Question

Nidhi deposited Rs7,500 in a bank which pays her 4% interest per annum compounded annually. Find the amount and the interest received by her after three years.

Answer 1

Hint: Before starting the simplification of the above formula we should have the basic idea on the simple interest and the compound interest. So we are going to start the solution of above problem with
the calculation of the amount of the principle by using the formula $ A=P{{\left( 1+\dfrac{r}{100} \right)}^{t}} $ . After that we have to use the formula, $ CI=A-P $ to determine the compound interest. We have to find the amount on the principle which is provided by the bank, then use the compound interest formula to calculate the interest amount. If in the problem time is not given compounded, then we have to use the simple interest formulas for the calculation.

Complete step-by-step answer:
The amount deposited by Nidhi is, (P)=7500
The rate of interest paid by the bank is, (r)= 4% per annum compounded annually.
We have to find the amount received by the Nidhi after (t)=3 years.
So we are going to determine the amount as follows,
 $ \begin{align}
\Rightarrow & A=7500{{\left( 1+\dfrac{4}{100} \right)}^{3}} \\
\Rightarrow & A= 7500 {{\left( 1+\dfrac{1}{25} \right)}^{3}} \\
 & =8436.48
\end{align} $
After determining the amount, we are going to calculate the compound interest of the principal amount as follows:
 $ \begin{align}
\Rightarrow & CI=8436.48-7500 \\
 & =936.48
\end{align} $
Therefore, we have calculated the required amount 8436.48 rupees, and the required interest of the principal amount is 936.48 rupees.

Note: We have to be careful when the checking of rate of interest is compounded annually or half yearly or quarterly before calculating the amount. We also have to be careful during the calculation part of the amount of the principle. After calculating the amount, we have to calculate the compound interest.