Question

Find the amount when Rs. 10,800 for 3 years at 12.5% per annum compounded annually.

Answer 1

Hint: Compound interest is the interest calculated on the initial principal, which also includes all of the accumulated interest from previous periods on a deposit or loan. The formula for compound interest is-
${\text{A}} = {\text{P}}{\left( {1 + \dfrac{{\text{r}}}{{100}}} \right)^{\text{t}}}$
Here A is the final amount, P is the initial principal amount, r is the rate of interest, and t is the time in years.

Complete step-by-step answer:
We have been given that Rs. 10,800 for 3 years at 12.5% per annum is compounded annually. We have to find the final amount at the end of three years. This can be easily done as-
Substituting P = 10800, r = 12.5 and t = 3,
$\begin{align}
  &{\text{A}} = 10800{\left( {1 + \dfrac{{12.5}}{{100}}} \right)^3} \\
  &{\text{A}} = 10800{\left( {1.125} \right)^3} \\
  &{\text{A}} = 10800\left( {1.4238} \right) \\
  &{\text{A}} = Rs.\;15377.343 \\
\end{align} $

The total amount when Rs. 10,800 for 3 years at 12.5% per annum is compounded annually is Rs. 15377.343. This is the required answer.

Note: Students often get confused between compound interest and simple interest. Simple interest is calculated with respect to the initial principal only. For compound interest, the interest is applied on the previous amount, and increases exponentially each year. The formula for simple interest is-
${\text{I}} = \dfrac{{PRT}}{{100}}$