Question

Mr. Richard has a recurring deposit account in a post office for $3$ years at $7.5\%$ p.a. simple interest. If he gets $Rs8,325$ as interest at the time of maturity, find:
(i) the monthly instalment.
(ii) the amount of maturity.

Answer 1

$\left(i\right)$ Let the deposit per month $=Rs.p$
Number of months $\left(n\right)=36$ as given time is $3$ years
Rate of interest $\left(r\right)$ $=7.5\%$ p.a

Since, we have $S.I=P\times \frac{n(n+1)\times r}{2\times 12}$
Substituting given values, we get
$\Rightarrow S.I=P\times \frac{n\left(n+1\right)}{2\times 12}\times \frac{r}{100}$

$\Rightarrow 8325=P\times \frac{36\times 37}{2\times 12}\times \frac{7.5}{100}$

$\Rightarrow 8325=P\times \frac{3\times 37}{2}\times \frac{7.5}{100}$

$\Rightarrow P=\frac{8325\times 2\times 100}{3\times 37\times 7.5}=Rs.2000$
Therefore, monthly instalment amount is $Rs2000$

$\left(2\right)$ maturity value $=P\times n+S.I$
Substitute above values, we get
$=Rs.\left(2000\times 36+8325\right)$
$=Rs.80325$
Therefore, the amount of maturity is $Rs.80325$