Question

Manoj opened a recurring deposit account with Punjab National Bank and deposited Rs.
$500$ per month for $3$ years. The bank paid him Rs. $20,220$ on maturity. Find the rate of
interest paid by the bank.

Answer 1

Hint: Use the formula given below to find the interest paid by the bank to the Manoj.
Interest$ = \dfrac{{P \cdot n\left( {n + 1} \right)r}}{{2400}}$
Use the resultant interest to find the total amount paid by the bank, it helps to approach the
required result.

It is given that Manoj deposited Rs. $500$ per month for $3$ years and the bank paid him Rs.
$20,220$ on maturity.
We have to find the rate of interest paid by the bank.
Given,
Maturity value (Amount)$ = Rs.{\text{ }}20,220$;
Monthly installment (P)$ = Rs.{\text{ }}500$;
Time$\left( n \right) = 3$years
First, convert the years in months. We know that:
$1$Year$ = 12$months
$3$Year$ = 12 \times 3 = 36$months
So, Time$\left( n \right) = 36$months
The interest paid by the bank to the Manoj is given as:
Interest$ = \dfrac{{P \cdot n\left( {n + 1} \right)r}}{{2400}}$
Substitute the values maturity value (Amount)$ = Rs.{\text{ }}20,220$, monthly installment
(P)$ = Rs.{\text{ }}500$, time$\left( n \right) = 36$months into the formula:
Interest$ = \dfrac{{500 \cdot 36\left( {36 + 1} \right)r}}{{2400}}$
Simplify the value to get the interest:
Interest$ = \dfrac{{5 \cdot 36 \cdot 37 \cdot r}}{{24}}$

Interest$ = \dfrac{{555r}}{2}$
So, the interest paid by the bank to the Manoj is Rs.$\dfrac{{555r}}{2}$, where $r$ is the rate of
interest.
Now, the total amount paid by the bank to the Manoj is the sum of the amount paid by the Manoj
in installments and the interest on that amount. That is,
Total amount$ = {\text{Amount paid in 3 years}} + {\text{Interest paid by bank}}$
Total amount$ = P \cdot n + \dfrac{{555r}}{2}$
Substitute the total maturity amount as Rs.$20,220$,$P = 500$ and$n = 36$, so we have
$20,220 = 500 \cdot 36 + \dfrac{{555r}}{2}$
Solve the equation for:
$20,220 = 18,000 + \dfrac{{555r}}{2}$
$\dfrac{{555r}}{2} = 20220 - 18000$
$\dfrac{{555r}}{2} = 2220$
$r = \dfrac{{2220 \times 2}}{{555}}$
$r = 8$
Therefore, the rate of interest paid by the bank to the Manoj is$8\% $.

Note: The period of time, for which the Manoj paid the installment is taken in terms of months in
the formula of finding the interest.