Question

What sum of money will amount to Rs.5445 in 2 years at 10% per annum compound interest?

Answer 1

Hint: In the case of compound interest, we calculate the interest for the first period and then add it to the amount borrowed, then calculate the interest for the next period using the new amount and so on. In the given question, we are given the amount repaid, the compound interest on it and the time period for which the amount was borrowed, so using the formula for calculating the amount to be repaid on compound interest, we can find out the correct answer.

Complete step-by-step answer:
The amount that has to be repaid on compound interest is calculated by the formula,
 $ A = P{(1 + \dfrac{r}{{100}})^n} $ , where $ A = $ final amount, $ P = $ the amount borrowed, $ r = $ interest and $ n = $ number of periods.
Now, the amount to be paid after 2 years is Rs.5445 so \[A = Rs.5445\] and $ n = 2 $ , the compound interest per annum is 10% so $ r = 10\% $ and we have to find the principal amount.
Put the known values in the given above equation,
 $
  5445 = P{(1 + \dfrac{{10}}{{100}})^2} \\
  5445 = P{(\dfrac{{11}}{{10}})^2} \\
  5445 = P(\dfrac{{121}}{{100}}) \\
   \Rightarrow P = 100 \times \dfrac{{5445}}{{121}} \\
   \Rightarrow P = 100 \times 45 \\
   \Rightarrow P = Rs.4500 \;
  $
Hence, Rs.4500 will amount to Rs.5445 in 2 years at 10% per annum compound interest.
So, the correct answer is “Rs.4500”.

Note: Banks or money lenders lend money to the businessmen or the people who are in need and gain more money at the time of repayment because of the interest on the money lent. Interest is the amount paid after a regular interval of time by the borrower as rent for the money lent. There are two types of interests namely – Simple interest and Compound interest.