Compound Interest Questions Answers

• 15. On a sum of money, simple interest for 2 years is Rs 660 and compound interest is Rs 696.30, the rate of interest being the same in both cases.

  1. 8%
  2. 9%
  3. 10%
  4. 11%

  Answer And Explanation

  Answer: Option D

  Explanation:

  Difference between C.I and S.I for 2 years = 36.30
  S.I. for one year = 330.
  S.I. on Rs 330 for one year = 36.30
  
  So R% = \frac{100*36.30}{330*1} = 11%

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• 16. Effective annual rate of interest corresponding to nominal rate of 6% per annum compounded half yearly will be

  1. 6.09%
  2. 6.10%
  3. 6.12%
  4. 6.14%

  Answer And Explanation

  Answer: Option A

  Explanation:

  Let the amount Rs 100 for 1 year when compounded half yearly, n = 2, Rate = 6/2 = 3%
  
  

  $$\begin{aligned} Amount = 100(1+\frac{3}{100})^2 = 106.09 \end{aligned}$$
  
  Effective rate = (106.09 - 100)% = 6.09%

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• 17. A sum of money invested at compound interest to Rs. 800 in 3 years and to Rs 840 in 4 years. The rate on interest per annum is.

  1. 4%
  2. 5%
  3. 6%
  4. 7%

  Answer And Explanation

  Answer: Option B

  Explanation:

  S.I. on Rs 800 for 1 year = 40
  
  Rate = (100*40)/(800*1) = 5%

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• 18. We need to divide Total Sum Rs. 3364 between Ram and Sham so that Ram's share at the end of 5 years may equal to Sham's share at the end of seven years with compound interest rate at 5 percent.

  1. 1864 and 1500
  2. 1764 and 1600
  3. 1664 and 1700
  4. 1564 and 1800

  Answer And Explanation

  Answer: Option B

  Explanation:

  It is clear from question that Ram's share after five years = Sham's share after seven years
  Hence we can conclude following :
  

  $$\begin{aligned} \text{(Rams's present share)}\left(1 + \dfrac{5}{100}\right)^5 = \text{(Sham's present share)}\left(1 + \dfrac{5}{100}\right)^7\\ => \dfrac{\text{(Ram's present share)}}{\text{(Sham's present share)}}= \dfrac{\left(1 + \dfrac{5}{100}\right)^7}{\left(1 + \dfrac{5}{100}\right)^5} \\ = \left(1 + \dfrac{5}{100}\right)^{(7-5)} = \left(1 + \dfrac{5}{100}\right)^2 \\ = \left(\dfrac{21}{20}\right)^2 = \dfrac{441}{400} \end{aligned}$$
  Ram's present share : B's present share = 441 : 400
  
  $$\begin{aligned} \text{As amount is Rs.3364, Ram's share = }3364 \times \dfrac{441}{(441+400)} \\\\ = 3364 \times \dfrac{441}{841} = 4 \times 441 = \text{ Rs. 1764} \end{aligned}$$
  
  So Sham's share is = 3364-1764 = 1600

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