Simple and Compound Interest, Stock

PrepBank · পাতা ৬ / ৯ · ৫০১–৬০০ / ৮৫৮

৫০১.

What annual rate was paid if Tk. 50000 earned Tk. 3000 in interest in two years?

ক
12%
খ
9%
গ
6%
ঘ
3%

ব্যাখ্যা

Question: What annual rate was paid if Tk. 50000 earned Tk. 3000 in interest in two years?

Solution:
Tk. 50000 earned in 2 years Tk. 3000
∴ Tk. 100 earned in 1 year Tk. (3000 × 100)/(50000 × 2)
= 3%

৫০২.

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 (in Tk.) is:

ক
ক) Tk.645
খ
খ) Tk. 635
গ
গ) Tk. 625
ঘ
ঘ) Tk. 655

ব্যাখ্যা

Let the sum be Tk. x.
Then
C. I = x(1 + 4/100)² - x
= x(104/100)² - x
= x(26/25)² - x
= 676x/625 - x
= (676x - 625x)/625
= 51x/625

S.I =(x × 4 × 2)/100 = 2x/25

Now
(51x/625) - (2x/25) = 1
(51x - 50x)/625 = 1
x /625 = 1
x = 625

৫০৩.

The compound interest on a sum of Tk. 625 in 2 years is Tk. 51. Find the rate of interest.

ক
3%
খ
4%
গ
5%
ঘ
6%

ব্যাখ্যা

Question: The compound interest on a sum of Tk. 625 in 2 years is Tk. 51. Find the rate of interest.

Solution:
We know that A = CI + P
A = 51 + 625 = 676

Now going by the formula:
A = P[1+(R/100)]ⁿ
⇒ 676 = 625[1 + (R/100)]²
⇒ 676/625 = [1 + (R/100)]²
We can see that 676 is the square of 26 and 625 is the square of 25
Therefore,
⇒ (26/25)² = [1 + (R/100)]²
⇒ 26/25 = [1 + (R/100)]
⇒ 26/25 - 1 = R/100
⇒ 1/25 = R/100
⇒ R = 100/25
∴ R = 4

৫০৪.

By investing in (50/3)% stock at Tk. 64, one earns Tk. 1500. The investment made is:

ক
ক) Tk. 9600
খ
খ) Tk. 7560
গ
গ) Tk. 5760
ঘ
ঘ) Tk. 5640

ব্যাখ্যা

Question: By investing in (50/3)% stock at Tk. 64, one earns Tk. 1500. The investment made is:

Solution:
To earn Tk. 50/3, investment = Tk. 64
To earn Tk. 1, investment = Tk. 64 × (3/50)
To earn Tk. 1500, investment = Tk. {64 × (3/50) × 1500}
= Tk. 5760

৫০৫.

The simple interest at m% for m years will be Tk. m on a sum of?

ক
Tk. 100/m
খ
Tk. m/100
গ
Tk. 100m
ঘ
Tk. m

ব্যাখ্যা

Question: The simple interest at m% for m years will be Tk. m on a sum of?

Solution:
Given,
Rate of interest, r = m%
Interest, I = m Tk.
Time, n = m yeras.

We know,
I = Pnr
P = I/nr
= (m × 100)/(m × m)
= 100/m Tk.

৫০৬.

What is the compound interest on Tk. 2500 for 2 years at rate of interest 4% per annum?

ক
Tk. 180
খ
Tk. 220
গ
Tk. 210
ঘ
Tk. 204

ব্যাখ্যা

Question: What is the compound interest on Tk. 2500 for 2 years at rate of interest 4% per annum?

Solution:
Here,
C = 2500(1 + 4/100)²
= 2500 × 1.04 × 1.04
= 2704

∴ compound interest = 2704 - 2500 = 204

৫০৭.

If Tk. 3000 is loaned for 4 months at a 4.5% annual rate, how much interest is earned?

ক
Tk. 45
খ
Tk. 60
গ
Tk. 120
ঘ
Tk. 135

ব্যাখ্যা

Question: If Tk. 3000 is loaned for 4 months at a 4.5% annual rate, how much interest is earned?

Solution:
P = 3000
n = 4 months = 4/12 years = 1/3 year
r = 4.5%

I = Pnr
= {3000 × (1/3) × (4.5)}/100
= 45

৫০৮.

How many shares of market value Tk. 25 each can be purchased for Tk. 20,400, brokerage being 2% ?

ক
500
খ
700
গ
600
ঘ
800

ব্যাখ্যা

Question: How many shares of market value Tk. 25 each can be purchased for Tk. 20,400, brokerage being 2% ?

Solution:
CP of each share = Tk. (25 + 2% of 25) = Tk. 25.50.

Number of shares= 20400/25.50
= 800

৫০৯.

Mr. Kalam deposited a certain amount of money for a fixed period of time. On maturity, he received a total of Tk. 42,000 when the ratio of interest and investment became 2 : 5. If the simple interest rate was 4%, calculate the time period for which the money was invested.

ক
9.5 years
খ
15 years
গ
8.5 years
ঘ
10 years
ঙ
12 years

ব্যাখ্যা

Question: Mr. Kalam deposited a certain amount of money for a fixed period of time. On maturity, he received a total of Tk. 42,000 when the ratio of interest and investment became 2 : 5. If the simple interest rate was 4%, calculate the time period for which the money was invested.

Solution:
Let, time n.
Sum of these ratios = 2 + 5 = 7
We are given that, ratio of interest & Investment - 2 : 5.
So, interest is, 42000 × (2/7) = Tk. 12000
Investment is, 42000 × (5/7) = Tk. 30000

We know,
Principal × Interest rate × Time = Total Interest
⇒ 30000 × 4% × n = 12000
⇒ n = (12000 × 100)/(30000 × 4) = 10

So the money was invested for 10 years.

৫১০.

At the rate of 15% simple interest per annum, how much profit will be earned on Tk. 900 as principal in 7 years?

ক
Tk. 785
খ
Tk. 850
গ
Tk. 945
ঘ
Tk. 895

ব্যাখ্যা

Question: At the rate of 15% simple interest per annum, how much profit will be earned on Tk. 900 as principal in 7 years?

Solution:
Given,
Sum P = Tk. 900
Time n = 7 years
Rate r = 15%
= 15/100
= 3/20

We know,
Profit = Prn
= 900 × 3/20 × 7
= 945

৫১১.

Namita borrowed Tk. 50000 for 3 years at the rate of 3.5% per annum. Find the interest accumulated at the end of 3 years.

ক
Tk. 5500
খ
Tk. 5550
গ
Tk. 5450
ঘ
Tk. 5350
ঙ
Tk. 5250

ব্যাখ্যা

Question: Namita borrowed Tk. 50000 for 3 years at the rate of 3.5% per annum. Find the interest accumulated at the end of 3 years.

Solution:
P = 50000
n = 3
r = 3.5%

∴ I = Pnr
= (50000 × 3 × 3.5)/100
= 5250

৫১২.

Make it compound: Rumi works hard so that she can complete the task.

ক
Rumi wants to complete the task and so she works hard.
খ
Works hard and Rumi can complete the task.
গ
She works hard in order to complete the task.
ঘ
So Rumi works hard and she complete the task.

ব্যাখ্যা

• Complex to compound
• Sentence এর Transformation এর ক্ষেত্রে যে কাজ গুলো করতে হয়।

• Add (যোগ করা),
• Deduct (বাদ দেয়া),
• Retain (যেভাবে আছে সেভাবে রাখা)।

• অর্থাৎ - বাক্যের ধরন অনুযায়ী Preposition/Conjunction একটা যোগ ও একটা বিয়োগ করতে হবে,
- এবং ২টি Clause এর মধ্যে ১টি Clause যেভাবে আছে সেভাবে রেখে দিতে হবে।

• Complex to compound এর সময়,
• so that দ্বারা গঠিত বাক্যকে Complex to compound করার নিয়ম:
• এ ধরনের বাক্যে Compound Sentence এ ৩টি কাজ করতে হয়। যথা:

1. Clause গুলোর অবস্থান উল্টে যাবে।
2. Want to অতিরিক্ত যোগ করতে হবে।
3. so that এর পরিবর্তে ‘And so/ therefore’ conjunction যোগ হবে।

Complex: Rumi works hard so that she can complete the task.
Compound: Rumi wants to complete the task and so she works hard.

Source: Live MCQ English Wizard Lecture.

৫১৩.

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

ক
Tk. 2300
খ
Tk. 2315.25
গ
Tk. 2310.25
ঘ
Tk. 2325.50

ব্যাখ্যা

Here, principal = Tk. 2100
Time, n = 2 years
Annual interest rate, r = 5%
The amount after two years, C = ?
We know, C= P(1 + r)ⁿ
= 2100(1 + 5/100)²
= Tk. 2315.25

৫১৪.

A sum invested at simple interest grows to Tk. 1665 in 3 years and Tk. 1782 in 4 years. Determine the original sum.

ক
1302
খ
1308
গ
1314
ঘ
1288

ব্যাখ্যা

Question: A sum invested at simple interest grows to Tk. 1665 in 3 years and Tk. 1782 in 4 years. Determine the original sum.

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

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

৫১৫.

Sani borrows 2500 taka from a leasing company at 4.5% compound interest per year. Calculate the total must be paid after 36 months.

ক
2025.89
খ
2852.92
গ
2325.32
ঘ
2758.78
ঙ
2823.25

ব্যাখ্যা

Here, n = 36 months = 3 years

Compound interest rate = 4.5% = 4.5/100

We know, C = P ( 1 + r%)³ = P (1 + 4.5/100) ³ = tk. 2852.92

৫১৬.

An amount of Tk. 15,000 is invested at a compound interest rate of 6% per annum. What will be the total value of the investment after 2 years?

ক
Tk. 16,854
খ
Tk. 16,950
গ
Tk. 17,288
ঘ
Tk. 17,660
ঙ
None

ব্যাখ্যা

Question: An amount of Tk. 15,000 is invested at a compound interest rate of 6% per annum. What will be the total value of the investment after 2 years?

Solution:
Given,
Initial amount P = Tk. 15,000
Annual growth rate r = 6%
Time n = 2 years

We know,
Compount Interest = P × [1 + (r/100)]ⁿ

∴ The value of the investment after 2 years = 15,000 × [1 + (6/100)]²
= 15,000 × (106/100)²
= 15,000 × (53/50)²
= (15,000 × 53 × 53)/(50 × 50)
= 16,854

∴ The value of the investment after 2 years will be Tk. 16,854

৫১৭.

A company increases salary of an officer at 20% per year. In 2025 an employee receives Tk. 43,200. What was his salary in 2023?

ক
Tk. 24,000
খ
Tk. 27,000
গ
Tk. 30,000
ঘ
Tk. 34,000

ব্যাখ্যা

Question: A company increases salary of an officer at 20% per year. In 2025 an employee receives Tk. 43,200. What was his salary in 2023?

Solution:
Let, his salary in 2023 was 100 Tk.

At 20% increment,
Salary of 2024 is = 100(1 + 20/100)
= 120 Tk.

Salary of 2025 is = 120(1 + 20/100)
= 144 Tk.

Now,
144 Tk. corresponds to = 43,200 Tk.
1 Tk. corresponds to = 43,200/144 Tk.
∴ 100 Tk. corresponds to = (43,200 × 100)/144
= 30,000 Tk.

∴ His salary in 2023 was 30,000 Tk.

৫১৮.

The difference between simple and compound interest on Tk. 1400 for one year at 20% per annum reckoned half-yearly is -

ক
ক) Tk. 120
খ
খ) Tk. 3
গ
গ) Tk. 14
ঘ
ঘ) Tk. 154

ব্যাখ্যা

S.I. = (1400 × 20 × 1)/100 = Tk. 280
C.I. = [1400 × (1 + 10/100)² - 1400]
= [1400 × 11/10 × 11/10 -1400
= 1694 - 1400
= Tk. 294
Difference = (294 - 280) = Tk. 14.

৫১৯.

A sum invested at the rate of interest 5% S.I grows to Tk. 5400 in 4 years. The same amount in 3 years at the rate of 10% per annum S.I will grow to-

ক
Tk. 5750
খ
Tk. 5800
গ
Tk. 5850
ঘ
Tk. 5700

ব্যাখ্যা

Question: A sum invested at the rate of interest 5% S.I grows to Tk. 5400 in 4 years. The same amount in 3 years at the rate of 10% per annum S.I will grow to-

Solution:
In the first case,
The sum be Tk. P
I = 5400 - P
n = 4 years
r = 5%

∴ I = Pnr
⇒ 5400 - P = P × 4 × (5/100)
⇒ 5400 - P = P/5
⇒ 27000 - 5P = P
⇒ 6P = 27000
∴ P = 4500

In the second case,
P = 4500
r = 10%
n = 3 years
I =?

∴ I = Pnr
= 4500 × 3 × (10/100)
= 1350

∴ The same amount in 3 years at the rate of 10% per annum S.I will grow to (4500 + 1350) = 5850

৫২০.

A man deposits Tk. 5000 in a Bank at 10% interest rate compounded annually. At the end of the three year, the total amount including interest will become?

ক
ক) Tk. 6055
খ
খ) Tk. 6655
গ
গ) Tk. 6565
ঘ
ঘ) Tk. 6775

ব্যাখ্যা

Question: A man deposits Tk. 5000 in a Bank at 10% interest rate compounded annually. At the end of the three year, the total amount including interest will become?

Solution:
Given,
Principal, P = 5000 Tk.
Rate of interest, r = 10% = 10/100 = 1/10
Time, n = 3 years.

We know,
Compound Amount = P (1 + r)ⁿ
= 5000 × (1 + 1/10)³
= 5000 × (11/10)³
= 5000 × (11/10) × (11/10) × (11/10)
= 6655

৫২১.

On a sum of money, the simple interest for 2 years is Tk. 320, while the compound interest is Tk. 340, the rate of interest being the same in both the cases. The rate of interest is -

ক
ক) 12.5%
খ
খ) 14.25%
গ
গ) 15%
ঘ
ঘ) 10.5%

ব্যাখ্যা

Simple interest for 2 years is Tk. 320
⇒ Simple interest for first year = 320/2 = 160
⇒ Similarly, simple interest for the second year is also 160
Compound Interest for first year = 160
Compound Interest for second year = 340-160 = 180
we can see that compound Interest for the second year is more than
simple interest for the second year by 180-160 = 20
i.e., Tk. 20 is the simple interest on Tk. 160 for 1 year
R = 100 × S.I./PT
= (100 × 20)/(160 × 1)
= 12.5%

৫২২.

The principal that amounts to Tk. 4913 in 3 years at (25/4)% per annum compound interest compounded annually, is-

ক
ক) Tk. 4386
খ
খ) Tk. 4266
গ
গ) Tk. 4096
ঘ
ঘ) Tk. 4566

ব্যাখ্যা

Here
C. P = Tk. 4913
Time = 3 years
Rate = (25/4)% = 25/(4 × 100) = 1/16

Principal (P) = ?
C.P = P(1 + r)ⁿ
4913 =P(1 + 1/16)³
4913 =P(17/16)³
P = 4913/(17/16)³
P = 4913 × (16/17) × (16/17) × (16/17)
P = Tk. 4096

৫২৩.

A sum of money amount to Tk. 720 in 2 years and Tk. 780 in 3 years. The rate per cent is?

ক
ক) 8%
খ
খ) 9%
গ
গ) 10%
ঘ
ঘ) 7%

ব্যাখ্যা

Question: A sum of money amount to Tk. 720 in 2 years and Tk. 780 in 3 years. The rate per cent is?

Solution:
Simple interest for 1 year = Tk. (780 - 720) = Tk. 60
Simple interest for 2 year = Tk. (60 × 2) = Tk. 120
Sum = Tk. (720 - 120) = Tk. 600

We know,
I = Pnr
⇒ r = I/Pn
= (120 × 100)/(600 × 2)
∴ r = 10%

৫২৪.

Calculate the simple interest if the principal amount is Tk. 50000 and the rate is 2% for 4 years.

ক
Tk. 4000
খ
Tk. 40000
গ
Tk. 40
ঘ
Tk. 400

ব্যাখ্যা

Question: Calculate the simple interest if the principal amount is Tk. 50000 and the rate is 2% for 4 years.

Solution:
S.I. = PNR/100
⇒ S.I. = (50000 × 2 × 4)/100
= 4000

৫২৫.

A sum of money amounts to 3300 in 2 years and Tk. 3600 in 5 years. What is the principal amount?

ক
Tk. 3100
খ
Tk. 2950
গ
Tk. 2850
ঘ
Tk. 2700

ব্যাখ্যা

Question: A sum of money amounts to 3300 in 2 years and Tk. 3600 in 5 years. What is the principal amount?

Solution:
After two years the amount is Tk. 3300 and in the next three years it becomes Tk. 3600.

Therefore, S.I for three years = 3600 - 3300 = 300
S.I for one year = 300/3 = 100
S.I for two years = 100 × 2 = 200

∴ Principal = 3300 - 200 = 3100

৫২৬.

The simple interest on a sum of money at 10% per annum for 4 years is half the sum. What is the value of the sum?

ক
Tk. 5000
খ
Tk. 8000
গ
Tk. 10000
ঘ
Data is inadequate

ব্যাখ্যা

Question: The simple interest on a sum of money at 10% per annum for 4 years is half the sum. What is the value of the sum?

Solution:
ধরি, আসল = P
মুনাফার হার, r = 10%
সময়, n = 4 বছর
মুনাফা, I = P/2

আমরা জানি,
I = Pnr/100
⇒ P/2 = (P × 4 × 10)/100
⇒ P/2 = 40P/100
⇒ P/2 = 2P/5
⇒ (P/2) - (2P/5) = 0
⇒ (5P - 4P)/10 = 0
⇒ P/10 = 0
⇒ P = 0

যেহেতু আসলের মান 0 হতে পারে না, তাই প্রদত্ত তথ্যটি সঠিক নয় বা অপর্যাপ্ত।

৫২৭.

The banker's gain on a sum due 3 years hence at 12% per annum is Tk. 360. The banker's discount is:

ক
ক) 1360
খ
খ) 1000
গ
গ) 360
ঘ
ঘ) 640

ব্যাখ্যা

BG = Tk. 360
T = 3 years
R = 12%
TD = (BG×100)/TR
= (360×100)/(3×12)
= Tk. 1000
BG = BD - TD
⇒ BD = BG + TD = 360 + 1000 = Tk. 1360

৫২৮.

How many years will it take for an investment of Tk. 7500 to earn Tk. 2250 in simple interest rate of 6%?

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

ব্যাখ্যা

Question: How many years will it take for an investment of Tk. 7500 to earn Tk. 2250 in simple interest rate of 6%?

Solution:
Given that,
Principal, P = 7500
Simple Interest, SI = 2250
Rate of interest, r = 6%
Time, n = ?

We know,
SI = Pnr/100
⇒ n = (S × 100)/(P × r)
= (2250 × 100)/(7500 × 6)
= 5 years

So, it will take 5 years for the investment to earn Tk. 2250 at 6% simple interest.

৫২৯.

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

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

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.

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

৫৩০.

A and B invest in a business in the ratio 6 : 4. If 10% of the total profit goes to charity and A's share is Tk. 486, what is the total profit?

ক
ক) Tk. 800
খ
খ) Tk. 700
গ
গ) Tk. 900
ঘ
ঘ) Tk. 950

ব্যাখ্যা

Question: A and B invest in a business in the ratio 6 : 4. If 10% of the total profit goes to charity and A's share is Tk. 486, what is the total profit?

Solution:
Let,
The total profit be Tk. 100.
After paying 10% to charity,
∴ A's share = 90 × (6/10) = Tk. 54

If A's share is Tk. 54 then total profit = Tk. 100.
If A's share is Tk. 1 then total profit = Tk. 100/54
∴ If A's share is Tk. 486 then total profit = Tk. (100 × 486)/54
= Tk. 900

৫৩১.

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. 628
খ
Tk. 608
গ
Tk. 789
ঘ
Tk. 698
ঙ
None of these

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

৫৩২.

On a certain sum of money, the simple interest for 2 years is Tk. 450 at the rate of 4% 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
11 Tk
গ
8 Tk
ঘ
7 Tk

ব্যাখ্যা

Question: On a certain sum of money, the simple interest for 2 years is Tk. 450 at the rate of 4% 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
⇒ 450 = (P × 2 × 4)/100
∴ P = 5625

∴ Compound interest = P(1 + r)ⁿ - p
= 5625(1 + 0.04)² - 5625
= 6084 - 5625
= 459

∴ Difference = 459 - 450 = 9 Tk

৫৩৩.

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) 16 : 15
গ
গ) 3 : 5
ঘ
ঘ) 4 : 5

ব্যাখ্যা

Question: 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-

Solution:
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

৫৩৪.

If the simple interest on Tk. M at M% per annum for 4 years is Tk. M, what is the value of M?

ক
25
খ
30
গ
20
ঘ
15

ব্যাখ্যা

Question: If the simple interest on Tk. M at M% per annum for 4 years is Tk. M, what is the value of M?

Solution:
Given,
P = M
r = M% = M/100
n = 4 years
I = M

We know,
I = Prn
⇒ M = M × (M/100) × 4
⇒ M = M × M/25
∴ M = 25

৫৩৫.

A certain sum of money yields Tk. 1261 as compound interest for three years at 5% per annum. The sum is ?

ক
8000 Tk.
খ
6000 Tk.
গ
5000 Tk.
ঘ
10000 Tk.

ব্যাখ্যা

Question: A certain sum of money yields Tk. 1261 as compound interest for three years at 5% per annum. The sum is ?

Solution:
Let the principal be Tk. P

Now,
1261 = P(1 + r)n - P
1261 = P(1 + 5/100)3 - P
1261 = P(105/100)3 - P
1261 = P(21/20)3 - P
1261 = P(9261/8000 - 1)
1261 = P (1261/8000)
1 = P/8000
P = 8000

৫৩৬.

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

ব্যাখ্যা

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

৫৩৭.

At the rate of (17/2)% p.a. simple interest, a sum of Tk. 4800 will earn how much interest in 2 years 3 months?

ক
Tk. 956
খ
Tk. 818
গ
Tk. 718
ঘ
Tk. 918

ব্যাখ্যা

Question: At the rate of (17/2)% p.a. simple interest, a sum of Tk. 4800 will earn how much interest in 2 years 3 months?

Solution:
Time, n = 2 years 3 months = 2(1/4) years = 9/4 years.

We know,
I = Pnr
= 4800 × (9/4) × (17/2) × (1/100)
= Tk. 918

৫৩৮.

The difference in Taka between simple and compound interest at 5% annually on a sum of Tk. 5,000 after 2 years is

ক
12.5
খ
25
গ
50
ঘ
500

ব্যাখ্যা

Question: The difference in Taka between simple and compound interest at 5% annually on a sum of Tk. 5,000 after 2 years is

Solution:
Given that,
Principal, P = Tk. 5,000
Rate, r = 5% = 5/100 = 0.1
Time, n = 2 years

We know that,
Simple Interest = Prn
= (5000 × 5 × 2)/100
= 500
And
Compound Interest = P(1 + r)ⁿ - P
= 5000(1 + 0.05)² - 5000
= 5000(1.05)² - 5000
= 5512.5 - 5000
= 5512.5 - 5000

∴ Difference = 512.5 - 500 = 12.5
The difference between compound and simple profit is Tk. 12.5

৫৩৯.

The bankers discount on Tk. 1800 at 12% per annum is equal to the true discount on Tk 1872 for the same time at the same rate. Find the time.

ক
ক) 4 months
খ
খ) 5 months
গ
গ) 6 months
ঘ
ঘ) 3 months

ব্যাখ্যা

S.I. on Tk. 1800 = T.D. on Tk. 1872
P.W. of Tk. 1872 is Tk. 1800
Tk. 72 is S.I. on Tk. 1800 at 12%
Time = (100×72)/(12×1800)
= 1/3 years = 4months

৫৪০.

A man borrowed some money for 120 days. He asked the banker for the money and the banker charged Tk. 360 as interest @6% per annum. What was the amount he borrowed?

ক
ক) Tk. 18,000
খ
খ) Tk. 16,000
গ
গ) Tk. 15,000
ঘ
ঘ) None of these

ব্যাখ্যা

Question: A man borrowed some money for 120 days. He asked the banker for the money and the banker charged Tk. 360 as interest @6% per annum. What was the amount he borrowed?

Solution:
এখানে
সময় n = 120 দিন
= 4 মাস
= 4/12 বছর
= 1/3 বছর

মুনাফা I = 360 টাকা
মুনাফার হার r = 6% = 6/100 = 3/50
আসল P = ?

আমরা জানি
I = Pnr
Pnr = I
P = I/nr
= 360/{(1/3) × (3/50)}
=360/(1/50)
= 360 × 50
= 18000 টাকা

৫৪১.

Tk 1200 is lent out at 5% per annum simple interest for 3 years. Find the amount after 3 years.

ক
ক) Tk 1290
খ
খ) Tk 1380
গ
গ) Tk 1250
ঘ
ঘ) Tk 1360

ব্যাখ্যা

Question: Tk 1200 is lent out at 5% per annum simple interest for 3 years. Find the amount after 3 years.

Solution:
A = p(1 + nr)
= 1200{1 + (3 × 5)/100}
= 12000 × (115/100)
= 1380

৫৪২.

A man purchased 400 shares of the face value of Tk. 100 each from the market at Tk. 125 per share. If a dividend of 20% is declared, find his earning percent on the investment.

ক
10%
খ
24%
গ
20%
ঘ
16%

ব্যাখ্যা

Question: A man purchased 400 shares of the face value of Tk. 100 each from the market at Tk. 125 per share. If a dividend of 20% is declared, find his earning percent on the investment.

Solution:
Given,
Price of 1 share = Tk. 125.
∴ Price of 400 share = Tk. (125 × 400)
= Tk. 50000

Dividend per share=20% of 100 = Tk. 20
∴ Total dividend income = 400 × 20 = Tk. 8000

∴ Earning % = (Dividend/Market Price) × 100
=(8000/50000) × 100
= 16%.

৫৪৩.

If the simple interest on a sum of money at 6% per annum for 4 years is Tk.1600, then find the compound interest on the same sum for the same period at the same rate.

ক
ক) Tk. 1625.35
খ
খ) Tk. 1645.45
গ
গ) Tk. 1662.35
ঘ
ঘ) Tk. 1660.66

ব্যাখ্যা

From the question, you know that R = 6%, T = 4 years, S.I. = Tk.1600

If you apply the above values in the simple interest formula S.I. = PRT/100, you will get
1600 = (P x 4 x 6)/100
⇒ P = (1600 x 100)/6 × 4
⇒ P = 6333.33

Using the above value of P, you have to now calculate C.I. as shown below:
CI = [P(1 + R/100)ⁿ] – P
= [6333.33(1 + 6/100)⁴] - 6333.33
= [6333.33 (106/100)⁴] - 6333.33
= [6333.33× 53/50 × 53/50 × 53/50 × 53/50] - 6333.33
= 7995.68 - 6333.33
= Tk.1662.35

৫৪৪.

A sum of Tk.12,500 amounts to Tk.15,500 in 4 years at the rate of simple interest. What is the rate of interest?

ক
ক) 7%
খ
খ) 5.5%
গ
গ) 6.5%
ঘ
ঘ) 6%

ব্যাখ্যা

S.I. = Tk. (15500 - 12500)
= Tk. 3000.

Rate ={(100 x 3000)/(12500 x 4)}%
= 6%

৫৪৫.

A sum of money becomes 4 times itself in 20 years at simple interest. What is the annual interest rate?

ক
10%
খ
15%
গ
20%
ঘ
12.5%

ব্যাখ্যা

Question: A sum of money becomes 4 times itself in 20 years at simple interest. What is the annual interest rate?

Solution:
Let, Principal amount = P
Sum of amount = 4P
∴ Interest, I = 4P - P = 3P
Time, n = 20 years
Rate of interest = r

We know, I = Pnr/100
⇒ Pnr/100 = 3P
⇒ nr/100 = 3
⇒ 20 × r/100 = 3
⇒ 20r = 300
⇒ r = 300/20
⇒ r = 15

∴ The annual interest rate is 15%.

৫৪৬.

A sum of TK. 24,500 amounts to TK. 34,300 in 5 years at a simple interest rate. What is the rate of interest?

ক
ক) 5 %
খ
খ) 5%
গ
গ) 6%
ঘ
ঘ) 8%

ব্যাখ্যা

Here, interest = 34300 - 24500 = 9800 taka
We know, I = pnr
Or, r = (I×100)/pn
= (9800×100) / (24500×5)
= 8%

৫৪৭.

A man deposits Tk. 10000 in a Bank at 10% interest rate compounded annually. At the end of the second year, the total amount(nearest) including interest will become?

ক
Tk. 15000
খ
Tk. 11325
গ
Tk. 10100
ঘ
Tk. 18300
ঙ
Tk. 12100

ব্যাখ্যা

Question: A man deposits Tk. 10000 in a Bank at 10% interest rate compounded annually. At the end of the second year, the total amount(nearest) including interest will become?

Solution:
Given,
Principal, P = 10000 Tk.
Rate of interest, r = 10% = 10/100 = 0.1
Time, n = 2 years

We know,
Compound Amount = P(1 + r)ⁿ
= 10000 × (1 + 0.1)²
= 10000 × (1.1)²
= 10000 × 1.21
= 10000 × (19,683/15,625)
= 12100

৫৪৮.

A sum of Tk. 30,000 yields a compound interest of Tk. 4347 when invested at 7% per annum. What is the investment period in years?

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

ব্যাখ্যা

Question: A sum of Tk. 30,000 yields a compound interest of Tk. 4347 when invested at 7% per annum. What is the investment period in years?

Solution:
Given,
Principal, P = 30000
Rate, r = 7% per annum
Compound Interest, CI = 4347

We know,
Amount, A = P + CI = 30000 + 4347 = 34347

Using the compound amount formula:
A = P(1 + r/100)ⁿ
⇒ 34347 = 30000 × (1 + 7/100)ⁿ
⇒ 34347 = 30000 × (107/100)ⁿ
⇒ (107/100)ⁿ = 34347/30000
⇒ (1.07)ⁿ = 1.1449
⇒ (1.07)ⁿ = (1.07)²∴ n = 2 years

৫৪৯.

A man took out a loan from a bank at the rate of 8%per annum simple interest. After 4 years he had to pay Tk. 6200 interest only for the period. What was the principal amount borrowed by him?

ক
ক) Tk. 20245
খ
খ) Tk. 18230
গ
গ) Tk. 17322
ঘ
ঘ) Tk. 19375

ব্যাখ্যা

P = (100 × S.I)/RT
= (100 × 6200)/(8 × 4)
= 620000/32
= 775 × 25
= Tk. 19375.

৫৫০.

Jishan took a loan of Tk. 1500 with simple interest for as many years as the rate of interest. If he paid Tk. 540 as interest at the end of loan period, what was the rate of interest?

ক
2%
খ
3%
গ
4%
ঘ
6%

ব্যাখ্যা

Simple interest is the same as the rate of interest.
Hence,
Rate of interest = R% and Time = R years

S.I. = (P × R × R)/100
⇒ 60 = (1500 × R²)/100
⇒ 15R²= 540
⇒ R² = 36
⇒ R=6 %

Rate of Interest = 6%.

৫৫১.

At what rate of compound interest per annum will a sum of Tk. 4000 becomes Tk. 4840 in 2 years?

ক
10%
খ
15%
গ
12%
ঘ
20%

ব্যাখ্যা

Question: At what rate of compound interest per annum will a sum of Tk. 4000 becomes Tk. 4840 in 2 years?

Solution:
Principal, P = Tk. 4000
Compound Amount, C = Tk. 4840
Time, n = 2 years
Rate, r = ?

We know,
C = P × (1 + r/100)ⁿ
⇒ 4840 = 4000 × (1 + r/100)²
⇒ (1 + r/100)² = 4840/4000
⇒ (1 + r/100)² = 484/400
⇒ 1 + r/100 = 22/20 [উভয়পাশে বর্গমূল করে]
⇒ r/100 = (11/10) - 1
⇒ r/100 = (11 - 10)/10
⇒ r/100 = 1/10
⇒ r = (1 × 100)/10
∴ r = 10

∴ Interest Rate = 10%

৫৫২.

A man invested Tk. 36,000 when he bought Tk. 100 shares at Tk. 144. If 16% dividend is declared, find his annual income.

ক
Tk. 3200
খ
Tk. 2620
গ
Tk. 4000
ঘ
Tk. 3600

ব্যাখ্যা

Question: A man invested Tk. 36,000 when he bought Tk. 100 shares at Tk. 144. If 16% dividend is declared, find his annual income.

Solution:
For Tk. 144 he gets Tk. 16
∴ For Tk. 1 he gets Tk. 16/144
∴ For Tk. 36,000 he gets Tk. (16 × 36,000)/144
= Tk. (1/9) × 36,000
= Tk. 4,000

∴ The man's annual income is Tk. 4000.

৫৫৩.

A 10% stock yields 8%. What is the market value of the stock?

ক
Tk. 120
খ
Tk. 100
গ
Tk. 80
ঘ
Tk. 125

ব্যাখ্যা

Question: A 10% stock yields 8%. What is the market value of the stock?

Solution:
Earn Tk. 8 when market value Tk. 100
Earn Tk. 1 when market value Tk. 100/8
Earn Tk. 10 when market value Tk. (100 × 10)/8
= Tk. 125

৫৫৪.

Rakib needs money for 240 days. He asked the banker for a loan and the banker charged Tk. 720 at 6% per annum. What is the amount of loan?

ক
ক) Tk. 15000
খ
খ) Tk. 18000
গ
গ) Tk. 15500
ঘ
ঘ) Tk. 18500

ব্যাখ্যা

Question: Rakib needs money for 240 days. He asked the banker for a loan and the banker charged Tk. 720 at 6% per annum. What is the amount of loan?

Solution:
Time, n = 240 days = 240/30 months = 8 months = 8/12 year
r = 6% = 6/100
I = Tk. 720

P = I/(nr)
= 720/{(8/12) × (6/100)}
= (720 × 12 × 100)/(8 × 6)
= 18000

৫৫৫.

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. 20
খ
Tk. 10
গ
Tk. 12
ঘ
Tk. 15

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. (100/12 × 95)
= Tk.15

৫৫৬.

What is the compound interest on Tk. 5000 for 2 years at rate of interest 4% per annum?

ক
Tk. 360
খ
Tk. 408
গ
Tk. 420
ঘ
Tk. 428

ব্যাখ্যা

Question: What is the compound interest on Tk. 5000 for 2 years at rate of interest 4% per annum?

Solution:
C = P(1 + r)ⁿ
= 5000(1 + 4/100)²
= 5000 × 1.04 × 1.04
= 5408

∴ Compound intertest = 5408 - 5000 = 408

৫৫৭.

An amount of Tk. 8,000 yields a simple interest of Tk. 1,440 in 3 years. What is the annual rate of interest?

ক
5%
খ
6%
গ
8%
ঘ
10%

ব্যাখ্যা

Question: An amount of Tk. 8,000 yields a simple interest of Tk. 1,440 in 3 years. What is the annual rate of interest?

Solution:
Given,
Principal, P = 8000
Simple Interest, SI = 1440
Time, n = 3 years
Rate of interest, r = ?

We know,
I = Pnr/100
⇒ r = (I × 100)/(P × n)
⇒ r = (1440 × 100)/(8000 × 3)
⇒ r = 144000/24000
∴ r = 6%

So, the annual rate of interest is 6%.

৫৫৮.

A man buys Tk. 40 shares in a company which pays 10% dividend. If the man gets 12.5% on his investment, at what price did he buy the shares?

ক
ক) Tk. 28
খ
খ) Tk. 30
গ
গ) Tk. 32
ঘ
ঘ) None of above

ব্যাখ্যা

Question: A man buys Tk. 40 shares in a company which pays 10% dividend. If the man gets 12.5% on his investment, at what price did he buy the shares?

Solution:
Dividend on 40 share = 10%
∴ Dividend on 1 share = (10 × 40)/100
= Tk. 4
Tk. 12.50 is an income on an investment of Tk. 100
Tk. 4 is an income on an investment of = (100 × 4)/12.50
= (100 × 4 × 10)/125
= Tk. 32

∴ Cost of 1 share = Tk. 32

৫৫৯.

At 20% simple interest per year, a sum becomes Tk. 28,000 in 2 years. Calculate the original amount.

ক
Tk. 16000
খ
Tk. 20000
গ
Tk. 22000
ঘ
Tk. 18000

ব্যাখ্যা

Question: At 20% simple interest per year, a sum becomes Tk. 28,000 in 2 years. Calculate the original amount.

Solution:
Here,
A = 28000,
T = 2,
R = 20

Now,
⇒ A = P + SI
⇒ A = P + (P × R × T/100)
⇒ A = P [1 + (R × T/100)]
⇒ 28000 = P [1 + 0.4]
⇒ P = 28000/1.4
⇒ P = 20000

Thus, the original amount is Tk. 20000

৫৬০.

Find the simple interest on BDT 12000 at 4% per annum for 8 months.

ক
Tk. 120
খ
Tk. 220
গ
Tk. 320
ঘ
Tk. 420

ব্যাখ্যা

Question: Find the simple interest on BDT 12000 at 4% per annum for 8 months.

Solution:
Principal, P = 12000 Taka
Time, n = 8 months = 8/12 = 2/3 years
Rate of interest, r = 4% = 4/100

Simple Interest, I = P × n × r
= 12000 × (2/3) × (4/100)
= 40 × 2 × 4
= 320

∴ The simple interest is Tk. 320.

৫৬১.

There is 75% increase in an amount in 5 years at simple interest. What will be the compound interest of TK. 16,000 after 2 years at the same rate?

ক
Tk. 3,250
খ
Tk. 4,466
গ
Tk. 4,990
ঘ
Tk. 5,160

ব্যাখ্যা

Question: There is 75% increase in an amount in 5 years at simple interest. What will be the compound interest of TK. 16,000 after 2 years at the same rate?

Solution:
Let,
P = Tk. 100
Then, S.I = Tk. 75
and n = 5 years

So the rate r = (100 × 75)/(100 × 5)
= 15%

Now, P = Tk. 16,000
n = 2 years
r = 15% p.a.
= 3/20 p.a

C.I = 16,000 × {(1 + 3/20)² - 1}
= 16,000 × {(23/20)² - 1}
= 16,000 × (529/400 - 1)
= 16000 × 129/400
= 5,160

৫৬২.

At what rate percentage per annum will the simple interest on sum of money be 3/5 of the amount in 10 years?

ক
ক) 2%
খ
খ) 4%
গ
গ) 6%
ঘ
ঘ) 8%

ব্যাখ্যা

Let
sum = x
S. I = 3x/5
Time = 10 years

Rate = {(3x × 100)/(x × 5 × 10)}% = 6%

৫৬৩.

A sum of 20,000 Taka is invested at 8% per annum. If the interest is compounded quarterly, what is the amount after 9 months?

ক
Tk. 20,000
খ
Tk. 21,000.55
গ
Tk. 21,224.16
ঘ
Tk. 22,350.25

ব্যাখ্যা

Question: A sum of 20,000 Taka is invested at 8% per annum. If the interest is compounded quarterly, what is the amount after 9 months?

Solution:
এখানে, আসল (P) = 20,000 টাকা
বার্ষিক সুদের হার = 8%
সময় = 9 মাস
যেহেতু সুদ ত্রৈমাসিক (quarterly) ভিত্তিতে গণনা করা হয়,
∴ ত্রৈমাসিক সুদের হার = 8% ÷ 4 = 2%
9 মাসে চক্রবৃদ্ধির সংখ্যা = 9 মাস ÷ 3 মাস = 3 বার

প্রথম ত্রৈমাসিক:
সুদ = (20,000 এর 2%) = 400 টাকা
নতুন মূল = 20,000 + 400
= 20,400 টাকা

দ্বিতীয় ত্রৈমাসিক:
সুদ = (20,400 এর 2%) = 408 টাকা
নতুন মূল = 20,400 + 408
= 20,808 টাকা

তৃতীয় ত্রৈমাসিক:
সুদ = (20,808 এর 2%) = 416.16 টাকা
নতুন মূল = 20,808 + 416.16
= 21,224.16 টাকা

∴ 9 মাস পর চক্রবৃদ্ধি মূল হবে 21,224.16 টাকা।

৫৬৪.

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 p. c. p. a?

ক
ক) 10%
খ
খ) 15%
গ
গ) 18%
ঘ
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 p. c. p. a?

Solution:
Let
the rate be r% p. a

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% p. a

৫৬৫.

The compound interest on Tk. 2500 for 2 years at 10% p. a is-

ক
ক) Tk. 395.5
খ
খ) Tk. 375.5
গ
গ) Tk. 378.5
ঘ
ঘ) Tk. 525.0

ব্যাখ্যা

Given,
Principal, P = Tk. 2500
Compound rate , R = 10%
Time n = 2 years

Compound Principal = [2500(1 + 10/100)²]
= [2500(1.1)²]
=3025

∴C.I. = Tk.(3025 - 2500)=Tk. 525

৫৬৬.

If the interest of Tk. H of H% in 4 years is Tk.H, Then H = ?

ক
ক) 25
খ
খ) 20
গ
গ) 30
ঘ
ঘ) 32

ব্যাখ্যা

সরল মুনাফার ক্ষেত্রে,
I = Pnr
Or, H = H × 4 × H/100
Or, H = 100/4
Or, H = 25

৫৬৭.

A man invested Tk. 5940 in Tk.10 shares quoted at Tk. 8.25. If the rate of dividend be 12%, his annual income is:

ক
Tk. 864
খ
Tk. 846
গ
Tk. 468
ঘ
Tk. 684

ব্যাখ্যা

Question: A man invested Tk. 5940 in Tk.10 shares quoted at Tk. 8.25. If the rate of dividend be 12%, his annual income is:

Solution:
Number of shares =(5940/8.25) = 720

Face value = Tk.(720× 10)= Tk. 7200

Annual income = {(12/100) × 7200} = 864

৫৬৮.

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. 698
খ
Tk. 789
গ
Tk. 608
ঘ
Tk. 628

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

৫৬৯.

Samir borrows 2500 taka from a leasing company at 5% compound interest per year. Calculate the total that must be paid after 24 months.

ক
ক) 2,025.89
খ
খ) 2,756.25
গ
গ) 2,852.92
ঘ
ঘ) 2,758.78

ব্যাখ্যা

Here, n = 24 months = 2 years

Compound interest rate = 5% = 5/100

We know, C = P ( 1 + r%)² = 2500 (1 + 5/100)²= tk. 2,756.25

৫৭০.

Tk. 1400 is lent out at 5% per annum simple interest for 4 years. Find the amount after 4 years.

ক
Tk. 1580
খ
Tk. 1480
গ
Tk. 1680
ঘ
Tk. 1280

ব্যাখ্যা

Question: Tk. 1400 is lent out at 5% per annum simple interest for 4 years. Find the amount after 4 years.

Solution:
We know,
A = p(1 + nr)
= 1400 {1 + (4 × 5)/100}
= 1400 × (120/100)
= 1680

৫৭১.

A sum of money becomes 8/5 of itself in 5 years at a certain rate of interest. What is the rate of the interest?

ক
ক) 9%
খ
খ) 7%
গ
গ) 10%
ঘ
ঘ) 12%
ঙ
ঙ) 5%

ব্যাখ্যা

Let the sum of money be P(which is the principal value) and rate of interest be R.
According to the question,
Amount (principal +simple interest) = 8P/5
Time (T) = 5 years
Simple interest (SI) = PRT/100
SI = 5PR/100
Amount = P + SI
8P/5 = P + (5PR/100)
8P/5 = P(100 + 5R)/100
160 = 100 + 5R
5R = 60
R = 12
Therefore, rate of interest = 12% p.a.

Alternative Method:
Given A = 8/5p (8/5 of the sum) .
Time = 5years .
Let the sum be P = 100.
Then, the amount = 8/5p = (value of p is 100)
= 8/5 × 100
= 160 .
S. I. = A-P
= 160 - 100
= 60 .
Hence,
Rate = S.I. × 100/P × T
= 60 × 100/100 × 5
= 12% p.a.

৫৭২.

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

ক
114 Tk.
খ
118 Tk.
গ
125 Tk.
ঘ
140 Tk.

ব্যাখ্যা

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

Solution:
Interest rate, R = 9.5%
Principal amount, P = 600 tk
Time, T = 2 years

We Know, SI = PRT/100
= (600 × 2 × 9.5)/100
= 114 Tk.

∴ The interest for 2 years is Tk. 114.

৫৭৩.

A sum of money invested at compound interest triples itself in 3 years. In how many years will it become 27 times itself?

ক
6 years
খ
8 years
গ
9 years
ঘ
12 years

ব্যাখ্যা

Question: A sum of money invested at compound interest triples itself in 3 years. In how many years will it become 27 times itself?

Solution:
Since the sum triples in 3 years, we can write:

Thus, it will take 9 years for the amount to become 27 times itself.

৫৭৪.

Mr. Anwar deposits Tk. 7000 in a bank at 10% interest rate compounded annually. At the end of the three year, the total amount including interest will become?

ক
ক) 2317
খ
খ) 3197
গ
গ) 9317
ঘ
ঘ) 7317

ব্যাখ্যা

Question: Mr. Anwar deposits Tk. 7000 in a bank at 10% interest rate compounded annually. At the end of the three year, the total amount including interest will become?

Solution:
Given,
Principal, P = 7000 Tk.
Rate of interest, r = 10% = 10/100 = 1/10
Time, n = 3 years.

We know,
Compound Amount = P (1 + r)ⁿ
= 7000 × (1 + 1/10)³
= 7000 × (11/10)³
= 7000 × (11/10) × (11/10) × (11/10)
= 9317

৫৭৫.

A woman borrowed a certain amount of money for 8 months. She paid Tk. 1,200 as simple interest at a rate of 12% per year. What was the original amount (principal) she borrowed?

ক
Tk. 12,000
খ
Tk. 13,000
গ
Tk. 16,000
ঘ
Tk. 15,000

ব্যাখ্যা

Question: A woman borrowed a certain amount of money for 8 months. She paid Tk. 1,200 as simple interest at a rate of 12% per year. What was the original amount (principal) she borrowed?

Solution:
Simple Interest (SI) formula:
SI = [P (principal) × R (rate) × T (time)] / 100

Here,
SI = 1200
R = 12% per annum
T = 8 months = 8/12 = 2/3 year

Now,
1200 = [P × 12 × (2/3)] / 100
⇒ 1200 = (P × 8) / 100
⇒ P = (1200 × 100) / 8
⇒ P = 150000 / 8
⇒ P = Tk. 15000

৫৭৬.

A sum fetched a total simple interest of Tk 840 at the rate of 7 p.c.p.a. in 12 years. What is the sum?

ক
ক) Tk 1240
খ
খ) Tk 1200
গ
গ) Tk 1000
ঘ
ঘ) Tk 1080

ব্যাখ্যা

Question: A sum fetched a total simple interest of Tk 840 at the rate of 7 p.c.p.a. in 12 years. What is the sum?

Solution:
We know,
I = Pnr
⇒ P = I/nr
⇒ P = (840 × 100)/(7 × 12)
⇒ P = 1000

৫৭৭.

A sum becomes Tk 1352 in 2 years at 4% per annum compound interest. The sum is =?

ক
ক) 1225 Tk
খ
খ) 1200 Tk
গ
গ) 1250 Tk
ঘ
ঘ) 1220 Tk

ব্যাখ্যা

Question: A sum becomes Tk 1352 in 2 years at 4% per annum compound interest. The sum is =?

Solution
Let the sum be Tk p

∴ 1352 = p(1 + 4/100)²
⇒ 1352 = x(1 + 1/25)²
⇒ 1352 = x(26/25)²
⇒ x = (1352 × 25 × 25) / (26 × 26)
⇒ x = 1250

৫৭৮.

By investing Tk. 1620 in 8% stock, Mizan earns Tk. 135. The stock is then quoted at:

ক
ক) Tk. 80
খ
খ) Tk. 96
গ
গ) Tk 87
ঘ
ঘ) Tk 83
ঙ
ঙ) Tk 90

ব্যাখ্যা

To earn Tk. 135, investment = Tk. 1620.
To earn Tk. 8, investment = Tk.(1620/135 × 8)
= Tk 96
So, Market value of Tk. 100 stock = Tk. 96.

৫৭৯.

A sum of money amounts to Tk. 18000 in 5 years at 20% simple interest per annum. Find the sum.

ক
Tk. 8500
খ
Tk. 9000
গ
Tk. 10500
ঘ
Tk. 12000

ব্যাখ্যা

Question: A sum of money amounts to Tk. 18000 in 5 years at 20% simple interest per annum. Find the sum.

Solution:
দেওয়া আছে,
সুদ-আসল (Amount), A = 18000 টাকা
সময় (Time), n = 5 বছর
সুদের হার (Rate), r = 20%
মূলধন (Principal), P = ?

আমরা জানি,
সুদ (Interest), I = A - P
আবার, I = (Pnr)/100
সুতরাং, A - P = (Pnr)/100
⇒ 18000 - P = (P × 5 × 20)/100
⇒ 18000 - P = (100P)/100
⇒ 18000 - P = P
⇒ 18000 = P + P
⇒ 18000 = 2P
⇒ P = 18000/2
⇒ P = 9000
সুতরাং, নির্ণেয় মূলধন 9000 টাকা।

৫৮০.

What will be the ratio of simple interest earned by certain amount at the same rate of interest for 9 years and that for 6 years?

ক
3 : 4
খ
3 : 1
গ
3 : 2
ঘ
4 : 5

ব্যাখ্যা

Question: What will be the ratio of simple interest earned by certain amount at the same rate of interest for 9 years and that for 6 years?

Solution:
Let
The principal be P and rate of interest be r%

Required ratio = [(P × r × 9)/100]/[(P × r × 6)/100]
=9Pr/6Pr
= 9/6
= 3/2
= 3 : 2

৫৮১.

What is the difference between simple and compound interest at 10% per annum on a sum of Tk. 3000 at the end of 2 years?

ক
Tk. 80
খ
Tk. 60
গ
Tk. 30
ঘ
Tk. 50

ব্যাখ্যা

Question: What is the difference between simple and compound interest at 10% per annum on a sum of Tk. 3000 at the end of 2 years?

Solution:
Principal (P) = Tk. 3000
Rate (r) = 10% per annum
Time (n) = 2 years

Simple Interest (SI):
SI = (P × R × T)/100
= (3000 × 10 × 2)/100
= 60000/100
= Tk. 600

Compound Interest (CI):
Amount (A) = P × (1 + r/100)ⁿ
= 3000 × (1 + 10/100)²
= 3000 × (1.1)²
= 3000 × 1.21
= Tk. 3630

∴ CI = A - P = 3630 - 3000
= Tk. 630

∴ Difference between CI and SI = 630 - 600
= Tk. 30

৫৮২.

A man invested 1/3 of his capital at 7%, 1/4 at 8% and the remainder at 10%. If his annual income is Tk.561, The capital is-

ক
ক) Tk. 4600
খ
খ) Tk. 4800
গ
গ) Tk. 6600
ঘ
ঘ) Tk. 6400

ব্যাখ্যা

Let the capital be Tk. x
Then according to the question, we have
[{(x/3)× (7/100) × 1} + [{(x/4)×(8/100) × 1} + [{(5x/12)× (10/100) × 1}= 561
⇒(7x/300) + (8x/400) + (50x/1200) = 561
⇒(28x + 24x + 50x)/1200 = 561
⇒102x/1200 = 561
x = (561 × 1200)/102
x = 6600

৫৮৩.

The sum invested in scheme B is thrice the sum invested in scheme A. The investment in scheme A is made for 4 years at 8% p.a. simple interest and in scheme B for 2 years at 13% p.a. simple interest. The total interest earned from both the schemes is Tk. 1320. How much amount was invested in scheme A?

ক
ক) Tk. 1200
খ
খ) Tk. 1100
গ
গ) Tk. 960
ঘ
ঘ) Tk. 1500

ব্যাখ্যা

Let the amount invested in scheme A be Tk. x and that in B be Tk. 3x.
Then,
Then,
{(x × 4 × 8)/100 + (3x × 2 × 13)/100} = 1320
⇒ 32x/100 + 78x/100 = 1320
⇒ 110x/100 = 1320
⇒ x = (1320 × 100)/110
⇒ x = Tk. 1200

Hence, Tk. 1200 was invested in scheme A.

৫৮৪.

Some principal becomes Tk. 1,750 as profit-principal in 5 years and Tk. 2,250 as profit-principal in 10 years. Find the rate of profit.

ক
8%
খ
10%
গ
15%
ঘ
5%

ব্যাখ্যা

Question: Some principal becomes Tk. 1,750 as profit-principal in 5 years and Tk. 2,250 as profit-principal in 10 years. Find the rate of profit.

Solution:
Given,
Principal + Profit for 5 years = 1,750
Principal + Profit for 10 years = 2,250

So the profit of 5 years, I = 2250 - 1750 = Tk. 500
So the principal, P= 1750 - 500 = Tk. 1250

∴ The rate of profit, r = (I × 100)/(P × n)
= (500 × 100)/(1250 × 5)
= 50000/6250
= 8%

৫৮৫.

Compound interest on a certain sum at the rate of 12% per annum after 2 years is Tk. 1,42,464. Find the simple interest on that sum at the rate of 15% per annum for 7 years.

ক
ক) Tk. 5,68,000
খ
খ) Tk. 5,86,000
গ
গ) Tk. 5,88,000
ঘ
ঘ) Tk. 5,66,000

ব্যাখ্যা

Question: Compound interest on a certain sum at the rate of 12% per annum after 2 years is Tk. 1,42,464. Find the simple interest on that sum at the rate of 15% per annum for 7 years.

Solution:
Let the sum be, x.
Rate of interest = 12%
Period = 2 years

Hence, compound interest = x(1 + 12/100)² - x = 142464
x × 1.2544 - x = 142464

So, x = 142464/0.2544 = 560000

Hence, simple interest = 560000 × 15/100 × 7 = 588000

৫৮৬.

A sum of Tk. 1600 gives a simple interest of Tk. 252 in 2 years and 4 months. The rate of interest per annum is:

ক
3.45%
খ
4%
গ
5.25%
ঘ
6.75%

ব্যাখ্যা

Question: A sum of Tk. 1600 gives a simple interest of Tk 252 in 2 years and 4 months. The rate of interest per annum is:

Solution:
2 years and 4 months = 2 + (1/3) years
= 7/3 hours

let, rate of interest is r%

252 = 1600 × (7/3) × (r/100)
⇒ 252 = 112r/3
⇒ r = 6.75

৫৮৭.

A bank offers 10% compound interest calculated half-yearly. A customer deposits Tk. 2000 on 1st January and another Tk. 2000 on 1st July of the same year. How much interest will he earn at the end of the year?

ক
Tk. 295
খ
Tk. 305
গ
Tk. 315
ঘ
Tk. 330

ব্যাখ্যা

Question: A bank offers 10% compound interest calculated half-yearly. A customer deposits Tk. 2000 on 1st January and another Tk. 2000 on 1st July of the same year. How much interest will he earn at the end of the year?

Solution:
Here,
Half-yearly interest rate = 10% ÷ 2 = 5%
Now,
The first deposit of Tk. 2000 was made on 1st January.
It stays for 12 months, so it earns interest twice (i.e., 2 half-years).
∴ A₁ = P(1 + r/100)ⁿ
= 2000 × {1 + 5/100}²
= 2000 × (1.05)²
= 2000 × 1.1025
= 2205

Now,
The second deposit of Tk. 2000 was made on 1st July.
It stays for 6 months, so it earns interest only once (1 half-year).
∴ A₂ = P(1 + r/100)ⁿ
= 2000 × (1 + 5/100)¹
= 2000 × 1.05
= 2100

Total amount = 2205 + 2100 = 4305
Total money deposited = 2000 + 2000 = 4000

∴ Interest earned = 4305 - 4000 = Tk. 305

∴ The customer would have gained Tk. 305 by way of interest.

৫৮৮.

The compound interest on Taka 12,000 for 2 years at 10% per annum compounded half-yearly is -

ক
2,422 Taka
খ
2,444 Taka
গ
2,586 Taka
ঘ
2,678 Taka

ব্যাখ্যা

Question: The compound interest on Taka 12,000 for 2 years at 10% per annum compounded half-yearly is -

Solution:
Given,
P = 12,000 (Principal)
r = 10% = 0.1
Compounded half-yearly means, n = 2
Time, t = 2 years

Compound Interest = A - P
= 14586 - 12000
= 2586 Taka

৫৮৯.

If 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

৫৯০.

The difference between simple and compound interests compounded annually on a certain sum of money for 2 years at 5% per annum is Tk 3. The sum is:

ক
650 Tk
খ
900 Tk
গ
1200 Tk
ঘ
1400 Tk
ঙ
1550 Tk

ব্যাখ্যা

Question: The difference between simple and compound interests compounded annually on a certain sum of money for 2 years at 5% per annum is Tk 3. The sum is:

Solution:
Let, Sum = x
Here, r = 5% & n = 2

Now, S.I. = (x × 5 × 2)/100
= x/10

And, C.I. = [x{1 + (5/100)}² - x]
= [x{1 + (1/20)}² - x]
=[x(21/20)² - x]
= (441x - 400x)/400
= 41x/400

∴ (41x/400) - (x/10) = 3
⇒ (41x - 40x)/400 = 3
⇒ x = 1200

৫৯১.

Which amount to be received after 3 years at the rate of 7% p.a. of simple interest on a sum of Tk. 2800?

ক
ক) Tk. 3388
খ
খ) Tk. 2288
গ
গ) Tk. 4488
ঘ
ঘ) Tk. 2388

ব্যাখ্যা

Question: Which amount to be received after 3 years at the rate of 7% p.a. of simple interest on a sum of Tk. 2800?

Soution:
Given,
Rate of interest, r = 7%
Principal, P = 2800 Tk.
Time, n = 3 years.

∴ Total interest, I = Pnr
= (2800 × 3 × 7)/100
= 588 Tk.

So, amount = Principal + Simple interest
= (2800 + 588) Tk.
= 3388 Tk.

৫৯২.

Mizan took a loan of Tk. 1500 with simple interest for as many years as the rate of interest. If he paid Tk. 540 as interest at the end of the loan period, what was the rate of interest?

ক
3%
খ
9%
গ
5%
ঘ
8%
ঙ
6%.

ব্যাখ্যা

Simple interest is the same as the rate of interest.
Hence,
Rate of interest = R% and Time = R years

S.I. = (P × R × R)/100
⇒ 540 = (1500 × R²)/100
⇒ 15R²= 540
⇒ R² = 36
⇒ R = 6 %

Rate of Interest = 6%.

৫৯৩.

A sum becomes 4 times at simple interest in 10 years. What is the rate of interest?

ক
ক) 10%
খ
খ) 20%
গ
গ) 30%
ঘ
ঘ) 40%
ঙ
ঙ) 50%

ব্যাখ্যা

Here, the sum becomes 4 times that means 100, becomes 400.
Rate of such question is given by
R = interest/time = 300/10 = 30%

৫৯৪.

An agent allows a rebate of 4% to an investor while the bank pays an interest of 14% on the investment. What is the actual rate of interest earned by the investor on his investment?

ক
18.75%
খ
18%
গ
17.75%
ঘ
16%

ব্যাখ্যা

Let the investor invests Tk. 100

Rebate given = 4%

So, the actual investment = 100 - 4
= 96

The bank pays interest of 14% on the investment which is Tk. 100 without rebate and Tk. 96 with rebate.
Therefore required rate of interest = (114 - 96)/96 × 100
= 18.75%

৫৯৫.

The capital stock of a company is Tk. 500000 and is divided into 5000 shares of common stock. If the company pays a dividend of Tk. 64000, what amount will Rakib receive for his 50 shares?

ক
Tk. 700
খ
Tk. 640
গ
Tk. 680
ঘ
None of these

ব্যাখ্যা

Question: The capital stock of a company is Tk. 500000 and is divided into 5000 shares of common stock. If the company pays a dividend of Tk. 64000, what amount will Rakib receive for his 50 shares?

Solution:
5000 shares income Tk. 64000
1 share incomes Tk. 64000/5000
50 shares income Tk. (64000 × 50)/5000
= Tk. 640

৫৯৬.

Tk. 9800 are invested partly in 9% stock at 75 and 10% stock at 80 to have an equal amount of income. The investment in 9% stock is

ক
ক) Tk. 4800
খ
খ) Tk. 5000
গ
গ) Tk. 5200
ঘ
ঘ) Tk. 5400

ব্যাখ্যা

Question: Tk. 9800 are invested partly in 9% stock at 75 and 10% stock at 80 to have an equal amount of income. The investment in 9% stock is:

Solution:
Let,
the investment in 9% stock be tk. x.
Then, investment in 10% stock = tk.(9800 - x)

According to the question,
(9/75) × x = (10/80) × (9800 - x)
⇒ 3x/25 = (9800 - x)/8
⇒ 24x = (9800 × 25) - 25x
⇒ 24x + 25x = 245000
⇒ 49x = 245000
⇒ x = 245000/49
∴ x = 5000

৫৯৭.

A sum of Tk. 4000 will amount to TK. 4410 in 2 years if the interest is calculated every year. What is the rate of compound interest?

ক
4%
খ
5%
গ
6%
ঘ
8%
ঙ
10%

ব্যাখ্যা

Question: A sum of Tk. 4000 will amount to TK. 4410 in 2 years if the interest is calculated every year. What is the rate of compound interest?

Solution:
Here,
Principal, P = 4000 Tk.
Amount, A = 4410 Tk.
Time, n = 2 years
Let, Rate = r

By using formula,
A = P[1 + (r/100)]ⁿ
∴ 4410 = 4000 [1 + (r/100)]²
⇒ 441/400 = [1 + (r/100)]²
⇒ 21/20 = 1 + (r/100) [Taking square root of both sides]
⇒ 21/20 = (100 + r)/100
⇒ 20r + 2000 = 2100
⇒ 20r = 2100 - 2000
⇒ 20r = 100
⇒ r = 100/20
⇒ r = 5

∴ Rate of compound interest is 5%

৫৯৮.

The interest on a certain deposit at 4.5% p.a. is TK. 202.50 in one year. How much will the additional interest in one year be on the same deposit at 5% p.a. ?

ক
ক) Tk. 20.50
খ
খ) Tk. 24.50
গ
গ) Tk. 25.50
ঘ
ঘ) Tk. 22.50

ব্যাখ্যা

S.I = TK. 202.50
r = 4.5%
n = 1

Now
I = pnr/100
P = I × 100/nr = ( 202.50 × 100)/( 1× 4.5) = 4500 Tk.

Again
I = pnr
= 4500 × 1 × 5/100 = 225

The total additional interest = ( 225 - 202.50) Tk. = Tk. 22.50

৫৯৯.

A sum of money amounts of Tk. 460 in 3 years and to Tk. 500 in five years. Find the rate percent per annum

ক
ক) 5 Tk
খ
খ) 10 Tk
গ
গ) 15 Tk
ঘ
ঘ) 25 Tk

ব্যাখ্যা

৫ বছরের সুদ + আসল = ৫০০ টাকা
৩ বছরের সুদ + আসল = ৪৬০ টাকা

২ বছরের সুদ = ৪০ টাকা
৩ বছরের সুদ = (৪০ ×৩)/২ টাকা
= ৬০ টাকা
আসল = (৪৬০ - ৬০) টাকা = ৪০০ টাকা

৪০০ টাকায় ৩ বছরের সুদ ৬০ টাকা
১ টাকায় ১ বছরের সুদ ৬০/(৪০০ × ৩) টাকা
১০০ টাকায় ১ বছরের সুদ (৬০ × ১০০)/(৪০০ × ৩) টাকা
= ৫ টাকা

৬০০.

The market value of a 10.5% stock, in which an income of Tk. 756 is derived by investing Tk. 9000, brokerage being (1/4)% is -

ক
ক) Tk. 108.25
খ
খ) Tk. 112.20
গ
গ) Tk. 124.75
ঘ
ঘ) Tk. 125.25

ব্যাখ্যা

For an income of Tk. 756, investment
= Tk. 9000

For an income of Tk. (21/2), investment
= Tk. {(9000/756) × (21/2)}
= Tk. 125

∴ For a Tk. 100 stock, investment = Tk. 125

The market value of Tk. 100 stock
= Tk. {125 - (1/4)}
= Tk. 124.75