Compound Interest Problems Solutions

• 15. The least number of complete years in which a sum of money put out at 20% compound interest will be more than doubled is

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

  Answer :

  Option A

  Explanation:

  As per question we need something like following
  
  \begin{aligned}
  P(1+\frac{R}{100})^n > 2P \\
  (1+\frac{20}{100})^n > 2 \\
  (\frac{6}{5})^n > 2 \\
  \frac{6}{5} \times \frac{6}{5} \times \frac{6}{5}\times\frac{6}{5} > 2
  
  \end{aligned}
  
  So answer is 4 years
  

• 16. A man saves Rs 200 at the end of each year and lends the money at 5% compound interest. How much will it become at the end of 3 years.

  1. Rs 662
  2. Rs 662.01
  3. Rs 662.02
  4. Rs 662.03

  Answer :

  Option C

  Explanation:

  \begin{aligned}
  [200(1+\frac{5}{100})^3 + 200(1+\frac{5}{100})^2+ \\ 200(1+\frac{5}{100})]
  
  = [200(\frac{21}{20} \times \frac{21}{20} \times \frac{21}{20})\\
  + 200(\frac{21}{20}\times\frac{21}{20})+200(\frac{21}{20})] \\
  
  = 662.02
  \end{aligned}

• 17. 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 :

  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%