Question

Mr. Richard has a recurring deposit account in a post office for $3$ years at $7.5\%\mathrm{p}.\mathrm{a}.$ simple interest. If he gets $\mathrm{Rs}8,325$ as interest at the time of maturity, find: (i) the monthly installment. (ii) the amount of maturity.

Answer 1

Step 1. Find the monthly installment.

Let the deposit per month$=\mathrm{Rs}.p$

Number of months$,n=36$

$$\begin{gathered} \begin{array}{l}I=P\times \frac{n(n+1)}{2\times 12}\times \frac{r}{100}\end{array} \\ \Rightarrow 8,325=P\times \frac{36(36+1)}{2\times 12}\times \frac{7.5}{100} \\ \Rightarrow 8,325=P\times \frac{36\times 37}{2\times 12}\times \frac{7.5}{100} \\ \Rightarrow P=\frac{8325\times 2\times 12\times 100}{36\times 37\times 7.5} \\ \therefore P=\mathrm{Rs}.2000 \end{gathered}$$

Step 2. Find the amount of maturity.

Amount of maturity is,

$$\begin{gathered} A=n\times I+P \\ =36\times 8325+2000 \\ =\mathrm{Rs}.80325 \end{gathered}$$

Hence,

(i) The monthly installment is $\mathrm{Rs}.2000$.

(ii) Amount of maturity is $\mathrm{Rs}.80325$.