Mr. Richard has a recurring deposit account in a post office for 3 years at 7.5% p.a. simple interest. If he gets ₹ 8325 as interest at the time of maturity, find :

(i) the monthly installment.

(ii) the amount of maturity.

(i) Let monthly installment be ₹ x.

So,

P = ₹ x, r = 7.5% and n = (3 × 12) = 36 months.

I = $P \times \dfrac{n(n + 1)}{2 \times 12} \times \dfrac{r}{100}$

$\therefore I = ₹ x \times \dfrac{36 \times 37}{2 \times 12} \times \dfrac{7.5}{100} \\[1em] = \dfrac{9990x}{2400} \\[1em] = \dfrac{333x}{80}$

Given, interest = ₹ 8325

$\Rightarrow \dfrac{333x}{80} = 8325 \\[1em] \Rightarrow x = \dfrac{8325 \times 80}{333} \\[1em] \Rightarrow x = 25 \times 80 = ₹ 2000.$

Hence, Richard's monthly installment is ₹ 2000.

(ii) Maturity value = Sum deposited + Interest

= ₹ 2000 × 36 + ₹ 8325

= ₹ 72000 + ₹ 8325

= ₹ 80325.

Hence, the amount of maturity = ₹ 80325.