Question

Sameerrao has taken a loan of Rs. 12500 at a rate of 12 p.c.p.a. for 3 years. If the interest is compounded annually then how many rupees should he pay to clear his loan?

Answer 1

Hint: To calculate the final amount of a loan when the interest is compounded annually use $ F = P{\left( {1 + \dfrac{R}{{100}}} \right)^n} $ formula where F is the final amount, P is the principal amount, R is the rate of interest or interest rate, n is the time period.

Complete step-by-step answer:
We are given that Sameerrao has taken a loan of Rs. 12500 at 12 percent compound interest rate annually for 3 years.
We have to calculate the final amount to pay off his loan.
 $ F = P{\left( {1 + \dfrac{R}{{100}}} \right)^n} $
Substitute the values of P, R and n values to solve for F.
 $
  R = 12,P = 12500,n = 3 \\
  F = P{\left( {1 + \dfrac{R}{{100}}} \right)^n} \\
  F = 12500{\left( {1 + \dfrac{{12}}{{100}}} \right)^3} \\
  F = 12500{\left( {\dfrac{{100 + 12}}{{100}}} \right)^3} \\
  F = 12500{\left( {\dfrac{{112}}{{100}}} \right)^3} \\
  F = 12500{\left( {\dfrac{{28}}{{25}}} \right)^3} \\
  {\left( {\dfrac{{28}}{{25}}} \right)^3} = \dfrac{{{{28}^3}}}{{{{25}^3}}} = \dfrac{{21952}}{{15625}} \\
  F = 12500 \times \dfrac{{21952}}{{15625}} \\
  F = 17561.6 \\
 $
Therefore, to clear the loan Sameer Rao should pay 17,561 rupees and 60 paisa for a principal amount of Rs. 12500 with 12 percent compound interest for 3 years.

Note: Compound interest is adding interest to the principal sum of a loan or a deposit. It is the result of reinvesting interest, rather than paying it out, so the interest in the next period is then earned on the principal sum plus previously accumulated interest. In simple interest the interest will be constant. So do not confuse Compound interest with simple interest.