# Compound Interest Questions with Answers

## 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.

### 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.

### 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%

12.44%

4%

4%

18.43%

8%

8%

58.99%

9%

9%

10.14%

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%

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

65.41%

INR 4500.08

INR 4500.08

14.59%

INR 3987.76

INR 3987.76

9.73%

INR 3154.34

INR 3154.34

10.27%

=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

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

14.57%

2948

2948

64.9%

2700

2700

15.23%

4345

4345

5.3%

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

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

79.74%

3000

3000

5.23%

6000

6000

7.19%

5500

5500

7.84%

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

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

6.25%

18967.22

18967.22

15.97%

16612

16612

70.83%

19873

19873

6.94%

13560(1 + 7/100)³

Required population: 13560(1.07)³ = 16612

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

20%

20%

10.26%

10%

10%

14.53%

9.20%

9.20%

63.25%

8.90%

8.90%

11.97%

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%

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

8%

8%

8.11%

8.87%

8.87%

17.12%

5.01%

5.01%

69.37%

7.24%

7.24%

5.41%

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%

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

16.3%

5678

5678

16.3%

5643

5643

6.52%

4930

4930

60.87%

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

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%

11.54%

19%

19%

8.65%

19.05%

19.05%

16.35%

18%

18%

63.46%

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%.

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

8.26%

3002

3002

12.4%

3798

3798

10.74%

3542

3542

68.6%

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

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