}² - x
= x(26/25)² - x
= (676x/625) - x
= (676x - 625x)/625
= 51x/625

Simple interest = (x × 4 × 2)/100
= 2x/25

ATQ,
(51x/625) - (2x/25) = 1
⇒ (51x - 50x)/625 = 1
∴ x = 625

৮০৯.

What is the ratio of simple interest earned on certain amount at the rate of 12% per annum for 9 years and that for 12 years?

ক
1 : 2
খ
2 : 3
গ
3 : 4
ঘ
4 : 5

ব্যাখ্যা

Question: What is the ratio of simple interest earned on certain amount at the rate of 12% per annum for 9 years and that for 12 years?

Solution:
ধরি,
আসল = P টাকা
১২% হার বার্ষিক মুনাফায় P টাকার ৯ বছরের মুনাফা = P × ৯ × (১২/১০০) টাকা
= (১০৮P)/১০০ টাকা

১২% হার বার্ষিক মুনাফায় P টাকার ১২ বছরের মুনাফা = P × ১২ × (১২/১০০) টাকা
= (১৪৪P)/১০০ টাকা

অনুপাত = (১০৮P)/১০০ : (১৪৪P)/১০০
= ১০৮ : ১৪৪
= ৯ : ১২
= ৩ : ৪

৮১০.

To produce an annual income of TK 800 from a 8% stock at 80, the amount of stock needed is-

ক
10500 TK
খ
10,000 TK
গ
15000 TK
ঘ
12000 TK

ব্যাখ্যা

Question: To produce an annual income of TK 800 from a 8% stock at 80, the amount of stock needed is-

Solution:
since face value is not given, take it as TK 100
As it is a 8% stock, income(dividend) per stock = TK 8
ie, For an income of TK 8, the amount of stock needed = TK 100
For an income of TK 800, the amount of stock needed = (100 × 800)/8 = 10,000

৮১১.

An amount of money in invested in a saving account for two years. It increases by Tk 210 in two years after annual compounding at the rate of 10% per year. What is the amount invested initially?

ক
Tk. 900
খ
Tk. 1000
গ
Tk. 1100
ঘ
Tk. 1050

ব্যাখ্যা

Question: An amount of money in invested in a saving account for two years. It increases by Tk 210 in two years after annual compounding at the rate of 10% per year. What is the amount invested initially?

Solution:
Let, the principal be P

ATQ,
P + 210 = P(1 + 10/100)²
⇒ P + 210 = P(1 + 1/10)²
⇒ P + 210 = P(11/10)²
⇒ P + 210 = 121P/100
⇒ 121P = 100P + 21000
⇒ 21P = 21000
∴ P = 1000

৮১২.

An investor bought 40 shares of Tk 100 each at Tk 125 per share. If the dividend is 6%, what is the yield percent?

ক
4.8%
খ
5.5%
গ
6%
ঘ
7.2%

ব্যাখ্যা

Question: An investor bought 40 shares of Tk 100 each at Tk 125 per share. If the dividend is 6%, what is the yield percent?

Solution:
- Calculate Total Investment (মোট বিনিয়োগ):
Purchase price per share = Tk 125
Number of shares = 40
Total investment = 125 × 40 = Tk 5,000

- Calculate Annual Dividend (বার্ষিক লভ্যাংশ):
Dividend is paid on face value (not purchase price).
Face value = Tk 100/share
Dividend rate = 6%
Dividend per share = 100 × 6% = Tk 6/share
Total dividend for 40 shares = 40 × 6 = Tk 240/year

- Calculate Yield Percentage (লাভের শতকরা হার):
Yield% = (Annual Dividend / Total Investment) × 100
= (240 / 5,000) × 100
= 4.8%

৮১৩.

A vacuum cleaner is bought for Tk. 399 and loses 22% of its value per year compound interest. What is the value of the vacuum cleaner after 2 years?

ক
ক) Tk. 250
খ
খ) Tk. 245.75
গ
গ) Tk. 242.75
ঘ
ঘ) Tk. 248.50

ব্যাখ্যা

প্রশ্ন: A vacuum cleaner is bought for Tk. 399 and loses 22% of its value per year compound interest. What is the value of the vacuum cleaner after 2 years?

সমাধান:
Here,
P = Tk. 399
r = - 22% [we use (-), because it is decrease rate]
n = 2 years

We know that,
C = P(1 + r/100)ⁿ
= 399(1 - 22/100)²
= 399(1 - 0.22)²
= 399(0.78)²
= 399 × 0.6084
= 242.75

∴ The value of the vacuum cleaner after 2 years will be Tk. 242.75

৮১৪.

The difference (in taka) between simple and compound interest at 4% per annum on a sum of Tk 1500 after 2 years is:

ক
2.8 Tk
খ
3.4 Tk
গ
120 Tk
ঘ
122.4 Tk
ঙ
None of the above

ব্যাখ্যা

Question: The difference (in taka) between simple and compound interest at 4% per annum on a sum of Tk 1500 after 2 years is:

Solution:
Simple interest, I = Pnr/100
= (1500 × 2 × 4)/100
= 120 Tk

Compound interest, A = P{1 + (r/100)}²
= 1500{1 + (4/100)}²
= 1500{1 + (1/25)}²
= 1500 × (26/25)²
= 1622.4 Tk

Interest = 1622.4 - 1500 = 122.4 Tk
∴ Difference = 122.4 - 120 = 2.4 Tk

৮১৫.

A company issued 20000 shares of par value Tk. 10 each. If the total dividend declared by the company is Tk. 24000, find the rate of dividend paid by the company.

ক
ক) 14.5%
খ
খ) 12.5%
গ
গ) 14%
ঘ
ঘ) 12%

ব্যাখ্যা

Number of shares = 20000
Face value of each share = Tk. 10
dividend per share = (10 × R/100) where R is the Rate of interest.
Total dividend = 20000 ×10 ×R/100
20000 ×10 ×R/100 = 24000
R = 24000/2000
= 12
Hence the dividend is 12%.

৮১৬.

A farmer borrowed Tk. 3600 at 15% simple interest per annum. At the end of 4 years, he cleared this account by paying Tk. 4000 and a cow. The cost of the cow is:

ক
1200 Tk
খ
1550 Tk
গ
1760 Tk
ঘ
2000 Tk

ব্যাখ্যা

Question: A farmer borrowed Tk. 3600 at 15% simple interest per annum. At the end of 4 years, he cleared this account by paying Tk. 4000 and a cow. The cost of the cow is:

Solution:
P = 3600 tk, R = 15%, T = 4 yrs

S.I = PRT/100
= (3600 × 15 × 4)/100
= 2160 Tk.

Hence,
amount after 4 years = (3600 + 2160) = 5760 Tk.
∴ Cost of the cow = (5760 – 4000) = 1760 Tk.

৮১৭.

Jobayed buys 100 shares of par value Tk. 5 each, of a company, which pays an annual dividend of 12% at such a price that he gets 10% on his investment. Find the market value of a share.

ক
ক) Tk. 8
খ
খ) Tk. 4
গ
গ) Tk. 12
ঘ
ঘ) Tk. 6

ব্যাখ্যা

Face value of each share = Tk. 5
Total dividend received by Jobayed = {100 × 5 × (12/100)}
= Tk. 60
Let market value of 100 shares = Tk. x
x × (10/100) = 60
x = 600
ie, Market value of 100 shares = Tk. 600
Hence, Market value of each share = Tk. 6

৮১৮.

A man deposits Tk. 500 in a Bank at 10% interest rate compounded annually. At the end of the second year, the total amount including interest will become?

ক
Tk. 705
খ
Tk. 625
গ
Tk. 585
ঘ
Tk. 605

ব্যাখ্যা

Question: A man deposits Tk. 500 in a Bank at 10% interest rate compounded annually. At the end of the second year, the total amount including interest will become?

Solution:
Given,
Principal, P = 500 Tk.
Rate of interest, r = 10% = 10/100 = 1/10
Time, n = 2 years.

We know,
Compound Amount = P (1 + r)ⁿ
= 500 × (1 + 1/10)²
= 500 × (11/10)²
= 500 × (11/10) × (11/10)
= 605

৮১৯.

A man deposits Tk. 600 in a bank at 10% interest rate compounded annually. At the end of the second year, what will be the total amount including interest?

ক
680 Tk.
খ
710 Tk.
গ
840 Tk.
ঘ
726 Tk.

ব্যাখ্যা

Question: A man deposits Tk. 600 in a bank at 10% interest rate compounded annually. At the end of the second year, what will be the total amount including interest?

Solution:
Given,
Principal, P = 600 Tk
Rate of interest, r = 10% = 10/100 = 1/10
Time, n = 2 years

We know,
Compound Amount = P(1 + r)ⁿ
= 600 × (1 + 1/10)²
= 600 × (11/10)²
= 600 × (11/10) × (11/10)
= 600 × 121/100
= 726 Tk

৮২০.

A certain amount earns simple interest of Tk. 1750 after 7 year. Had the interest been 2% more, how much more interest would it have earned?

ক
ক) Tk.35
খ
খ) Tk.245
গ
গ) Tk.350
ঘ
ঘ) cannot be determined

ব্যাখ্যা

We need to know the S.I, principal and time to find the rate. Since the principal is not given, so data is inadequate.

৮২১.

What will be the simple interest on Tk. 730 at 9% per annum for the period from January 12, 2026 to May 31, 2026?

ক
30.50 Tk.
খ
28.25 Tk.
গ
29.50 Tk.
ঘ
25.20 Tk.
ঙ
None

ব্যাখ্যা

Question: What will be the simple interest on Tk. 730 at 9% per annum for the period from January 12, 2026 to May 31, 2026?

Solution:
January 12, 2026 to May 31, 2026 = 140 days

100 টাকার 365 দিনের মুনাফা = 9 টাকা
1 টাকার 1 দিনের মুনাফা = 9/(365 × 100) টাকা
730 টাকার 140 দিনের মুনাফা = (9 × 730 × 140)/(365 × 100) টাকা
= 25.20

৮২২.

An amount of Tk. 10,000 becomes Tk. 20,736 in 2 years. If the rate of interest is compounded half yearly, what is the annual rate of interest?

ক
ক) 25%
খ
খ) 20%
গ
গ) 40%
ঘ
ঘ) 30%

ব্যাখ্যা

Question: An amount of Tk. 10,000 becomes Tk. 20,736 in 2 years. If the rate of interest is compounded half yearly, what is the annual rate of interest?

Solution:
এখানে
মূলধন P = 10,000 টাকা
চক্রবৃদ্ধি মুলধন C = 20,736 টাকা

আমরা জানি
20,736 = 10000{1 + r/(2× 100)}^{2 × 2}
20736/10000 = {(200 + r)/200}⁴
20736/10000 = (200 + r)⁴/1600000000
20736 × 1600000000/10000 = (200 + r)⁴
20736 × 160000 = (200 + r)⁴
(200 + r)⁴ = 3,317,760,000
(200 + r)⁴ = (240)⁴
200 + r = 240
r = 240 - 200
r = 40

৮২৩.

There is 40% increase in an amount in 4 years at simple interest. What will be the compound interest of Tk.2000 after 2 years at the same rate?

ক
400
খ
380
গ
420
ঘ
440

ব্যাখ্যা

Question: There is 40% increase in an amount in 4 years at simple interest. What will be the compound interest of Tk.2000 after 2 years at the same rate?

Solution:
Let P = Tk. 100
Then, S.I. Tk. = 40 and n = 4 years
Rate = (100 × 40)/(100 × 4) = 10%
Now, P = Tk. 2000
n = 2 years and R = 10% p.a.
C.I. = 2000(1 + 10/100)² - 2000
= 2000(1.1)² - 2000
= 2000 × 1.21 - 2000
= 2420 - 2000
= 420

৮২৪.

In order to obtain an income of Tk. 720 from 8% stock at Tk. 90, one must make an investment of-

ক
Tk. 7200
খ
Tk. 8100
গ
Tk. 9000
ঘ
None of these

ব্যাখ্যা

Question: In order to obtain an income of Tk. 720 from 8% stock at Tk. 90, one must make an investment of-

Solution:
To obtain Tk. 8, investment = Tk. 90.
To obtain Tk. 720
investment = Tk. (90/8) × 720
= Tk. 8100

৮২৫.

An amount of tk.625 becomes Tk 1296 in 2 years if the interest is compounded half-yearly. What is the yearly rate of compound interest?

ক
30%
খ
35%
গ
40%
ঘ
50%

ব্যাখ্যা

Question: An amount of tk.625 becomes Tk 1296 in 2 years if the interest is compounded half-yearly. What is the yearly rate of compound interest?

solution:
let the rate be R%

Then,
625 {1 + R/(2 × 100)} ^{2 × 2} = 1296
⇒ (1 + R/200)⁴ = 1296/625
⇒ (1 + R/200)⁴ = (6/5)⁴
⇒ (1 + R/200) = 6/5
⇒ R/200 = 1/5
⇒ R = 40
∴ R = 40%

৮২৬.

If a sum of BDT 5,000 becomes BDT 6,728 in 2 years at compound interest, what is the rate of interest per annum?

ক
12%
খ
15%
গ
16%
ঘ
18%

ব্যাখ্যা

Question: If a sum of BDT 5,000 becomes BDT 6,728 in 2 years at compound interest, what is the rate of interest per annum?

Solution: Given,
A = Amount after interest = BDT 6,728
P = Principal amount = BDT 5,000
r = Rate of interest per annum
n = Time in years = 2

Thus, the rate of interest per annum is 16%.

৮২৭.

What would be a compound interest accrued on an amount of Tk. 8000 at the rate of 25% per annum in 3 years?

ক
ক) Tk.5765
খ
খ) Tk.7625
গ
গ) Tk8245
ঘ
ঘ) Tk.9570

ব্যাখ্যা

Question: What would be a compound interest accrued on an amount of Tk. 8000 at the rate of 25% per annum in 3 years?

Solution:
Amount,
= 8000 × (1 + 25/100)³
= [8000 × (125/100)³]
= [8000 × (125/100) × (125/100) × (125/100)]
= [8000 × (5/4) × (5/4) × (5/4)]
= Tk.15625

Compound Interest = Tk.(15625 - 8000) = Tk.7625

৮২৮.

Kuddus took a loan at simple interest rate of 6 p.c.p.a. in the first year and it increased by 1.5 p.c.p.a. every year. If he pays Tk. 8190 as interest at the end of 3 years, what was his loan amount?

ক
ক) Tk. 35400
খ
খ) Tk. 36000
গ
গ) Tk. 36800
ঘ
ঘ) Cannot be determined
ঙ
ঙ) None of these

ব্যাখ্যা

Let the loan amount be Tk. x
Then,
⇒ (6x/100)+(7.5x/100)+(9x/100) = 8190
⇒ 22.5x = 819000
⇒ x = 36400

৮২৯.

Shejan has borrowed Tk. 5000 at the rate of 6% S.I. what amount he needs to pay after 3 years to clear the debt?

ক
Tk. 5500
খ
Tk. 5900
গ
Tk. 6100
ঘ
Tk. 6300

ব্যাখ্যা

Question: Shejan has borrowed Tk. 5000 at the rate of 6% S.I. what amount he needs to pay after 3 years to clear the debt?

Solution:
P = Tk. 5000
r = 6%
n = 3

∴ I = Pnr
= (5000 × 3 × 6)/100
= 900

∴ Required amount = 5000 + 900 = 5900

৮৩০.

The compound interest on Tk. 2800 for 18 months at 10% p.a. is

ক
ক) Tk. 441.35
খ
খ) Tk. 434
গ
গ) Tk. 436.75
ঘ
ঘ) Tk. 420

ব্যাখ্যা

Given, Principal, P = 2800
Compound rate, R = 10% per annum = 10/2 = 5% half - yearly
Amount = [2800 × (1 + 10/100) × (1 + 5/100)]
= (2800 × 11/10 × 21/20)
= 3234
∴ C.I. = (3234 − 2800) = 434

৮৩১.

On a sum of money, the simple interest for 2 years is Tk. 880, while the compound interest is Tk. 928.4, the rate of interest being the same in both cases. The rate of interest is -

ক
10%
খ
10.2%
গ
10.5%
ঘ
11%

ব্যাখ্যা

Question: On a sum of money, the simple interest for 2 years is Tk. 880, while the compound interest is Tk. 928.4, 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. (928.4 - 880) = Tk. 48.4
Simple interest for 1 years = 880/2 = Tk. 440

Simple interest on 440 for 1 year = 48.4
Interst rate = {(48.4 × 100)/440}% = 11%

৮৩২.

A man purchased 300 shares of the face value of Tk. 100 each from the market at Tk. 800 per share. If a dividend of 24% is declared, find his earning percent on the investment.

ক
2.4%
খ
30%
গ
3%
ঘ
8%

ব্যাখ্যা

Question: A man purchased 300 shares of the face value of Tk. 100 each from the market at Tk. 800 per share. If a dividend of 24% is declared, find his earning percent on the investment.

Solution:
Price of 1 share = Tk. 800.
Dividend rate = 24%.

∴ Earning % on investment = (24/800) × 100 = 3%.

৮৩৩.

A sum of money triples itself in 25 years at simple interest. What is the annual interest rate?

ক
5%
খ
8%
গ
10%
ঘ
12%

ব্যাখ্যা

Question: A sum of money triples itself in 25 years at simple interest. What is the annual interest rate?

Solution:
ধরি, আসল = P টাকা
∴ 25 বছরে সুদে-আসলে হয় (A) = 3P টাকা
সুতরাং, সুদ (I) = A - P = 3P - P = 2P টাকা
সময় (n) = 25 বছর
সুদের হার (r) = ?

আমরা জানি,
I = (Pnr)/100
⇒ r = (I × 100)/(P × n)
⇒ r = (2P × 100)/(P × 25)
⇒ r = (2 × 100)/25
⇒ r = 2 × 4
⇒ r = 8%
সুতরাং, বার্ষিক সুদের হার 8%।

৮৩৪.

Two equal sum of money were lent at simple interest at 11% p. a for the 7/2 years and 9/2 years respectively. If the difference in interests for two periods was Tk. 411.4, Then each sum is:

ক
ক) Tk. 3740
খ
খ) Tk. 3760
গ
গ) Tk. 3750
ঘ
ঘ) Tk. 3780

ব্যাখ্যা

Let the each sum be x
Now
{(x × 11 × 9)/(100 × 2)} - {(x × 11 × 7)/(100 × 2)} = 411.4
(99x - 77x)/200 = 411.4
22x = 82,280
x= 82,280/22
x = 3740

৮৩৫.

Tk. 10000 becomes Tk. 12000 in 4 years at a certain rate of simple interest. If the rate becomes 2.5 times of itself, the amount of same principal in 6 years will be -

ক
Tk. 17000
খ
Tk. 17500
গ
Tk. 18600
ঘ
Tk. 19200

ব্যাখ্যা

Question: Tk. 10000 becomes Tk. 12000 in 4 years at a certain rate of simple interest. If the rate becomes 2.5 times of itself, the amount of same principal in 6 years will be -

সমাধান:
10000 টাকা 4 বছরে 12000 টাকা হয়।
∴ 4 বছরে সুদ = 12000 - 10000 টাকা = 2000 টাকা
1 বছরে সুদ = 2000/4 = 500 টাকা

2.5 গুণ বৃদ্ধিতে নতুন 1 বছরের সুদ = 500 × 2.5 টাকা
= 1250 টাকা

6 বছরে মোট সুদ = 1250 × 6 টাকা = 7500 টাকা
সুতরাং, 6 বছর পর সুদাসলে হবে = 10000 + 7500 টাকা
= 17500 টাকা

৮৩৬.

Calculate the simple interest on Tk. 4000 for 15 months at 6 paise per taka per month.

ক
Tk. 3600
খ
Tk. 4200
গ
Tk. 2400
ঘ
Tk. 3000

ব্যাখ্যা

Question : Calculate the simple interest on Tk. 4000 for 15 months at 6 paise per taka per month.

Solution :
Given,
Principal P = Tk. 4000
interest rate r = 6 paise per Taka per month
∴ Tk. 1 = 6 paise
∴ Tk. 100 = (6 × 100) paise
= 600 paise
= 6 taka
= 6% per month
= 6/100

Time t =15 months

We know,
The simple interest I = Prn
= 4000 × (6/100) × 15
= 360000/100
= 3600

So the simple interest = Tk. 3600

৮৩৭.

What will be the difference in taka between simple and compound interest at 10% on a sum of TK. 1000 after 4 years?

ক
ক) 31.90
খ
খ) 32.10
গ
গ) 44.90
ঘ
ঘ) 64.10

ব্যাখ্যা

10% সুদে, 1,000 টাকার 4 বছরের সুদ = (10 × 4 × 1000)/100
= 400 টাকা ।
আমরা জানি,
Compound amount, c = p(1 + r)ⁿ
= 1000{1 + (10/100)}⁴
= 1000(11/10)⁴
= 1464.10 টাকা
∴ Compound interest = 1464.10 - 1000
= 464.10 টাকা
∴ Simple এবং Compound interest এর মধ্যে পার্থক্য = 464.10 - 400
= 64.10 টাকা
Answer: 64.10

৮৩৮.

মুনাফা আসলের ১/৪ অংশ। কোন মূলধন মুনাফা-আসলে ৫ বছরে একসাথে ৮৭৫ টাকা হয় হলে, শতকরা মুনাফার হার =?

ক
৪%
খ
৬%
গ
৭%
ঘ
৫%
ঙ
কোনটিই নয়

ব্যাখ্যা

প্রশ্ন: মুনাফা আসলের ১/৪ অংশ। কোন মূলধন মুনাফা-আসলে ৫ বছরে একসাথে ৮৭৫ টাকা হয় হলে, শতকরা মুনাফার হার =?

সমাধান:
ধরি,
মুনাফা = ক টাকা
∴ আসল = ৪ক টাকা

∴ মুনাফা-আসল = ক + ৪ক = ৫ক টাকা

প্রশ্নমতে,
৫ক = ৮৭৫
বা, ক = ৮৭৫/৫
∴ ক = ১৭৫ টাকা

মুনাফা = ১৭৫ টাকা এবং আসল = (১৭৫ × ৪) = ৭০০ টাকা

৭০০ টাকার ৫ বছরের মুনাফা ১৭৫ টাকা
১ টাকার ১ বছরের মুনাফা ১৭৫/(৭০০ × ৫) টাকা
∴ ১০০ টাকার ১ বছরের মুনাফা (১৭৫ × ১০০)/(৭০০ × ৫) টাকা
= ৫ টাকা

∴ শতকরা মুনাফার হার ৫%

৮৩৯.

A town experiences a 10% decrease in its population every year. If the population was 20,000 two years ago, what is the population now?

ক
24,200
খ
22,000
গ
16,200
ঘ
13,200

ব্যাখ্যা

Question: A town experiences a 10% decrease in its population every year. If the population was 20,000 two years ago, what is the population now?
(এক শহরের জনসংখ্যা প্রতি বছরে ১০% কমে যায়। যদি দুই বছর আগে জনসংখ্যা ২০,০০০ ছিল, তাহলে বর্তমানে জনসংখ্যা কত হবে?)

Solution:
বর্তমান জনসংখ্যা = 20000(1 - 10/100)² {[C = p(1 - r)ⁿ] অনুসারে।}
= 20000 × 0.9 × 0.9
= 16,200

৮৪০.

In how much simple interest rate 2000 Taka becomes 4000 in 4 years?

ক
ক) 25%
খ
খ) 20%
গ
গ) 18%
ঘ
ঘ) 50%

ব্যাখ্যা

Question: In how much simple interest rate 2000 Taka becomes 4000 in 4 years?

Solution:
এখানে,
P = 2000 Tk
I = 4000 - 2000 = 2000 Tk
n = 4 years

আমরা জানি,
I = Pnr
r = (I/pn) × 100%
= (2000/8000) × 100%
= 25%

৮৪১.

A man buys Tk. 20 shares paying 9% dividend. The man wants to have an interest of 12% on his money. The market value of each share is-

ক
Tk. 12
খ
Tk. 15
গ
Tk. 18
ঘ
Tk. 21

ব্যাখ্যা

Question: A man buys Tk. 20 shares paying 9% dividend. The man wants to have an interest of 12% on his money. The market value of each share is-

Solution:
From Tk. 100 one can earn dividend Tk. 9
From Tk. 1 one can earn dividend Tk. 9/100
From Tk. 20 one can earn dividend Tk. (9 × 20)/100 = Tk. 9/5

If interest Tk. 12 then the market Value Tk. 100
If interst Tk. 1 then the market Value Tk. 100/12
If interst Tk. 9/5 then the market Value Tk. (100 × 9)/(12 × 5)
= Tk. 15

৮৪২.

If 6,250 Taka is invested at 12% simple interest, how much time will it take for the interest to reach 3,000 Taka?

ক
4 years
খ
5 years
গ
6 years
ঘ
7 years

ব্যাখ্যা

Question: If 6,250 Taka is invested at 12% simple interest, how much time will it take for the interest to reach 3,000 Taka?

Answer:
Given,
P = 6250 Taka
I = 3000 Taka
r = 12% = 0.12
Time = n

We know,
I = Pnr
n = I/Pr
n = 3000/(6250×0.12)
n = 4 years

৮৪৩.

There is 60% increase in an amount in 6 years at simple interest. What will be the compound interest of Tk. 12000 after 3 years at the same rate?

ক
Tk. 3972
খ
Tk. 4100
গ
Tk. 3784
ঘ
Tk. 4248

ব্যাখ্যা

Question: There is 60% increase in an amount in 6 years at simple interest. What will be the compound interest of Tk. 12000 after 3 years at the same rate?

Solution:
Given that,
Increase in amount after 6 years = 60%

We know,
A = P(1 + r/100)n
simple Interest = (principal × rate × time)/100

Now,
Let the amount at the 1^st year be 100x
∴ Increased in amount = 60% of 100x = 60x
⇒ 60x = (100x × 6 × r)/100
⇒ 6r = 60
⇒ r = 60/6 = 10
∴ r = 10%

∴ Compound Interest after 3 years = P(1 + r/100)ⁿ - P
= 12000(1 + 10/100)³ - 12000
= 12000 × (11/10)³ - 12000
= 12000 × (11/10) × (11/10) × (11/10) - 12000
= 15972 - 12000
= Tk. 3972

∴ The required answer is Tk. 3972

৮৪৪.

In what time will the simple interest on 1200 Tk. at 4% per annum be the same as that on 600 Tk. at 8% per annum in 2 years?

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

ব্যাখ্যা

Question: In what time will the simple interest on 1200 Tk. at 4% per annum be the same as that on 600 Tk. at 8% per annum in 2 years?

Solution:
the interest of 600 Tk. at 8% per annum in 2 years is = 600 × 2 × 8%
= 96 Tk.

let, the time is n years.
I = 96 Tk.
P = 1200 Tk.
r = 4%

as we know,
I = Pnr
n = I / Pr
= 96 / (1200 × 4%)
= 2 years

৮৪৫.

A certain amount becomes Tk. 3000 at a simple interest of 12%. Keeping the time period the same, if the rate of simple interest is increased by 3%, the amount will become 300 Tk/- more than in the previous setting. What is the amount? Also find the time period.

ক
ক) Tk. 1500 and 7 years
খ
খ) Tk. 1800 and 5.5 years
গ
গ) Tk. 1900 and 8.25 years
ঘ
ঘ) Tk. 2000 and 20 years

ব্যাখ্যা

Let Simple Interest be S
Original sum 'P' and Time 'T' remains the same
Also, 3% increase in rate of interested means, New rate = 15%
Increase of 300 Rs/- in the final amount means, New amount = Tk. 3300/-

So, Amount 2 - Amount 1 = (P + S₁) - (P + S₂) = S₁ - S₂
∴ 3300 - 3000 = S₁ - S₂
∴ S₁ - S₂ = 300

∴ {(P × R × T)/100} - {(P × 12 × T)/100 = 300
3PT/100 = 300
PT = 10000
For R = 15%,

Simple interest = (P × 15 × T)/100
= (10000 × 15)/100
= Tk. 1500

Original sum = Amount - Interest = 3300 - 1500 = Tk. 1800 (Principle amount)

Also, PT = 10000
T = 10000/1800
= 5.55 years.

৮৪৬.

The compound interest on Tk 30,000 at 7% per annum is TK.4357. The period (in years) is:

ক
ক) 2
খ
খ) 2.5
গ
গ) 3
ঘ
ঘ) 4

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

৮৪৭.

A person takes a loan of 200 taka at 5% simple interest. He returns 100 taka at the end of 1 year. In order to clear his dues at the end of 2 years, he would pay-

ক
ক) 100 taka
খ
খ) 110 taka
গ
গ) 110.5 taka
ঘ
ঘ) 115.5 taka

ব্যাখ্যা

Question: A person takes a loan of 200 taka at 5% simple interest. He returns 100 taka at the end of 1 year. In order to clear his dues at the end of 2 years, he would pay-

Solution:
১ বছরে সুদ = ২০০ × ৫/১০০ টাকা
= ১০ টাকা

১ বছর শেষে সে ১০০ টাকা ফেরত দেয়।

বাকি আছে = ২১০ - ১০০ টাকা
= ১১০ টাকা

১১০ টাকা এক বছরে সুদাসলে হয় = ১১০ + ১১০ × ৫/১০০
= ১১৫.৫ টাকা

অতএব, ২য় বছর শেষে তাকে ১১৫.৫ টাকা দিতে হবে।

৮৪৮.

A man lends Tk. 10000 in four parts. If he gets 8% on TK. 2000, 7.5% on TK. 4000 and 8.5% on TK. 1400, what percent must he get for the remainder, if the average interest is 8.13%?

ক
7
খ
9.25
গ
9
ঘ
10.5
ঙ
None of these

ব্যাখ্যা

Question: A man lends Tk. 10000 in four parts. If he gets 8% on TK. 2000, 7.5% on TK. 4000 and 8.5% on TK. 1400, what percent must he get for the remainder, if the average interest is 8.13%?

Solution:
∵ [(2000 × 8 × 1)/100] + [(4000 × 7.5 × 1)/100] + [(1400 × 8.5 × 1)/100] + [(2600 × R × 1)/100] = (10000 × 8.13 ×1)/100
⇒ 160 + 300 + 119 + 26R = 813
⇒ 26R = 234
⇒ R = 9%

৮৪৯.

Modric puts Tk. 100 in the bank for two years at 10% interest compounded annually. At the end of the two years, what will be his balance?

ক
ক) Tk. 100.00
খ
খ) Tk. 105.00
গ
গ) Tk. 110
ঘ
ঘ) Tk. 121

ব্যাখ্যা

Question: Modric puts Tk. 100 in the bank for two years at 10% interest compounded annually. At the end of the two years, what will be his balance?

Solution:
Here,
p = 100
n = 2
r = 10% = 10/1000 = 1/10
C = ?

We know,
C = p(1 + r)ⁿ
= 100{1 + (1/10)}²
= 100(11/10)²
= 100 (121/100)
= 121

৮৫০.

A person took a loan of Tk. 2500 with simple interest for as many years as the rate of interest. If they paid Tk. 1600 as interest at the end of the loan period, what was the rate of interest?

ক
5%
খ
6%
গ
8%
ঘ
10%

ব্যাখ্যা

Question: A person took a loan of Tk. 2500 with simple interest for as many years as the rate of interest. If they paid Tk. 1600 as interest at the end of the loan period, what was the rate of interest?

Solution:
ধরি, সুদের হার = r%
যেহেতু সময় এবং সুদের হার সমান,
∴ সময়, n = r বছর
আসল (P) = 2500 টাকা
মোট সুদ (I) = 1600 টাকা
আমরা জানি,
সরল সুদ, SI = (P × r × n)/100
⇒ 1600 = (2500 × r × r)/100 [এখানে, n = r]
⇒ 1600 = 25 × r²
⇒ r² = 1600/25
⇒ r² = 64
⇒ r = √64
⇒ r = 8

∴ সুদের হার ছিল 8%।

৮৫১.

How many years will it take for an investment of Tk.5000 to earn Tk. 1200 in simple interest rate of 6%?

ক
4
খ
3
গ
5
ঘ
2.5

ব্যাখ্যা

Question: How many years will it take for an investment of Tk.5000 to earn Tk. 1200 in simple interest rate of 6%?

Solution:
Given that,
Principal, P = 5000
Simple Interest, SI = 1200
Rate of interest, r = 6%
Time, n = ?

We know,
n = I/Pr
= 1200/(5000 × 6%)
= (1200 × 100)/(5000 × 6)
= 4

So, it will take 4 years for the investment to earn Tk. 1200 at 6% simple interest.

৮৫২.

What is the total interest on Tk. 1,200 at 10% per annum for 9 months?

ক
100 Tk
খ
80 Tk
গ
110 Tk
ঘ
90 Tk

ব্যাখ্যা

Question: What is the total interest on Tk. 1,200 at 10% per annum for 9 months?

Solution:
Given,
Principal (P) = Tk. 1200
Rate (R) = 10%
Time (T) = 9 months
= 9/12 year
= 3/4 year

By Formula,
SI = PRT/100
= {1200 × 10 × (3/4)}/100
= (1200 × 10 × 3)/400
= 90 Tk

৮৫৩.

What is the difference between the compound interests on Tk. 5000 for 1 (1/2) years at 4% per annum compounded yearly and half-yearly?

ক
ক) 2.04
খ
খ) 3.24
গ
গ) 4.65
ঘ
ঘ) 5.78
ঙ
ঙ) 3.72

ব্যাখ্যা

C.I. when interest compound yearly = Tk. [5000 × (1 + 4/100) (1 + 1/2 × 4/100)]
= Tk. 5304.
C.I. when interest is compounded half-yearly = Tk. 5000 (1 + 2/100)³
= Tk. 5306.04
Difference = Tk. (5306.04 - 5304)
= Tk. 2.04

৮৫৪.

At what rate percent of simple interest will a sum of money double itself in 10 years?

ক
ক) 5%
খ
খ) 10%
গ
গ) 20%
ঘ
ঘ) 25%

ব্যাখ্যা

Question: At what rate percent of simple interest will a sum of money double itself in 10 years?

Solution:
ধরি,
আসল = ১০০ টাকা
তাহলে ১০ বছর পর দ্বিগুণ অর্থ সুদ সহ আসল হবে = ২ × ১০০ = ২০০
∴ মোট সুদ = (২০০ - ১০০) টাকা = ১০০ টাকা

∴ ১০ বছরের সুদ ১০০ টাকা হলে ১ বছরের সুদ = ১০০/১০ = ১০%

৮৫৫.

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

ক
30 years
খ
40 years
গ
25 years
ঘ
20 years

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

৮৫৬.

The difference between compound interest and simple interest on a sum for 2 years at 8% is Tk 768. The sum is -

ক
ক) 120000 Tk
খ
খ) 100000 Tk
গ
গ) 124000 Tk
ঘ
ঘ) 800000 Tk

ব্যাখ্যা

Question: The difference between compound interest and simple interest on a sum for 2 years at 8% is Tk 768. The sum is -

Solution:
Let the sum be p

Then, Compound Interest = p(1+ 8/100)² - p
= p(108/100)² - p
= p(27/25)² - p
= 729p/625 - p
= 104p/625

Again, Simple Interest = p × 2 × (8/100) = 4p/25

ATQ,
104p/625 - 4p/25 = 768
⇒ 4p/625 = 768
⇒ p = (768 × 625)/4
⇒ p = 120000