Mrs. Karna has a recurring deposit account in Punjab National Bank for 3 years at 8% p.a. If she gets ₹ 9990 as interest at the time of maturity, find :

(i) the monthly instalment

(ii) the maturity value of the account.

(i) Given,

Time (n) = 3 years = 3 × 12 = 36 months.

Rate = 8%

Let monthly instalment be ₹ P.

By formula,

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

Substituting values we get

$\Rightarrow 9990 = P \times \dfrac{36 \times 37}{2 \times 12} \times \dfrac{8}{100} \\[1em] \Rightarrow 9990 = P \times \dfrac{3 \times 37}{2} \times \dfrac{8}{100} \\[1em] \Rightarrow 9990 = P \times \dfrac{3 \times 37}{25} \\[1em] \Rightarrow P = \dfrac{9990 \times 25}{3 \times 37} \\[1em] \Rightarrow P = \dfrac{249750}{111} \\[1em] \Rightarrow P = ₹ 2250.$

Hence, monthly installment = ₹ 2250.

(ii) Maturity value of recurring deposit = Total sum deposited + Interest on it

= P × n + 9990

= 2250 × 36 + 9990

= 81000 + 9990

= ₹ 90990.

Hence, the maturity value of this account = ₹ 90990.