Compound Interest Questions with Answers

September 15, 2023

Compound Interest Questions with Answers

Basic concept of Compound Interest and Compound Interest Questions with Answers are  provided here to help the students understand the applications of compound interest in our daily existence.

Compound Interest Questions and Answers

Important Formulae to solve Compound Interest Questions :

  • P [1+ \frac{R}{100}]^{T}

    This formula is applied to calculate when money is compounded annually.

  • P [1+ \frac{R}{2\times 100}]^{2T}

    This formula is applied to calculate when money is compounded half-yearly

  • P [1+ \frac{R}{12\times 100}]^{12T}

    This formula is applied when money in compounded monthly.

Formula of Compound Interest Problems

Situations where we can use Compound Interest formulas.

  • Increase or decrease in population
  • The growth of a bacteria (when the rate of growth is known)
  • The value of an item, if its price increases or decreases in the intermediate years

Compound Interest Questions and Answers

Example 1:

The compound interest on Rs. 10,000 in 2 years at 4% per annum, the interest being compounded yearly, is

Options:

a. Rs 636.80
b. Rs 816
c. Rs 912
d. Rs 882.82

Explanation:

Rate of interest = 4%

Therefore, applying the net% effect formula for effective rate of compound interest for 2 years , we get

Net% effect = x + y + \frac{xy}{100}\%

x = y = 4%

= 4 + 4 + \frac{4\times 4}{100} = 8 + .16 = 8.16\%

CI = 8.16% of 10,000

= \frac{8.16\times  10000}{100} = ₹ 816

Hence, option B is correct,

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Practice Compound Interest Questions with Answers

1. If 50000 sums to 58694 in 2 years. Find out the rate of interest.

5%

5%

18.52%

4%

4%

22.22%

8%

8%

40.74%

9%

9%

18.52%

Given: A = 58694 P = 50000 n = 2 years r=?
A = P (1 + r/100)n
=>58694 = 50000 (1 + r/100)²
=>58694/50000 = (1 + r/100)²
=>(1+ r/100) = sqrt (1.17)=1.08
=>r/100=1.08-1=0.08
=>r = 0.08 x 100 = 8%

Good Job! Did you know? : With $8.5 billion in their kitty, Wipro is the 4th largest Indian IT company in terms of revenue.

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2. Calculate the compound interest on Rs 9,000 at an annual rate of 15% for 2 years and 4 months?

INR 3497.625

INR 3497.625

64.29%

INR 4500.08

INR 4500.08

14.29%

INR 3987.76

INR 3987.76

10.71%

INR 3154.34

INR 3154.34

10.71%

=9000(1+15/100)2⅓

=9000(1+3/20)² x (1+3/20x3)

=9000* (23/20)  x (23/20)  x  (21/20)

=12497.625

∴ Compound Interest = Rs. (12497.625– 9000) = Rs. 3497.625

Good Job! Did you know? : With $8.5 billion in their kitty, Wipro is the 4th largest Indian IT company in terms of revenue.

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3. What would be the compound interest on Rs 8000 for 4 years at 8 % per annum?

Note: the interest is calculated half-yearly.

3900

3900

7.69%

2948

2948

69.23%

2700

2700

15.38%

4345

4345

7.69%

Given: P = Rs.8000, rate of interest = 8%, T = 4years, n = 2

calculation: half-yearly, therefore, r=   8 %=4%

nT=2 x 4=8

A=8000( 1 + 8/100 x 2)⁸ =8000× (26/25)⁸

=8000 x 1.3685=10948

Interest = Amount - Principal = `10948 - 8000 = 2948

Good Job! Did you know? : With $8.5 billion in their kitty, Wipro is the 4th largest Indian IT company in terms of revenue.

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4. The difference between Simple interest and compound interest for 2 years at the rate of 10% per annum on a particular amount of money is Rs20. Calculate the amount:

2000

2000

69.57%

3000

3000

4.35%

6000

6000

8.7%

5500

5500

17.39%

Let the sum be `100.

Therefore, SI=100×10×2/100 = `20

and CI=100 (1 + 10/100)² - 100 = 121 − 100 = 21

Difference of CI and SI = 21 − 20= 1

Now if the difference is 1 , then the total= 100

So if the difference is 20 then the total will be= 100× 20 = INR 2000

Good Job! Did you know? : With $8.5 billion in their kitty, Wipro is the 4th largest Indian IT company in terms of revenue.

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5. If the annual increase in the inhabitants of a particular city is 7% and the total number of residents in that specific locality is 13560 what will be the population of that same city in the coming 3 years?

17000

17000

19.05%

18967.22

18967.22

23.81%

16612

16612

47.62%

19873

19873

9.52%

13560(1 + 7/100)³

Required population: 13560(1.07)³ = 16612

Good Job! Did you know? : With $8.5 billion in their kitty, Wipro is the 4th largest Indian IT company in terms of revenue.

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6. Calculate the actual rate of interest corresponding to an itemized rate of 9% compound semi-annually.

20%

20%

17.65%

10%

10%

17.65%

9.20%

9.20%

41.18%

8.90%

8.90%

23.53%

Measurement shows that 100 at 9% compounded semi-annually will grow to

A=100 (1 + .09/2)² = 100(1.045)²

=100(1.09)=109.20

So the actual rate=109.20 - 100=9.20. Thus if we get 9.20 % 100 in 1 year with yearly compounding, then the rate will be 9.20/100=0.092=9.20 so the actual rate = 9.20%

Good Job! Did you know? : With $8.5 billion in their kitty, Wipro is the 4th largest Indian IT company in terms of revenue.

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7. Sumit invested in the bank on which he gets an interest of 4.9% compounded monthly. Calculate the actual interest rate.

8%

8%

22.22%

8.87%

8.87%

11.11%

5.01%

5.01%

55.56%

7.24%

7.24%

11.11%

Given r=.049 and m= 12.

Value of `p after n years = p (1+ r/100)n

Effective rate is re = (1 + .049/12)12 − 1

=1.050115575-1=.0501

or 5.01%

Good Job! Did you know? : With $8.5 billion in their kitty, Wipro is the 4th largest Indian IT company in terms of revenue.

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8. Manoj bought a microwave on which he has to pay INR 2000 cash as a down payment. After this he is supposed to pay INR 1,500 at the completion of 1st year, INR 1,050 at the completion of 2nd year and INR 930 at the completion of 3rd The interest rate on this is 10%. Compute the total cash price:

9800

9800

42.86%

5678

5678

14.29%

5643

5643

7.14%

4930

4930

35.71%

Down payment = INR 2000

So at the completion of 1st-year x will become INR 1500.

So, 1500 = x (1 + 10/100) or

x = (1500×100/110) = 1363.63

Similarly, 1050 = y (1 + 10/100)² or y= (1050×20×20/22×22) = 420,000/484=867.76

and z = (930×20×20x20/22×22×22) = 698.72

Hence, CP = 2000+1363.63+867.76+698.72 = 4930.11 or 4930

Good Job! Did you know? : With $8.5 billion in their kitty, Wipro is the 4th largest Indian IT company in terms of revenue.

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9. Amanpreet invested his savings in such a way that his money grows up to INR 4645 in every two years and up to 5500 in 3 every year including the interest compounded. Calculate the interest rate applicable to earn this much of money?

20%

20%

11.11%

19%

19%

16.67%

19.05%

19.05%

11.11%

18%

18%

61.11%

As given, P+ Compound Interest of 3 years = 5500.......(i)
P+ Compound Interest of 2 yrs = 4645.......(ii)
By solving the equations we get Compound Interest of 3rd year = 5500-4645 = 855
Alternate method:
Difference of sum after n years and n + 1 years × 100 /Amount after n years
Here n=2
Rate = [(5500−4645) × 100] /4645= (855×100)/4645 = 18.40% or 18%.

Good Job! Did you know? : With $8.5 billion in their kitty, Wipro is the 4th largest Indian IT company in terms of revenue.

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10. Calculate the compound interest on INR 28,750 for 2 years. The interest was calculated as 4% in the first year and 8% in second year.

2500

2500

21.05%

3002

3002

15.79%

3798

3798

5.26%

3542

3542

57.89%

After first year the amount =

28750 (1 + (4/100)) = 28750 (104/100)

After 2 nd year the amount = 28750 (104/100) (108/100)

=28750 (26/25) (27/25) = (1.12 x 28750)=32292

CI = 32292-28750 = 3542

Good Job! Did you know? : With $8.5 billion in their kitty, Wipro is the 4th largest Indian IT company in terms of revenue.

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Compound Interest Important Formulas
How to solve Compound Interest Questions Quickly
Compound Interest Shortcuts, Tips and Tricks
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