Question

Vaideesh deposits $Rs.500$ at the beginning of every month for $5$ years in a post office. If the rate of interest is $7.5\% $, find the amount he will receive at the end of five years.

Answer 1

Hint: We can calculate the total number of months the amount is deposited. Multiplying the number of months with the deposited amount we get the principal. Then we can calculate the period for recurring deposit. Substituting the principal, period and rate of interest, we get the interest. Adding interest to the principal, we get the due amount.

Formula used: Period for recurring deposit, $N = \dfrac{1}{{12}}[\dfrac{{n(n + 1)}}{2}]$ years, where $n$ is the number of months.
The interest is given by, $I = \dfrac{{PNr}}{{100}}$
Where, $P$ is the principal, $N$ is the period and $r$ is the rate of interest.

Complete step-by-step answer:
Given that Vaideesh deposits $Rs.500$ every month for $5$ years.
Also the rate of interest is given as $r = 7.5\% $.
We have to find the amount he will receive at the end of five years.
Let the principal amount deposited by Vaideesh is \[P\] and the number of months be $n$.
This gives, $n = 5 \times 12 = 60$ months.
And $P = 500 \times n = 500 \times 60 = 30000$
We know the period for recurring deposit, $N = \dfrac{1}{{12}}[\dfrac{{n(n + 1)}}{2}]$ years.
Substituting the values we get the period for recurring deposit, $N = \dfrac{1}{{12}}[\dfrac{{60(60 + 1)}}{2}]$
Simplifying we get,
$N = \dfrac{{60 \times 61}}{{24}} = \dfrac{{305}}{2}$
So we get the period as $\dfrac{{305}}{2}$ years.
The interest is given by, $I = \dfrac{{PNr}}{{100}}$
Substituting the values we get,
$I = \dfrac{{500 \times \dfrac{{305}}{2} \times 7.5}}{{100}}$
This can be written as,
$I = \dfrac{{500 \times 305 \times 15}}{{100 \times 2 \times 2}}$
Simplifying we get
$I = \dfrac{{5 \times 305 \times 15}}{4} = 5718.75$
Now the total amount he will receive is the sum of principal amount and the interest.
So we have,
Total amount due, $A = P + I$
Substituting we get,
$A = 30000 + 5718.75 = 35718.75$

$\therefore $ The answer is $Rs.35718.75$

Note: If the deposit is made in a single time, it is easy to calculate the interest amount. Simply we can substitute the principal, rate of interest and number of years. But since here the deposit is made every month, we had to calculate the period for recurring deposits.