Mr. Kumar has a recurring deposit account in a bank for 4 years at 10% p.a. rate of interest. If he gets ₹ 21,560 as interest at the time of maturity, find :

(i) the monthly instalment paid by Mr. Kumar.

(ii) the amount of maturity of this recurring deposit account.

(i) Let monthly deposit be ₹ P.

Given,

Time = 4 years = 4 × 12 = 48 months.

By formula,

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

Substituting values we get :

$\Rightarrow 21560 = P \times \dfrac{48 \times (48 + 1)}{2 \times 12} \times \dfrac{10}{100} \\[1em] \Rightarrow 21560 = P \times \dfrac{48 \times 49}{24} \times \dfrac{1}{10} \\[1em] \Rightarrow P = \dfrac{21560 \times 24 \times 10}{48 \times 49} \\[1em] \Rightarrow P = \dfrac{107800}{49} = ₹ 2,200.$

Hence, monthly installment = ₹ 2,200.

(ii) By formula,

Maturity value = P × n + Interest

= ₹ 2200 × 48 + ₹ 21560

= ₹ 105600 + ₹ 21560

= ₹ 1,27,160.

Hence, amount of maturity = ₹ 1,27,160.