Simple and Compound Interest, Stock

PrepBank · পাতা ৪ / ৯ · ৩০১–৪০০ / ৮৫৮

৩০১.

A man deposits Tk 600 in a Bank at 10% interest rate compounded annually. At the end of the second year, the total amount including interest will become Tk-

ক
660
খ
720
গ
160
ঘ
726
ঙ
None of these

ব্যাখ্যা

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

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)
= 726

৩০২.

A sum of money at simple interest amounts to Tk.815 in 3years and to Tk.854 in 4 years. What is the sum?

ক
Tk 720
খ
Tk 650
গ
Tk 698
ঘ
Tk 875
ঙ
Tk 659

ব্যাখ্যা

S.I. for 1 year = 854 - 815
= 39
S.I. for 3 years = 39 × 3
= 117
∴ Required Sum = 815 - 117
= Tk. 698.

৩০৩.

Tk. 6000 becomes Tk. 7200 in 4 years at a certain rate of simple interest. If the rate becomes 1.5 times of itself, the amount of same principal in 5 years will be -

ক
Tk. 8000
খ
Tk. 8250
গ
Tk. 9000
ঘ
Tk. 9250

ব্যাখ্যা

Question: Tk. 6000 becomes Tk. 7200 in 4 years at a certain rate of simple interest. If the rate becomes 1.5 times of itself, the amount of same principal in 5 years will be -

Solution:
৬০০০ টাকা ৪ বছরে ৭২০০ টাকা হয়।
৪ বছরে সুদ = ৭২০০ - ৬০০০ টাকা
= ১২০০ টাকা
১ বছরে সুদ = ১২০০/৪ = ৩০০ টাকা

১.৫ গুণ বৃদ্ধিতে ১ বছরে সুদ = ৩০০ × ১.৫ টাকা
= ৪৫০ টাকা

৫ বছরে সুদ = ৪৫০ × ৫ টাকা
= ২২৫০ টাকা

∴ ৫ বছর পর সুদাসলে হবে = ৬০০০ + ২২৫০ টাকা
= ৮২৫০ টাকা

৩০৪.

A man invests some money partly in 9% stock at 96 and partly in 12% stock at 120. To obtain equal dividends from both, he must invest the money in the ratio -

ক
ক) 3 : 4
খ
খ) 13 : 15
গ
গ) 4 : 5
ঘ
ঘ) 16 : 15

ব্যাখ্যা

For an income of Tk. 1 in 9% stock at 96,
investment = Tk. (96/9)
= Tk. 32/3

For an income of Tk. 1 in 12% stock at 120,
investment = Tk. (120/12)
= Tk. 10

Ratio of investments = (32/3) : 10
= 32 : 30
= 16 : 15.

৩০৫.

An amount of money in invested in a saving account for two years. It increases by Tk. 645 in two years after annual compounding at the rate of 15% per year. What is the amount in Tk. invested initially?

ক
Tk. 1500
খ
Tk. 2000
গ
Tk. 2200
ঘ
Tk. 1800

ব্যাখ্যা

Question: An amount of money in invested in a saving account for two years. It increases by Tk. 645 in two years after annual compounding at the rate of 15% per year. What is the amount in Tk. invested initially?

Solution:
Let, the principal be p

ATQ,
p + 645 = p(1 + 15/100)²
⇒ p + 645 = p(1 + 3/20)²
⇒ p + 645 = p(23/20)²
⇒ p + 645 = (529p)/400
⇒ 529p = 400p + 258000
⇒ 129p = 258000
⇒ p = 258000/129
∴ p = 2000

৩০৬.

2100 Taka is lent at compound interest of 5% per annum for 2 years. Find the amount after two years.

ক
Tk. 2315.25
খ
Tk. 2325.25
গ
Tk. 2425
ঘ
Tk. 2575
ঙ
None

ব্যাখ্যা

Question: 2100 Taka is lent at compound interest of 5% per annum for 2 years. Find the amount after two years.

Solution:
Here,
p = Tk. 2100
r% = 5%
n = 2 years

C = p[1 + (r/100)]ⁿ
= 2100 [1 + (5/100)]2
= 2100 × [105/100]²
= (2100 × 11025)/10000
= 2315.25

Hence, the amount after two years is Tk. 2315.25

৩০৭.

If a principal P becomes Q in 2 years when interest R% is compounded half-yearly. And if the same principal P becomes Q in 2 years when interest S% is compound annually, then which of the following is true.

ক
ক) R > S
খ
খ) R = S
গ
গ) R < S
ঘ
ঘ) None

ব্যাখ্যা

Since interest is compounded half yearly at R% p.a. the value of R will be lesser than the value of S

৩০৮.

A sum of Tk. 2500 amounts to Tk. 2809 in 2 years at compound interest. Find the rate of interest per annum.

ক
10%
খ
15%
গ
12%
ঘ
6%

ব্যাখ্যা

Question: A sum of Tk. 2500 amounts to Tk. 2809 in 2 years at compound interest. Find the rate of interest per annum.

Solution:
Here,
Principal, P = 2500 Tk.
Final amount, A = 2809 Tk.
Time, n = 2 years
Interest rate, r = ?

প্রশ্নমতে,
A = P × (1 + r/100)ⁿ
⇒ 2809 = 2500 × (1 + r/100)²
⇒ (1 + r/100)² = 2809/2500
⇒ (1 + r/100) = √(2809/2500)
⇒ 1 + r/100 = 53/50
⇒ r/100 = (53/50) - 1
⇒ r/100 = 3/50
⇒ r = (3/50) × 100
⇒ r = 6

∴ The annual rate of interest is 6%.

৩০৯.

Karim borrowed Tk. 10000 at a certain rate of simple interest for 4 years. If he paid Tk. 2500 as interest, find the rate of interest per annum.

ক
6.25%
খ
5.25%
গ
7.25%
ঘ
8.25%
ঙ
None of these

ব্যাখ্যা

Question: Karim borrowed Tk. 10000 at a certain rate of simple interest for 4 years. If he paid Tk. 2500 as interest, find the rate of interest per annum.

Solution:
Given that,
Principal, P = Tk. 10,000
Simple Interest, SI = Tk. 2,500
Time, n = 4 years

We know,
SI = (Principal × Rate × Time)/100
⇒ 2500 = (10,000 × r × 4)/100
⇒ 2500 = (40,000 × r)/100
⇒ 2500 = 400 × r
⇒ r = 2500/400
∴ r = 6.25%

Therefore, the rate of interest per annum is 6.25%.

৩১০.

If the rate of simple interest is 12% per annum the amount that would fetch interest of Tk. 6,000 per annum is?

ক
ক) Tk. 45,000
খ
খ) Tk. 30,000
গ
গ) Tk. 37,000
ঘ
ঘ) Tk. 50,000

ব্যাখ্যা

Given that
r = 12%= 12/100
I = Tk. 6,000
n = 1

We Know,
I=Pnr
Pnr =I
P = I/nr
= (6000×100)/12
=50,000 Tk.

৩১১.

A sum of money at simple interest amounts to Tk. 715 in 4 years and to Tk. 754 in 5 years. The sum is:

ক
ক) Tk. 459
খ
খ) Tk. 500
গ
গ) Tk. 523
ঘ
ঘ) Tk. 559

ব্যাখ্যা

Question: A sum of money at simple interest amounts to Tk. 715 in 4 years and to Tk. 754 in 5 years. The sum is:

Solution:
১ বছরের সুদ = ৭৫৪ - ৭১৫ টাকা
= ৩৯ টাকা

∴ ৪ বছরে সুদ = (৩৯ × ৪) টাকা
= ১৫৬ টাকা

∴ আসল = ৭১৫ - ১৫৬ টাকা
= ৫৫৯ টাকা

৩১২.

A person invests Tk. 3100 at a rate of 4% per annum under simple interest. After how many years will the total interest earned be Tk. 372?

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

ব্যাখ্যা

Question: A person invests Tk. 3100 at a rate of 4% per annum under simple interest. After how many years will the total interest earned be Tk. 372?

Solution:
Given that,
Principal, P = Tk. 3100
Rate, r = 4%
Simple Interest, SI = Tk. 372

We know,
SI = (P × R × T) / 100
⇒ 372 = (3100 × 4 × n)/100
⇒ 372 = 124 × n
⇒ n = 372 ÷ 124
∴ n = 3 years

∴ Number of years = 3

৩১৩.

If the simple interest on 6,000 Taka for 3 years is 1,800 Taka, what is the rate of interest per annum?

ক
8%
খ
10%
গ
12%
ঘ
6%

ব্যাখ্যা

Question: If the simple interest on 6,000 Taka for 3 years is 1,800 Taka, what is the rate of interest per annum?

Solution:
Given, I = 1,800 Taka
P = 6,000 Taka
n = 3 years

We know,
I = Pnr
⇒ r = I/Pn
⇒ r = 1800/(6000×3)
⇒ r = 0.1
∴ r = 10%

৩১৪.

A sum of money on compound interest amounts to Tk. 13200 in 3 years and Tk. 12000 in 2 years. The rate of interest per annum is?

ক
15%
খ
12%
গ
10%
ঘ
8.5%

ব্যাখ্যা

Question: A sum of money on compound interest amounts to Tk. 13200 in 3 years and Tk. 12000 in 2 years. The rate of interest per annum is?

Solution:
Let,
Sum = Tk. P
Rate = r% = r/100

ATQ,
P(1 + r/100)² = 12000............(1)
P(1 + r/100)³ = 13200.........(2)

Dividing equation (2) by (1):
1 + r/100 = 13200/12000
⇒ (100 + r)/100 = 11/10
⇒ 100 +r = (11 × 100)/10
⇒ 100 +r = 110
⇒ r = 110 - 100
∴ r = 10

৩১৫.

What is the difference between the simple interest on a principal of Tk. 2500 being calculated at 5% per annum for 3 years and 6% per annum for 4 years?

ক
Tk. 200
খ
Tk. 175
গ
Tk. 320
ঘ
Tk. 225
ঙ
None of these

ব্যাখ্যা

Question: What is the difference between the simple interest on a principal of Tk. 2500 being calculated at 5% per annum for 3 years and 6% per annum for 4 years?

Solution:
We know that,
SI₁ = Prn/100
= (2500 × 5 × 3)/100 ;[P = 2500, r = 5%, n = 3]
= 375

And,
SI₂ = Prn/100
= (2500 × 6 × 4)/100 ;[P = 2500, r = 6%, n = 4]
= 600

∴ Difference = SI₂ - SI₁
= 600 - 375
= 225

৩১৬.

How many years will it take for an investment of Tk.10000 to earn Tk. 1200 in simple interest rate of 6%?

ক
2.5
খ
4
গ
3
ঘ
2

ব্যাখ্যা

Question: How many years will it take for an investment of Tk.10000 to earn Tk. 1200 in simple interest rate of 6%?
(Officer Cash 2022 অনুযায়ী)

Solution:
Given that,
Principal, P = 10000
Simple Interest, SI = 1200
Rate of interest, r = 6%
Time, n = ?

We know,
n = I/Pr
= 1200/(10000 × 6%)
= (1200 × 100)/(10000 × 6)
= 2

So, it will take 2 years for the investment to earn Tk. 1200 at 6% simple interest.

৩১৭.

What is the profit of Tk. 650 in 6 years at the simple rate of profit Tk. 7 percent per annum?

ক
ক) 223 tk
খ
খ) 250 tk
গ
গ) 273 tk
ঘ
ঘ) 280 tk

ব্যাখ্যা

Question: What is the profit of Tk. 650 in 6 years at the simple rate of profit Tk. 7 percent per annum?

Solution:
profit = Pnr
= 650 × 6 × 7/100
= 273 tk.

৩১৮.

The difference between simple and compound interest at 5% annually on a sum of TK. 10000 at the end of 2 years -

ক
ক) 25
খ
খ) 50
গ
গ) 100
ঘ
ঘ) 250

ব্যাখ্যা

SI = 10000 × 2 × 5/100 = 1000
CI = 10000(1 + 5/100)² – 10000 = 1025
∴ Difference = 1025 - 1000 = 25

৩১৯.

At what rate percent per annum will the simple interest on a sum of money 2/5 of the amount in 10 years?

ক
ক) 4%
খ
খ) 5%
গ
গ) 6%
ঘ
ঘ) 10%

ব্যাখ্যা

Question: At what rate percent per annum will the simple interest on a sum of money 2/5 of the amount in 10 years?

Solution:
Let the principal be p Tk
So, interest = 2p/5 Tk
Time = 10 years
rate of interest, r =?

Now,
I = pnr
r = I / pn
= (2p/5) / (p × 10)
= (1/25) × 100%
= 4%

৩২০.

The population of a town is 20,000, and it increases by 5% each year. What will the population be after 3 years?

ক
10,153
খ
13,153
গ
23,153
ঘ
25000
ঙ
None

ব্যাখ্যা

Question: The population of a town is 20,000, and it increases by 5% each year. What will the population be after 3 years?

Solution:
We can use the compound interest formula for population growth:

Population after n years = P × [1 + (r/100)]ⁿ

Here,
P = 20,000, r = 5%, n = 3

∴ Population after 3 years = 20,000 × [1 + (5/100)]³= 20,000 × (105/100)³
= 20,000 × 1.157625
= 23,152.5

∴ The population of the town after 3 years will be approximately 23,153.

৩২১.

Find the difference between the compound interest (compounded annually) and the simple interest on Tk. 2000 for 3 years at the rate of 8% per annum.

ক
Tk. 39.42
খ
Tk. 19.42
গ
Tk. 29.42
ঘ
Tk. 52

ব্যাখ্যা

Simple interest = Pnr
= 2000 × 3 × 8%
= Tk. 480
A = P(1 + r)ⁿ
= 2000(1 + 8/100)³
= Tk. 2519.42
Compound interest = Tk. 2519.42 - Tk. 2000
= Tk. 519.42
Required difference = Tk. 519.42 - Tk. 480
= Tk. 39.42

৩২২.

An amount of Tk. 12,000 yields a simple interest of Tk. 2,160 in 4 years. What is the annual rate of interest?

ক
4.5%
খ
5%
গ
6.4%
ঘ
10%

ব্যাখ্যা

Question: An amount of Tk. 12,000 yields a simple interest of Tk. 2,160 in 4 years. What is the annual rate of interest?

Solution:
Given, Principal, P = 12000
Simple Interest, SI = 2160
Time, n = 4 years
Rate of interest, r = ?

We know, I = Pnr/100
⇒ r = (I × 100)/(P × n)
⇒ r = (2160 × 100)/(12000 × 4)
⇒ r = 216000/48000
⇒ r = 4.5%

So, the annual rate of interest is 4.5%.

৩২৩.

A sum of money at simple interest amounts to Tk. 721 in 3 years and to Tk. 754 in 4 years. The sum is-

ক
Tk. 622
খ
Tk. 655
গ
Tk. 755
ঘ
Tk. 645

ব্যাখ্যা

Question: A sum of money at simple interest amounts to Tk. 721 in 3 years and to Tk. 754 in 4 years. The sum is-

Solution:
Simple interest for 1 year = Tk. (754 - 721)
= Tk. 33

∴ Simple interest for 3 years = Tk.(33 × 3)
= Tk. 99

∴ Sum = (721 - 99)
= Tk. 622

৩২৪.

A sum of Taka 50,000 is invested at 6% simple interest for the first 3 years and 8% compound interest for the next 2 years. What is the total amount after 5 years?

ক
Taka 68,000.50
খ
Taka 68,817.60
গ
Taka 70,200.20
ঘ
Taka 69,500.25

ব্যাখ্যা

Question: A sum of Taka 50,000 is invested at 6% simple interest for the first 3 years and 8% compound interest for the next 2 years. What is the total amount after 5 years?

Solution:
Given,
Tk. 50,000 is invested.
6% simple interest for the first 3 years.
8% compound interest for the next 2 years.

Simple Interest, I = Pnr
= 50000 × 3 × (6/100)
= 9000

New Principal = 50,000 + 9,000 = 59,000

Compound Principal = P × (1 + r)ⁿ
= 59000 × (1 + (8/100))²
= 59000 × (1.08)²
= 68,817.60

৩২৫.

If the compound interest of a certain sum of money for two successive years be Tk. 225 and Tk. 238.50 . What is the rate of interest per annum

ক
ক) 5%
খ
খ) 6%
গ
গ) 9%
ঘ
ঘ) 10%

ব্যাখ্যা

225 টাকার 1 বছরের সরল সুদ = 238.50 - 225 = 13.50 টাকা

আমরা জানি,
হার = সুদ / (আসল × সময়)
= 13.50/(225 × 1) × 100%
= 6%

৩২৬.

The difference in Taka between simple and compound interest at 4% annually on a sum of Tk. 8,000 after 2 years is:

ক
Tk. 22
খ
Tk. 12.8
গ
Tk. 15
ঘ
Tk. 16.5

ব্যাখ্যা

Question: The difference in Taka between simple and compound interest at 4% annually on a sum of Tk. 8,000 after 2 years is:

Solution:
Given that, Principal, P = Tk. 8,000
Rate, r = 4%
Time, n = 2 years

We know that,
Simple Interest = Prn/100
= (8000 × 4 × 2)/100
= 640

And Compound Interest = P(1 + r/100)ⁿ - P
= 8000{1 + (4/100)}² - 8000
= 8000(104/100)² - 8000
= {8000 × (104/100) × (104/100)} - 8000
= 8652.8 - 8000
= 652.8

∴ Difference = 652.8 - 640 = 12.8

The difference between compound and simple interest is Tk. 12.8

৩২৭.

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
ক) 12
খ
খ) 15
গ
গ) 18
ঘ
ঘ) 21
ঙ
ঙ) 23

ব্যাখ্যা

Dividend on Tk.20 = Tk. (9/100 × 20) = Tk. 9/5
Tk.12 is income of Tk.100.
∴Tk. 9/5 is an income of = Tk (100/12 × 9/5) = Tk.15

৩২৮.

If the simple interest on a certain sum of money after 3(1/8) years is (1/4) of the principal, what is the rate of interest per annum?

ক
ক) 4%
খ
খ) 12%
গ
গ) 6%
ঘ
ঘ) 8%

ব্যাখ্যা

Let the sum be x
Then,
Simple interest = x/4
T = 3(1/8)
= 25/8 years
R = {100 × (x/4)}/{x × (25/8)}
= 8
Hence Required interest rate = 8%

৩২৯.

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

ক
45 years
খ
42 years
গ
35 years
ঘ
48 years

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

৩৩০.

At what rate percent per annum will the simple interest on a sum of money be 2/5 of the amount in 10 years?

ক
ক) 5%
খ
খ) 4%
গ
গ) 6%
ঘ
ঘ) 7%

ব্যাখ্যা

Principal P = x
S.I.= (2/5) of x = 2x/5
Time n = 10 years

S.I. = (P × r × n)/100
⇒ (2x/5)= (x × r × 10)/100
⇒ (2/5) = (r × 10)/100
⇒ (2/5) = r/10
⇒ 2 = r/2
⇒ r = 4%

∴ Rate is 4% per annum

৩৩১.

If the simple interest on a sum of money is 40% of the principal over 8 years, what is the annual interest rate?

ক
5%
খ
6%
গ
7%
ঘ
7.5%

ব্যাখ্যা

Question: If the simple interest on a sum of money is 40% of the principal over 8 years, what is the annual interest rate?

Solution:
We know, Simple Interest, I = Pnr

Given,
Simple Interest = 0.4 × Principal (since 40% of the principal)
= 0.4 × P

Where, Principal = P
Rate = r
Time, n = 8 years

So, 0.4 × P = P × 8 × r
⇒ r = 0.4/8
⇒ r = 0.05 × 100%
∴ r = 5%

৩৩২.

A sum of Tk. 25000 amounts to Tk. 31000 in 4 years at the rate of simple interest, what is the rate of interest?

ক
3%
খ
4%
গ
5%
ঘ
6%

ব্যাখ্যা

Question: A sum of Tk. 25000 amounts to Tk. 31000 in 4 years at the rate of simple interest, what is the rate of interest?

Solution:
সুদ = ৩১০০০ - ২৫০০০ টাকা
= ৬০০০ টাকা

ধরি, সুদের হার r%

I = pnr
⇒ ৬০০০ = ২৫০০০ × ৪ × r/১০০
⇒ r = (৬০০০ × ১০০)/(২৫০০০ × ৪)
⇒ r = ৬

সুদের হার ৬%

৩৩৩.

A sum of money at simple interest doubles in 10 years. In how many years, at the same rate, will it be tripled?

ক
20 years
খ
15 years
গ
30 years
ঘ
18 years

ব্যাখ্যা

Question: A sum of money at simple interest doubles in 10 years. In how many years, at the same rate, will it be tripled?

Solution:
Given that,
Principal = P
Simple interest doubles the money in 10 years
∴ SI = P in 10 years.

We know,
SI = Prn/100
⇒ P = Prn/100
⇒ r × 10 = 100
⇒ r = 100/10
∴ r = 10% per annum

Again,
To triple, total amount = 3P, SI = 2P
2P = (P × 10 × n)/100
⇒ 2 = n/10
∴ n = 20

∴ Time taken to triple the amount is 20 years.

৩৩৪.

A finance company declares that, at a certain compound interest rate, a sum of money deposited by anyone will become 8 times in 3 years. If the same amount is deposited at the same compound rate of interest, then in how many years will it become 16 times?

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

ব্যাখ্যা

Question: A finance company declares that, at a certain compound interest rate, a sum of money deposited by anyone will become 8 times in 3 years. If the same amount is deposited at the same compound rate of interest, then in how many years will it become 16 times?

Solution:

৩৩৫.

A man invested tk. 1500 in a stock at 95 to obtain an income of tk. 130. What is the dividend from the stock?

ক
ক) 7.57
খ
খ) 8.32
গ
গ) 9.57
ঘ
ঘ) 7.27
ঙ
ঙ) 8.21

ব্যাখ্যা

By investing Tk. 1500, the man obtained an income of Tk. 130.
So, by investing Tk. 95, the income will be = (130/1500) × 96
= Tk 8.32
So, the divided = 8.32%

৩৩৬.

P charges at 7% p.a. simple interest to Q and R and lends a certain sum to R and Tk. 2,500 to Q. After 4 years, P completely receives Tk. 1,120 as interest from Q and R. Find the sum lent to R?

ক
ক) Tk. 1,500
খ
খ) Tk. 3,100
গ
গ) Tk. 6,400
ঘ
ঘ) Tk. 900

ব্যাখ্যা

Question: P charges at 7% p.a. simple interest to Q and R and lends a certain sum to R and Tk. 2,500 to Q. After 4 years, P completely receives Tk. 1,120 as interest from Q and R. Find the sum lent to R?

Solution:
ধরি,
R এর মুলধন x টাকা

প্রশ্নমতে,
(2500 × 7 × 4)/100) + (x × 7 × 4/100) = 1120
⇒ 7x × 25 = (1120 - 700)
⇒ x = (420 × 257)
∴ x = 1500

R এর মুলধন 1500 টাকা।

৩৩৭.

A man invested Tk.1552 in a stock at 97 to obtain an income of Tk. 128. The dividend from of the stock is-

ক
ক) 5%
খ
খ) 6%
গ
গ) 7%
ঘ
ঘ) 8%

ব্যাখ্যা

By investing Tk. 1552, income Tk. 128
By investing Tk. 97, income = (128 ×97)/1552
= 8

৩৩৮.

One-third of Farid's capital was invested at 7%, one-fourth at 8%, and the rest at 10%. He earned 561 taka annually. How much is his total capital?

ক
6,600 taka
খ
7,600 taka
গ
9,000 taka
ঘ
None of the above

ব্যাখ্যা

Question: One-third of Farid's capital was invested at 7%, one-fourth at 8%, and the rest at 10%. He earned 561 taka annually. How much is his total capital?
(ফরিদের মূলধনের এক-তৃতীয়াংশ ৭% সুদে, এক-চতুর্থাংশ ৮% সুদে এবং বাকি অংশ ১০% সুদে বিনিয়োগ করা হয়েছিল। তার বার্ষিক আয় ছিল ৫৬১ টাকা। তার মোট মূলধন কত?)

Solution:
ধরি,
আসল x টাকা
আমরা জানি, I = Pnr

561 = {(x × 7)/(100 × 3)} + {(x × 8)/(100 × 4)} + {(5x × 10)/(12 × 100)}
⇒ 561 = (7x/300) + (x/50) + (x/24)
⇒ 561 = 102x/1200
⇒ 561 = 51x/600
∴x = 6,600 taka

৩৩৯.

Work hard or you will fail the examination. (Simple)

ক
ক) If you don't work hard, you will fail the examination.
খ
খ) Without working hard, you will fail the examination.
গ
গ) In spite of working hard, you will fail the examination.
ঘ
ঘ) Working hard, you will not fail the examination.

ব্যাখ্যা

♦ Simple sentence এর ক্ষেত্রে:

Or যুক্ত compound sentence কে Simple করার নিয়ম:
- প্রথমে Without বসবে
- প্রথম বাক্যের মূল verb এর সাথে ing যোগ হয়।
- ক্রিয়ার পরের অংশ বসবে।
- or উঠে যাবে ও তার পরিবর্তে comma বসবে।
- দ্বিতীয় বাক্য বসবে।

Structure: Without + প্রথম বাক্যের মূল verb এর সাথে ing যোগ হয় + ক্রিয়ার পরের অংশ + or উঠে যাবে ও তার পরিবর্তে comma + দ্বিতীয় বাক্য বসবে।

Source: Advanced Learner's by Chowdhury & Hossain.

৩৪০.

How much time will it take for an amount of Tk. 450 to yield Tk. 99 as interest at 5.5% per annum of simple interest?

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

ব্যাখ্যা

Question: How much time will it take for an amount of Tk. 450 to yield Tk. 99 as interest at 5.5% per annum of simple interest?

Solution:
Here
Principal = Tk. 450
S.I = Tk. 99
R = 5.5%

Time = (100 × 99)/(450 × 5.5)
= 4 years

৩৪১.

A man invested tk.1552 in a stock at 97 to obtain an income of tk. 128. The dividend from the stock is:

ক
ক) 7.5%
খ
খ) 8%
গ
গ) 9.7%
ঘ
ঘ) None of these

ব্যাখ্যা

By investing tk. 1552, income = tk. 128.
By investing tk. 97, income = tk.128/1552 x 97= tk. 8.
Dividend = 8%

৩৪২.

Find the difference between the compound profit and the simple profit on Tk. 12,000 for 2 years at 25% per annum.

ক
Tk 550
খ
Tk 350
গ
Tk 750
ঘ
Tk 480

ব্যাখ্যা

Question: Find the difference between the compound profit and the simple profit on Tk. 12,000 for 2 years at 25% per annum.

Solution:
Given that,
P = 12000 Tk
r = 25%
= 25/100
= 1/4

t = 2 years

We know,
The compound profit = P (1 + r)ⁿ- P
= 12000 (1 + 1/4)²- 12000
= (12000 × 25/16)- 12000
= 18750 - 12000
= 6750 Tk

and
Simple profit I = Prn
= 12000 × 1/4 × 2
= 6000

∴ The different between compound profit and simple profit = (6750 - 6000) Tk
= Tk 750

৩৪৩.

The difference between simple interest for 4 years and 6 years at 5.5% per annum is BDT 220. Find the principal amount.

ক
Tk. 2000
খ
Tk. 3600
গ
Tk. 1800
ঘ
Tk. 2400

ব্যাখ্যা

Question: The difference between simple interest for 4 years and 6 years at 5.5% per annum is BDT 220. Find the principal amount.

Solution:
Given that,
Rate of interest, r = 5.5%
Difference in simple interest for 6 years and 4 years = 220
Time difference, n = 6 - 4 = 2 years

We know that,
I = (P × r × n)/100
⇒ 220 = (P × 5.5 × 2)/100
⇒ 11 × P = 22000
⇒ P = 22000/11
∴ P = 2000
∴ The sum is Tk. 2000.

৩৪৪.

How much time will it take for an amount of Tk. 900 to yield Tk. 81 as interest at 9% per annum of simple interest?

ক
2 years
খ
1.5 years
গ
1 years
ঘ
3 years

ব্যাখ্যা

Question: How much time will it take for an amount of Tk. 900 to yield Tk. 81 as interest at 9% per annum of simple interest?

Solution:
I = Pnr
⇒ 81 = 900 × n × (9/100)
⇒ n = (81 × 100)/(900 × 9)
∴ n = 1 years.

৩৪৫.

An amount of Tk. 6000 lent 5% per annum compounded interest for 2 years will become?

ক
Tk. 6610
খ
Tk. 6615
গ
Tk. 4610
ঘ
Tk 5615

ব্যাখ্যা

Question: An amount of Tk. 6000 lent 5% per annum compounded interest for 2 years will become?

Solution:
Here,
Principal, P = Tk. 6000
Rate of interest, r = 5% = 5/100 = 1/20
Time, n = 2 years.

We know,
C = P (1 + r)ⁿ
= 6000 × {1+ (1/20)}²
= 6000 × {(21/20) × (21/20)}
= 6000 × (441/400)
= 6615

∴ Compound Interest Tk. 6615.

৩৪৬.

At what rate of compound interest per annum will a sum of Tk. 1200 become Tk. 1348.32 in 2 years?

ক
ক) 7.5%
খ
খ) 6.5%
গ
গ) 7%
ঘ
ঘ) 6%

ব্যাখ্যা

Given amount = Tk. 1348.32
Principle = Tk. 1200
And time = 2 years

According to the law,
A = P(1 + R/100)ⁿ
1348.32 = 1200(1 + R/100)²
1348.32/1200 = (1 + R/100)²
11236/10000 = (1 + R/100)²
(106/100)² = (1 + R/100)²
(1 + 6/100)² = (1 + R/100)²
R = 6% per annum.

৩৪৭.

In how many years will the profit of Tk. 10,000 be Tk. 4,800 at the rate of 12% profit?

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

ব্যাখ্যা

Question: In how many years will the profit of Tk. 10,000 be Tk. 4,800 at the rate of 12% profit?

Solution:
Given,
P = Tk. 10000
I = Tk. 4800
r = 12% = 12/100

We know,
n = I/Pr
= 4800/(10000 × 12/100)
= (4800 × 100)/(10000 × 12)
= 4 years

৩৪৮.

Though Zaman was a rich man, he preferred humility in his interactions. (Make it compound)

ক
Zaman was a rich man and prefer humility in his interactions.
খ
Zaman was a rich man yet preferred humility in his interactions.
গ
Zaman was a rich man yet he prefer humility in his interactions.
ঘ
Zaman is a rich man yet he preferred humility in his interactions.

ব্যাখ্যা

♦ Complex sentence to compound sentence:

• Though/Although যুক্ত complex sentence কে compound sentence- এ পরিবর্তন করতে but/yet coordinate marker ব্যবহার করতে হয়।

- অর্থাৎ দুইটা sentence- এর অর্থ যদি পরস্পর বিপরীত হয় তাহলে but/yet দ্বারা compound sentence করতে হয়।

Example:
• Complex: Though Zaman was a rich man, he preferred humility in his interactions.
• Compound: Zaman was a rich man yet preferred humility in his interactions.

৩৪৯.

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

ক
75
খ
133
গ
80
ঘ
120

ব্যাখ্যা

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

Solution:
এখানে ৪% লাভ দেয়া স্টকটি বর্তমানে ৫% লাভ দেয়।

অর্থাৎ,
বর্তমানে ৫ টাকা লাভ করতে বিনিয়োগ করতে হবে ১০০ টাকা
বর্তমানে ১ টাকা লাভ করতে বিনিয়োগ করতে হবে ১০০/৫ টাকা
বর্তমানে ৪ টাকা লাভ করতে বিনিয়োগ করতে হবে (১০০ × ৪)/৫ টাকা
= ৮০ টাকা

∴ স্টকটির বাজারমূল্য ৮০ টাকা।

৩৫০.

To find the difference between the compound interest (compounded annually) and the simple interest on Tk. 17700 deposited at a 4% annual interest rate for 2 years.

ক
Tk. 32.32
খ
Tk. 26
গ
Tk. 28.32
ঘ
Tk. 32
ঙ
None of these

ব্যাখ্যা

Question: To find the difference between the compound interest (compounded annually) and the simple interest on Tk. 17700 deposited at a 4% annual interest rate for 2 years.

Solution:
Given that,
Principal, P = Tk. 17700
Rate of Interest, r = 4% per annum
Time, n = 2 years

We know,
Simple Interest(SI) = (P × r × n)/100
SI = (17700 × 4 × 2)/100
= (141600)/100
= Tk. 1,416

Compound Interest (CI),
CI = 17700 × (1 + 4/100)² - 17700
= {17700 × (104/100)²} - 17700
= {17700 × (104/100) × (104/100)} - 17700
= {(177 × 10816)/100} - 17700
= 19144.32 - 17700
= Tk. 1,444.32

∴ Difference = CI - SI = 1444.32 - 1416 = 28.32

৩৫১.

Present population of a city is 20 lac. What will be the population of the city after 3 years if the growth rate of population of that city is 50 per thousand ?

ক
21,15,250
খ
23,15,250
গ
22,05,000
ঘ
21,00,000

ব্যাখ্যা

Question : Present population of a city is 20 lac. What will be the population of the city after 3 years if the growth rate of population of that city is 50 per thousand ?

Solution :
Given that,
The present population of the city is P = 20,00,000
Groth rate of population r = 50/1000
= 5/100
= 1/20
Time n= 3 years

So the population of the city after 3 years will be = P(1 + r)ⁿ
= 20,00,000 × {1 + (1/20)}³
= 20,00,000 × (21/20)³
= 20,00,000 × 9,261/8,000
= 23,15,250

∴ After 3 years, population of the city will be 23,15,250.

৩৫২.

How much time will it take for an amount of Tk. 450 to yield Tk. 81 as interest at 9% per annum of simple interest?

ক
2 years
খ
3 years
গ
4 years
ঘ
None of these

ব্যাখ্যা

Question: How much time will it take for an amount of Tk. 450 to yield Tk. 81 as interest at 9% per annum of simple interest?

Solution:
I = Pnr
⇒ 81 = 450 × n × 9/100
∴ n = (81 × 100)/(450 ×9)
= 2 years

৩৫৩.

An amount of Tk. 10000 becomes Tk. 14641 in 2 years if the interest is compounded half-yearly. What is the rate of compound interest per annum?

ক
10%
খ
15%
গ
18%
ঘ
20%

ব্যাখ্যা

Question: An amount of Tk. 10000 becomes Tk. 14641 in 2 years if the interest is compounded half-yearly. What is the rate of compound interest per annum?

Solution:
Let
the rate be r% per annum

Now
10000 × {1 + r/(2 × 100)}^{2 × 2} = 14641
⇒ {1 + r/(2 × 100)}⁴ = 14641/10000
⇒ (1 + r/200)⁴ = (11/10)⁴
⇒ 1 + r/200 = 11/10
⇒ r/200 = (11/10) - 1
⇒ r/200 = (11 - 10)/10
⇒ r/200 = 1/10
⇒ r = 200/10
∴ r = 20

The rate be 20% per annum.

৩৫৪.

The compound interest on Tk. 30000 at 7% per annum is Tk. 4347. The period (in years) is-

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

ব্যাখ্যা

Question: The compound interest on Tk. 30000 at 7% per annum is Tk. 4347. The period (in years) is-

Solution:
Given that,
Principal, P = Tk. 30000
Compound Interest, CI = Tk. 4347
Rate, r = 7% per annum
And, Amount, A = P + CI = 30000 + 4347 = 34347

We know,
A = P(1 + r/100)ⁿ
⇒ 34347 = 30000(1 + 7/100)ⁿ
⇒ (107/100)ⁿ = 34347/30000
⇒ (107/100)ⁿ = 11449/10000
⇒ (107/100)ⁿ = (107/100)²
∴ n = 2

Hence, the period = 2 years.

৩৫৫.

Puja invested 50000 for 2 years at 15% compound rate. What is the simple interest rate that she needs to put the same amount for the same time to ensure the same amount of return?

ক
18.126%
খ
16.125%
গ
16.5%
ঘ
12.126%

ব্যাখ্যা

Question: Puja invested 50000 for 2 years at 15% compound rate. What is the simple interest rate that she needs to put the same amount for the same time to ensure the same amount of return?

Solution:
P = 50000
n = 2 years
r = 15%

C = p(1 + r)ⁿ
= 50000(1 + 15/100)²
= 50000 ( 115/100)²
= 66125

return = 66125 - 50000 = 16125Tk

Let the simple interest rate is X%
we know,
I = PnX/100
X = (100 × I)/ Pn
= (100 × 16125)/(50000 × 2)
= 16.125%

৩৫৬.

Evaluate the compound interest on Tk. 10101 for 3 years at the rate of 9% per annum compounded annually.

ক
Tk. 2980
খ
Tk. 30000
গ
Tk. 10101
ঘ
Tk. 33333

ব্যাখ্যা

Question: Evaluate the compound interest on Tk. 10101 for 3 years at the rate of 9% per annum compounded annually.

Solution:
A = P (1 + R/100)ⁿ
⇒ A = 10101(1 + 9/100)³ = 10101(109/100)³ = 13081.08

C.I. = A - P = 13081.08 - 10101 = 2980.08.

৩৫৭.

A man sells 4000 common shares of a Company x (each of par value Tk. 10), which pays a dividend of 40% at Tk. 30 per share. He invests the sale proceeds in ordinary shares of Company Y (each of par value Tk. 25) that pays a dividend of 15%. If the market value of Company Y is Tk. 15, find the number of shares of Company Y purchased by the man -

ক
ক) 16000
খ
খ) 20000
গ
গ) 12000
ঘ
ঘ) 8000

ব্যাখ্যা

Just too much information is given in the question to confuse. This is a straight and simple question
Market Value of Company X (his selling price) = Tk. 30
Total shares sold = 4000
The amount he gets = Tk. (4000 × 30)
He invests this amount in ordinary shares of Company Y
Market Value of Company Y(His purchasing price) = 15
Number of shares of company Y which he purchases = (4000 × 30)/15
= Tk. 8000.

৩৫৮.

A sum of money at simple interest amounts to Tk 902 in 3 years and to Tk 962 in 5 years. The sum is-

ক
ক) Tk 722
খ
খ) Tk 718
গ
গ) Tk 780
ঘ
ঘ) Tk 812

ব্যাখ্যা

Question: A sum of money at simple interest amounts to Tk 902 in 3 years and to Tk 962 in 5 years. The sum is-

Solution:
S.I. for 2 year = Tk (962 - 902) = Tk 60
S.I. for 1 year = Tk 60/2
S.I. for 3 years = Tk (60 × 3)/2= Tk 90

Therefore Principal = 902 - 90 = Tk 812

৩৫৯.

How much time will it take for an amount of Tk. 900 to yield Tk. 180 as interest at 5% per annum of simple interest?

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

ব্যাখ্যা

Question: How much time will it take for an amount of Tk. 900 to yield Tk. 180 as interest at 5% per annum of simple interest?

Solution:
I = Pnr
n = I / pr
= 180 /(900 × 5%)
= 4 years

৩৬০.

A sum of money lent out at simple interest amounts to Tk. 720 after 2 years and Tk. 1020 after a further period of 5 years. Find the principal?

ক
Tk. 400
খ
Tk. 450
গ
Tk. 500
ঘ
Tk. 550
ঙ
None

ব্যাখ্যা

Question: A sum of money lent out at simple interest amounts to Tk. 720 after 2 years and Tk. 1020 after a further period of 5 years. Find the principal?

Solution:
According to the question,
Principal + Simple interest for 2 years = Tk. 720 ------------- (1)
Principal + Simple interest for 7 years = Tk. 1020 ------------ (2)

Subtracting equation (1) from (2)
Principal + Simple interest for 7 years = Tk. 1020
Principal + Simple interest for 2 years = Tk. 720
--------------------------------------------------------
∴ Simple interest for 5 years = Tk. 300
⇒ Simple interest for 1 years = Tk. 300/5
⇒ Simple interest for 1 year = Tk. 60
⇒ Simple interest for 2 years = Tk. (60 × 2)
∴ Simple interest for 2 years = = Tk. 120

∴ Principal amount = (Amount after 2 years - 2 years Simple interest)
⇒ Principal amount = Tk. (720 - 120)
∴ Principal amount = Tk. 600

৩৬১.

A sum of money amounts to Tk. 5200 in 5 years and to Tk. 5680 in 7 years at simple interest. The rate of interest per annum is?

ক
7%
খ
4%
গ
6%
ঘ
8%

ব্যাখ্যা

Question: A sum of money amounts to Tk. 5200 in 5 years and to Tk. 5680 in 7 years at simple interest. The rate of interest per annum is?

Solution:
Simple interest for 2 years = (5680 - 5200) Tk.
= Tk. 480
∴ Simple Interest for 2 years = Tk. 480
∴ Simple Interest for 5 years = Tk. (480 × 5/2)
= Tk. 1200
∴ Principal = 5200 - 1200 = Tk. 4000.

We know,
I = Pnr
⇒ r = I/Pn
⇒ r = (1200 × 100)/(4000 × 5)
∴ r = 6%

৩৬২.

Find the simple interest on BDT 12000 at 8% per annum for 6 months.

ক
Tk. 480
খ
Tk. 560
গ
Tk. 400
ঘ
Tk. 420

ব্যাখ্যা

Question: Find the simple interest on BDT 12000 at 8% per annum for 6 months.

Solution:
Principal, P = 12000 Taka
Time, n = 6 months = 6/12 = 1/2 years
Rate of interest, r = 8% = 8/100

Simple Interest, I = P × n × r
= 12000 × (1/2) × (8/100)
= (12000 × 1 × 8)/(2 × 100)
= 96000/200
= 480

∴ The simple interest is Tk. 480.

৩৬৩.

A sum of money amounts to Tk. 5200 in 5 years and to Tk. 5680 in 7 years at simple interest. The rate of interest per annum is?

ক
5%
খ
7%
গ
6%
ঘ
8%

ব্যাখ্যা

৩৬৪.

The population of a town was 3600 three years back. It is 4800 right now. What will be the population three years down the line, if the rate of growth of population has been constant over the years and has been compounding annually?

ক
ক) 6200
খ
খ) 6400
গ
গ) 6500
ঘ
ঘ) 6798
ঙ
ঙ) 6543

ব্যাখ্যা

The population grew from 3600 to 4800 in 3 years.
That is a growth of 1200 on 3600 during a three year span.
Therefore, the rate of growth for three years has been constant.

The rate of growth during the next three years will also be the same.
Therefore, the population will grow from 4800 by 4800 × 1/3 = 1600
Hence, the population three years from now will be 4800 + 1600 = 6400

৩৬৫.

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

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

ব্যাখ্যা

S.I. for 1 year=Tk.(854−815)=Tk.39
S.I. for 3 year=Tk.(39×3)=Tk. 117
∴Principal=Tk.(854−117)=Tk. 698

৩৬৬.

A person invested in some account at the rate of 12% simple interest and a certain amount at rate of 10% simple interest. He received yearly interest of Tk. 130. But if he had interchanged the amounts invested, he would have received Tk. 4 more as interest. How much did he invest at 12% simple interest?

ক
ক) Tk. 400
খ
খ) Tk. 500
গ
গ) Tk. 700
ঘ
ঘ) Tk. 800

ব্যাখ্যা

Let,
The amount invested at 12% be Tk. x and that invested at 10% be Tk. y
Then, 12% x + 10% of y = 130
⇒ 12x + 10y = 13000
⇒ 6x + 5y = 6500 .............(i)

And, 10% x + 12% of y = 134
⇒ 10x + 12y = 13400
⇒ 5x + 6y = 6700 .......(ii)

Adding (i) and (ii) we get,
11(x + y) = 13200
⇒ x + y = 1200 ..........(iii)

Subtracting (i) from (ii) we get,
x + y = 200 .........(iv)

Adding (iii) and (iv) we get,
2y = 1400
⇒ y = 700

∴ x = 1200 - 700 = 500

So,
The amount invested at 12% is TK 500
And the amount invested at 10% is TK 700.

৩৬৭.

A certain principal amount, invested at simple interest, grows to Tk. 920 after 2 years and Tk. 1010 after 5 years. What is the original principal amount?

ক
Tk. 860
খ
Tk. 890
গ
Tk. 900
ঘ
Tk. 960

ব্যাখ্যা

Question: A certain principal amount, invested at simple interest, grows to Tk. 920 after 2 years and Tk. 1010 after 5 years. What is the original principal amount?

Solution:
Given,
Amount after 2 years = Tk. 920
Amount after 5 years = Tk. 1010

∴ Interest for (5 - 2) = 3 years = 1010 - 920
= Tk. 90
∴ Interest for 1 year = 90/3 = Tk. 30
∴ Interest for 2 years = 30 × 2 = Tk. 60

∴ Principal = 920 - 60 = Tk. 860

৩৬৮.

On a certain sum of money, the simple interest for 2 years is Tk. 200 at the rate of 5% per annum. If it was invested at compound interest at the same rate for the same duration as before, how much more interest would be earned?

ক
9 Tk
খ
3 Tk
গ
5 Tk
ঘ
10 Tk

ব্যাখ্যা

Question: On a certain sum of money, the simple interest for 2 years is Tk. 200 at the rate of 5% per annum. If it was invested at compound interest at the same rate for the same duration as before, how much more interest would be earned?

Solution:
Simple Interest (I) = (P × r × n)/100
⇒ 200 = (P × 2 × 5)/100
∴ P = 2000

∴ Compound Interest = P(1 + r)ⁿ - P
= 2000(1 + 0.05)² - 2000
= 2000 × 1.1025 - 2000
= 2205 - 2000
= 205

∴ Difference = 205 - 200 = 5 Tk

৩৬৯.

A sum of money amounts to Tk. 1800 in 5 years and Tk. 2400 in 8 years at simple interest. Find the annual rate of interest.

ক
10%
খ
15%
গ
20%
ঘ
25%

ব্যাখ্যা

Question: A sum of money amounts to Tk. 1800 in 5 years and Tk. 2400 in 8 years at simple interest. Find the annual rate of interest.

Solution:
দেওয়া আছে,
5 বছরের সুদ-আসল = 1800 টাকা
8 বছরের সুদ-আসল = 2400 টাকা
^{——————————————————}∴ 3 বছরের সুদ = (2400 - 1800) = 600 টাকা
∴ 1 বছরের সুদ = 600/3 = 200 টাকা

এখন,
আসল = 5 বছরের সুদ-আসল - 5 বছরের সুদ
⇒ আসল = 1800 - (5 × 200)
⇒ আসল = 1800 - 1000
⇒ আসল = 800 টাকা

এখানে,
মোট সুদ (I) = 1000 টাকা
আসল (P) = 800 টাকা
সময় (n) = 5 বছর
আমরা জানি, সুদের হার, r = (I × 100)/(P × n)
⇒ r = (1000 × 100)/(800 × 5)
⇒ r = 100000/4000
⇒ r = 25
অতএব, বার্ষিক সুদের হার 25%।

৩৭০.

Anik dey invested in two accounts, which pay 5% and 10% interest annually. The amount invested at 10% rate is 110% of the amount invested at 5% rate. After three years, he earns 5760 taka in interest. How much did he invest at the 10% rate?

ক
18285 tk.
খ
13200 tk.
গ
12000 tk.
ঘ
10000 tk.

ব্যাখ্যা

Question: Anik dey invested in two accounts, which pay 5 % and 10% interest annually. The amount invested at 10% rate is 110% of the amount invested at 5% rate. After three years, he earns 5760 taka in interest. How much did he invest at the 10% rate?

Solution:
5% সুদের জন্য আসল x টাকা
10% সুদের জন্য আসল 110%x = 1.1x টাকা

5% হারে সুদ = x × 3 × 5/100 = 3x/20 টাকা
10% হারে সুদ = 1.1x × 3 × 10/100 = 3.3x/10 টাকা

(3x/20) + (3.3x/10) = 5760
⇒ (3x + 6.6x)/20 = 5760
⇒ 9.6x = 5760 × 20
⇒ x = (5760 × 20)/9.6
= 12000 tk.

10% সুদের হারের জন্য আসল = 1.1 × 12000
= 13200 tk.

৩৭১.

An amount of Tk. 4000 lent 5% per annum compounded interest for 2 years will become?

ক
ক) Tk. 4410
খ
খ) Tk 4420
গ
গ) Tk. 5510
ঘ
ঘ) Tk. 3310

ব্যাখ্যা

Question: An amount of Tk. 4000 lent 5% per annum compounded interest for 2 years will become?

Solution:
Here,
Principal, P = Tk. 4000
Rate of interest, r = 5% = 5/100 = 1/20
Time, n = 2 years.

We know,
C = P (1 + r)ⁿ
= 4000 × {1+ (1/20)}²
= 4000 × {(21/20) × (21/20)}
= 4000 × (441/400)
= 4410

∴ Compounded Interest Tk. 4410.

৩৭২.

A sum of money doubles itself in 8 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
24
খ
32
গ
28
ঘ
30

ব্যাখ্যা

Question: A sum of money doubles itself in 8 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:
Given that,
The sum doubles itself in 8 years.
Amount after 8 years = 2P
Simple Interest for 8 years = P

We know,
SI = (P × r × n)/100
⇒ P = (P × r × 8)/100
⇒ 8r = 100
⇒ r = 100/8
∴ r = 12.5% per year

Now, we want to find in how many years the sum becomes four times itself.
Amount = 4P
Interest needed = 4P - P = 3P

We know,
SI = (P × r × n)/100
⇒ 3P = (P × 12.5 × n)/100. ; [r = 12.5%]
⇒ 3 = (12.5 × n)/100
⇒ n = (3 × 100)/12.5
∴ n = 24 years

∴ The sum will become four times itself in 24 years.

৩৭৩.

What is the difference between the compound interests on Tk. 5000 for 1 year at 4% per annum compound yearly and half yearly?

ক
ক) Tk. 1.04
খ
খ) Tk. 2
গ
গ) Tk. 5.14
ঘ
ঘ) Tk. 6

ব্যাখ্যা

Question: What is the difference between the compound interests on Tk. 5000 for 1 year at 4% per annum compound yearly and half yearly?

Solution:
Interest compounded half yearly = 5000(1 + 2/100)² - 5000
= 5000(102/100)² - 5000
= 5000(1.02)² - 5000 .........(i)

As we know, A = P(1 + R/100)t
Interest compound yearly = 5000(1 + 4/100)¹ - 5000
= 5000(104/100) - 5000
= 5000(1.04) - 5000 ............(ii)

From (i) and (ii)
Required difference = 5000(1.02)² - 5000 - 5000(1.04)¹ + 5000
= 5000(1.0404) - 5000(1.04)
= 5202 - 5200
= 2

৩৭৪.

An amount of money is invested in a savings account for two years. It increased by Tk. 52.50 in two years. after annual compounding at the rate of 10% per year. What is the amount invested initially?

ক
ক) Tk. 400
খ
খ) Tk. 300
গ
গ) Tk. 250
ঘ
ঘ) Tk. 200

ব্যাখ্যা

Question: An amount of money is invested in a savings account for two years. It increased by Tk. 52.50 in two years. after annual compounding at the rate of 10% per year. What is the amount invested initially?

Solution:
ধরি
আসল = P টাকা
সময় n = 2 বছর
মুনাফার হার r = 10% = 10/100 = 1/10

এখন
P(1 + r)ⁿ - P = 52.50
P(1 + 1/10)² - P = 52.50
P(11/10)² - P = 52.50
(121P/100) - P = 52.50
(121P - 100p)/100 = 52.50
21P/100 = 52.50
21P = 52.50 × 100
P = (52.50 × 100)/21
P = 250

৩৭৫.

A person who pays income tax at the rate of 4 paise per tk finds that a fall in the interest rate from 4% to 3.75% diminishes his net yearly income by tk 48. What is his capital?

ক
24000 tk
খ
23000 tk
গ
20000 tk
ঘ
25000 tk
ঙ
None

ব্যাখ্যা

Question: A person who pays income tax at the rate of 4 paise per tk finds that a fall in the interest rate from 4% to 3.75% diminishes his net yearly income by tk 48. What is his capital?

Solution:
If the capital after tax deduction be p, then
p × (4 - 3.75) % = 48
⇒ (p × 0.25)/100 = 48
⇒ (p × 25)/10000 = 48
⇒ p/400 = 48
⇒ p = 48 × 400 = tk 19200

∴ Required capital = (19200 × 100)/96
= 20000 tk

৩৭৬.

On a certain sum the simple interest for 12.5 years is 3/4 of the sum. Then the rate of interest is-

ক
4%
খ
5%
গ
6%
ঘ
7%

ব্যাখ্যা

Question: On a certain sum the simple interest for 12.5 years is 3/4 of the sum. Then the rate of interest is-

Solution:
Let sum = x
Interest = 3x/4

Interest = Pnr /100
⇒ 3x/4 = (x × r × 12.5)/100
∴ r = 6%

৩৭৭.

What is the compound amount of Tk. 4000 for 2 years at a rate of interest 5% per annum?

ক
Tk. 5200
খ
Tk. 4520
গ
Tk. 4410
ঘ
Tk. 3810

ব্যাখ্যা

Question: What is the compound amount of Tk. 4000 for 2 years at a rate of interest 5% per annum?

Solution:
Given,
Principal, P = 4000
Rate, r = 5% = 5/100 = 1/20
Time, n = 2 years

We know,
A = P(1 + r)ⁿ
= 4000 × (1 + 1/20)²
= 4000 × (21/20)²
= (4000 × 21 × 21)/(20 × 20)
= (4000 × 441)/400
= 4410

∴ The compound amount is Tk. 4410.

৩৭৮.

If simple interest on a certain sum of money is Tk. 400 and the rate of interest per annum equals the number of years, then the rate of interest is-

ক
15%
খ
20%
গ
25%
ঘ
30%

ব্যাখ্যা

Question: If simple interest on a certain sum of money is Tk. 400 and the rate of interest per annum equals the number of years, then the rate of interest is-

Solution:
Let,
The rate of interest is x%
∴ Number of years is x

The interest of 1 year of 100 taka is x
∴ The interest of x years of 100 Taka is x × x = x²

ATQ,
x² = 400
∴ x = 20

∴ The rate of interest is 20%

৩৭৯.

Mr. Sohan is planning to buy a mobile after two years time from now. He expects that after two years he will need Tk. 18150 to buy the mobile. How much money does Mr. Sohan need to invest now at 10% interest rate compounded annually?

ক
Tk. 12000
খ
Tk. 15000
গ
Tk. 14000
ঘ
Tk. 11000

ব্যাখ্যা

Question: Mr. Sohan is planning to buy a mobile after two years time from now. He expects that after two years he will need Tk. 18150 to buy the mobile. How much money does Mr. Sohan need to invest now at 10% interest rate compounded annually?

Solution:
Given,
Compounded Amount = Tk. 18150
Time n = 2 years
Rate r = 10% = 10/100 = 1/10

We know,
Compounded Amount = P(1 + r)ⁿ
⇒ 18150 = P(1 +1/10)²
⇒ 18150 = P(11/10)²
⇒ 18150 =121P/100
⇒ 121P =18150 × 100
⇒ P =1815000 ÷ 121
∴ P = 15000

৩৮০.

The difference between simple and compound interests compounded annually on a certain sum of money for 2 years at 4% per annum is 10 taka. The sum is:

ক
ক) 250 taka
খ
খ) 6050 taka
গ
গ) 6150 taka
ঘ
ঘ) 6250 taka

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 10 taka. The sum is:

Solution:
ধরি,
আসল x টাকা

সরল সুদ = x × 2 × 4/100
= 2x/25
= 0.08 x

চক্রবৃদ্ধি সুদ = x (1 + 0.04)² - x
= x × 1.04 × 1.04 - x
= 1.0816 x - x
= 0.0816 x

প্রশ্নমতে,
0.0816 x - 0.08 x = 10
⇒ 0.0016 x = 10
⇒ x = 10/0.0016
∴ x = 6250

৩৮১.

Mohan lent some amount of money at 8% simple interest and an equal amount of money at 10% simple interest each for two years. If his total interest was TK. 720, what amount was lent in each case ?

ক
TK. 1700
খ
TK. 1800
গ
TK. 1900
ঘ
TK. 2000

ব্যাখ্যা

Question: Mohan lent some amount of money at 8% simple interest and an equal amount of money at 10% simple interest each for two years. If his total interest was TK. 720, what amount was lent in each case ?

Solution:
Let the amount invested = TK. P
According to the questions,
⇔ (P × 8 × 2)/100 + (P × 10 × 2)/100 = 720
⇔ (16P + 20P)/100 = 720
⇔ 36P = 72000
⇔ P = 2000

৩৮২.

Find the simple interest on BDT 8,000 at 6% per annum for 9 months.

ক
BDT 360
খ
BDT 480
গ
BDT 540
ঘ
BDT 720

ব্যাখ্যা

Question: Find the simple interest on BDT 8,000 at 6% per annum for 9 months.

Solution:
Given, P = 8000 Taka
n = 9 months = 0.75 years
r = 6%

Simple Interest, I = Pnr
= 8000 × 0.75 × 6/100
= 80 × 4.5
= 360 Taka

৩৮৩.

The compound interest on Tk. 3000 for 2 years at 10% is-

ক
ক) Tk. 630
খ
খ) Tk. 600
গ
গ) Tk. 3600
ঘ
ঘ) Tk. 3630

ব্যাখ্যা

Question: The compound interest on Tk. 3000 for 2 years at 10% is-

Solution:
Givent that,
P = Tk. 3000
n = 2 years
r = 10%

Required amount
= P(1 + r)ⁿ
= [3000 × {1 + (10/100)²}]
= [3000 × (11/10) × (11/10) ]
= 3630

Compound Interest = 3630 - 3000 = 630

৩৮৪.

If principal M becomes N in 2 years when interest R% is compounded half-yearly. And if the same principal M becomes N in 2 years when interest S% is compound annually, then which of the following is true?

ক
R > S
খ
R = S
গ
R < S
ঘ
None

ব্যাখ্যা

Question: If principal M becomes N in 2 years when interest R% is compounded half-yearly. And if the same principal M becomes N in 2 years when interest S% is compound annually, then which of the following is true?

Solution:
ধরি, আসল = M এবং সবৃদ্ধি মূলধন = N
সময় n = 2 বছর

অর্ধবার্ষিক চক্রবৃদ্ধির ক্ষেত্রে (মুনাফার হার R%):
N = M(1 + (R/2)/100)^{2 × 2}
= M(1 + R/200)⁴

বার্ষিক চক্রবৃদ্ধির ক্ষেত্রে (মুনাফার হার S%):
N = M(1 + S/100)²

যেহেতু উভয় ক্ষেত্রে আসল (M), সময় (2 বছর) এবং সবৃদ্ধি মূলধন (N) একই,
সেহেতু যে পদ্ধতিতে বছরে বেশিবার মুনাফা গণনা করা হয় (Half-yearly), সেখানে কাঙ্ক্ষিত মুনাফা পেতে তুলনামূলক কম সুদের হার প্রয়োজন।
∴ R < S

৩৮৫.

Rabi borrowed Tk 20,000 at 10% compound interest to invest in business. What was his actual profit or loss after 2 years if he earned 12% per year on the borrowed amount?

ক
Tk 600 profit
খ
Tk 800 profit
গ
Tk 800 loss
ঘ
Tk 4800 profit

ব্যাখ্যা

Question: Rabi borrowed Tk 20,000 at 10% compound interest to invest in business. What was his actual profit or loss after 2 years if he earned 12% per year on the borrowed amount?

Solution:
If he earned 12% on the borrowed Tk 20,000 after 2 years,
His profit = Tk 20000 × 12 × (2/100)
= Tk 4800

∴ He got in total = Tk (20000 + 4800 )
= Tk 24800

At 10% compound interest on Tk 20000, he had to pay = Tk 20000{(1 + 10)/100}²
= Tk 20000(11/10)²
= Tk 20000 × (11/10) × (11/10)
= Tk 200 × 121
= Tk 24200

∴ His actual profit = Tk (24800 - 24200)
= Tk 600

৩৮৬.

Mr. Anis 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) 4%
খ
খ) 5%
গ
গ) 6%
ঘ
ঘ) 7%

ব্যাখ্যা

Question: Mr. Anis 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?

Solution:
Given that n = r

We know,
S.I = (P × n × r)/100
⇒ 686 = (1400 × r × r)/100
⇒ 686 = 14r²⇒ r² = 686/14
⇒ r²= 49
∴ r = 7%

৩৮৭.

A sum of Tk. 10 is given as a loan, to be returned in six monthly installments of Tk. 3.What is the simple interest rate?

ক
ক) 820%
খ
খ) 620%
গ
গ) 640%
ঘ
ঘ) 720%

ব্যাখ্যা

Let the rate of interest be R%
Amount due in 6 months
= 10 + simple interest on Tk. 10 for six months.
= {10 + 10 × R × (1/2)}/100
= 10 + (R/20)
With the formula mentioned,
3 = 100(10 + 9R/20)/{(100 × 6) + R × 6(6 - 1)}/(2 × 12)
⇒ 3 = (1000 + 5R)/{600 + (5R/4)}
⇒ 1800 + 15R/4 = 1000 + 5R
⇒ 5R/4 = 800
⇒ R = 640.
Hence interest rate is 640%

৩৮৮.

How many years will it take for an investment of Tk.1000 to earn Tk. 200 in simple interest rate of 5%?

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

ব্যাখ্যা

Question: How many years will it take for an investment of Tk.1000 to earn Tk. 200 in simple interest rate of 5%?

Solution:
Given that,
Principal, P = 1000
Simple Interest, SI = 200
Rate of interest, r = 5%
Time, n = ?

We know,
n = I/Pr
= 200/(1000 × 5%)
= (200 × 100)/(1000 × 5)
= 4

So, it will take 4 years for the investment to earn Tk. 200 at 5% simple interest.

৩৮৯.

A man invests Tk. 8,100 partly in 14% stock at 294 and partly in 12% stock at 288. If his income from both is the same, find his investment in the 14% stock.

ক
3780 Tk
খ
3980 Tk
গ
3820 Tk
ঘ
4120 Tk
ঙ
3020 Tk

ব্যাখ্যা

Question: A man invests Tk. 8,100 partly in 14% stock at 294 and partly in 12% stock at 288. If his income from both is the same, find his investment in the 14% stock.

Solution:
Let he invests x at 14% stock.
x Investment at 12% stock = 8100 - x

As income is same.
x × (14/100) × (1/294) = (8100 - x) × (12/100) × (1/288)
⇒ x/2100 = (8100 - x)/2400
⇒ x = {(8100 - x)/2400} × 2100
⇒ 24x = 170100 - 21x
⇒ 45x = 170100
∴ x = 3780 Tk

৩৯০.

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. 600
খ
Tk. 628
গ
Tk. 650
ঘ
Tk. 698

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

৩৯১.

The simple interest on Tk. 36000 for the period from 5th January to 31st May 2013 at 9.5% per annum is =?

ক
Tk. 1388.25
খ
Tk. 1368.00
গ
Tk. 1568.50
ঘ
Tk. 1377.36

ব্যাখ্যা

Question: The simple interest on Tk. 36000 for the period from 5^th January to 31^st May 2013 at 9.5% per annum is =?

Solution:
Number of days = 27 + 28 + 31 + 30 + 31
= 147 days

We know,
I = Pnr
Or, I = (36000 × 147 × 9.5)/(100 × 365)
∴ I = Tk. 1,377.36

৩৯২.

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. 8500
খ
Tk. 10000
গ
Tk. 12800
ঘ
Tk. 15000

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।

৩৯৩.

Find the rate of interest if the amount after 2 years of simple interest on a capital of Tk. 1200 is Tk. 1440.

ক
ক) 20%
খ
খ) 15%
গ
গ) 12%
ঘ
ঘ) 10%

ব্যাখ্যা

Question: Find the rate of interest if the amount after 2 years of simple interest on a capital of Tk. 1200 is Tk. 1440.

Solution:
Given,
Amount, A = Tk.1440
Principal, P = Tk.1200
Interest, I = Tk.(1440 - 1200) = Tk. 240
Time, n = 2 years.

We know,
I = Pnr
⇒ r = I/Pn
⇒ r = (240 × 100)/(1200 × 2)
∴ r = 10%

৩৯৪.

A machine is purchased for Tk. 625000. Its value depreciates at the rate of 8% per annum. What will be its value after 2 years?

ক
Tk. 525000
খ
Tk. 600000
গ
Tk. 529000
ঘ
Tk. 590000
ঙ
None of these

ব্যাখ্যা

Question: A machine is purchased for Tk. 625000. Its value depreciates at the rate of 8% per annum. What will be its value after 2 years?

Solution:
To find the depreciated value of the machine after 2 years, we can use the formula for depreciation:
A = P(1 - r/100)^t
P is the initial value of the machine = 625,000 Tk,
r is the rate of depreciation per annum = 8%,
t is the time in years = 2.

∴ A = 625000(1 - 8/100)²
= 625000 × 0.92 × 0.92
= 529000

৩৯৫.

An investment doubles in 8 years at simple interest. In how many years will it become four times?

ক
8
খ
16
গ
24
ঘ
32

ব্যাখ্যা

Question: An investment doubles in 8 years at simple interest. In how many years will it become four times?

Solution:
Given:
In 8 years, interest earned = P (because, P + interest = 2P)

To become 4 times (Total amount = 4P):
Interest needed = 4P - P = 3P

Since interest is earned linearly with time at simple interest:

P interest in = 8 years
3P interest in = 8 × 3 = 24 years

∴ 24 years

৩৯৬.

A sum of Tk. 8000 will amount to Tk. 8820 in 2 years if the interest is calculated every year. The rate of compound interest is?

ক
ক) 8%
খ
খ) 6%
গ
গ) 5%
ঘ
ঘ) 4%

ব্যাখ্যা

Question: A sum of Tk. 8000 will amount to Tk. 8820 in 2 years if the interest is calculated every year. The rate of compound interest is?

Solution:
Principal = Tk. 8000
Amount = Tk. 8820
Let Rate = R
Time = 2 years

By using formula,
8000{1 + (R/100)}² = 8820
⇒ {1 + (R/100)}² = 8820/8000
⇒ {1 + (R/100)}² = 441/200
⇒ {1 + (R/100)}² = (21/20)²
⇒ 1 + (R/100) = 21/20
⇒ R/100 = (21/20) - 1
⇒ R/100 = 1/20
∴ R = 5%

৩৯৭.

A man invested Tk. 14400 in Tk. 100 shares of a company at 20% premium. If the company declares 5% dividend at the end of the year, then how much does he get?

ক
ক) Tk. 600
খ
খ) Tk. 450
গ
গ) Tk. 630
ঘ
ঘ) Tk. 500

ব্যাখ্যা

Number of shares = 14400/120 = 120
Face value = Tk. (120 × 100) = Tk. 12000

Annual income = (5/100) × 12000 = Tk . 600

৩৯৮.

Tk. 6100 was partly invested in Scheme A at 10% p.a. compound interest for 2 years and partly in Scheme B at 10% p.a. simple interest for 4 years. Both the schemes pay equal interests. How much was invested in Scheme A?

ক
Tk. 4500
খ
Tk. 2000
গ
Tk. 5000
ঘ
Tk. 4000

ব্যাখ্যা

Question: Tk. 6100 was partly invested in Scheme A at 10% p.a. compound interest for 2 years and partly in Scheme B at 10% p.a. simple interest for 4 years. Both the schemes pay equal interests. How much was invested in Scheme A?

Solution:
Total sum = Tk. 6100
In Scheme A, Compound interest
Principal = P
R = 10% per annum for 2 years

In Scheme B, Simple interest
Principal = 6100 - P
R = 10% per annum for 4 years

Here,
Compound interest = Simple interest
⇒ P[{1 + (R/100)}ⁿ - 1] = (PRN)/100
⇒ P[{1 + 10/100}² - 1] = [(6100 - P) × 4 × 10]/100
⇒ P× (21/100) = [(6100 - P) × 4 × 10]/100
⇒ 21P = 6100 × 40 - 40P
⇒ 61P = 6100 × 40
∴ P = 4000

∴ The amount invested in Scheme A is Tk. 4000

৩৯৯.

The rate at which a sum becomes four times of itself in 25 years at simple interest, will be-

ক
30%
খ
25%
গ
12%
ঘ
49%

ব্যাখ্যা

Question: The rate at which a sum becomes four times of itself in 25 years at simple interest, will be-

Solution:
Let sum, P = x.
Then, simple interest, I = 3x
Time, n = 25 years
Rate = r

r = I/(Pn)
= 3x/(x × 25)
= (3 × 100)/25%
= 12%

৪০০.

What will be the total amount after 3 years if Tk. 1200 is invested at a simple interest rate of 5% annually?

ক
Tk. 1380
খ
Tk. 1320
গ
Tk. 1430
ঘ
Tk. 1560

ব্যাখ্যা

Question: What will be the total amount after 3 years if Tk. 1200 is invested at a simple interest rate of 5% annually?

Solution:
Here,
Principal, P = Tk. 1200
Rate of Interest, r = 5% = 5/100
Time, n = 3 years

We know,
Simple Interest, I = P × n × r
I = 1200 × 3 × (5/100)
I = 1200 × 3 × 5/100
I = 3600 × 5/100
I = 180 Tk.

Now, the Amount after 3 years, A = P + I
A = 1200 + 180
A = 1380 Tk.

∴ The amount after 3 years will be Tk. 1380.