Question

A sum of Rs $13240$ is borrowed from a money lender at the rate of $10\mathrm{\%}$ p.a. compounded annually. If the amount is to be paid back in three yearly instalments, find the annual installment?

Answer 1

Hint: Interest is the amount of money paid for using someone else’s money. There are two types of interest. $1)$ Simple Interest and $2)$ Compound interest. Interest can be calculated on the basis of various factors. Here we will calculate the amount after one year. Use formula –
 $A=P{\left(1+{\displaystyle \frac{R}{100}}\right)}^T$ Where A is the amount, P is the Principal amount and R is the rate of interest.

Complete step-by-step answer:
Given that: Principal Amount, $P=\text{Rs}\text{. 13240}$
Rate of interest, $R=10\mathrm{\%}$
Term period, $T=3\text{ years}$
Here we will find Amount to be paid annually; therefore take Term T is equal to one here.
 $A=P{\left(1+{\displaystyle \frac{R}{100}}\right)}^T$
Place the known values in the above equations –
 $$A=13240\left(1+{\displaystyle \frac{10}{100}}\right)$$
Simplify the above equation-
 $$\begin{gathered} A=13240\left({\displaystyle \frac{100+10}{100}}\right) \\ A=13240\left({\displaystyle \frac{110}{100}}\right) \\ A=14564\text{Rs}\text{.} \end{gathered}$$
Therefore, Interest = Amount – Principal
 $$\begin{gathered} \therefore I=A-P \\ \therefore I=14564-13240 \\ \therefore I=Rs.\text{ 1324} \end{gathered}$$
Hence, the required answer - the annual instalment will be Rs. $1324$
So, the correct answer is “Rs. $1324$ ”.

Note: In other words present value shows that the amount received in the future is not as worth as an equal amount received today. Always remember the relation among the present value and the principal amount. Always convert the percentage rate of interest in the form of fraction or the decimals and then substitute further for the required solutions. Know the difference between the simple interest method and compound interest method. Simple interest is calculated on the basis of the principal amount whereas the compound interest is calculated on the basis of the principal amount and the interest accumulated in all the previous years of the term period.