A cumulative deposit account of monthly installment of ₹ 3,600 at 9% p.a. simple interest earns an interest of ₹ 17,982. Find the number of installments paid.

Given,

Monthly installment = ₹ 3,600

Rate = 9%

Interest = ₹ 17,982

Let no. of installments paid be n.

So, months = n.

By formula,

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

Substituting values we get :

$\Rightarrow 17982 = 3600 \times \dfrac{n(n + 1)}{2 \times 12} \times \dfrac{9}{100} \\[1em] \Rightarrow 17982 = \dfrac{27}{2} \times (n^2 + n) \\[1em] \Rightarrow n^2 + n = \dfrac{17982 \times 2}{27} \\[1em] \Rightarrow n^2 + n = 1332 \\[1em] \Rightarrow n^2 + n - 1332 = 0 \\[1em] \Rightarrow n^2 + 37n - 36n - 1332 = 0 \\[1em] \Rightarrow n(n + 37) - 36(n + 37) = 0 \\[1em] \Rightarrow (n - 36)(n + 37) = 0 \\[1em] \Rightarrow n - 36 = 0 \text{ or } n + 37 = 0 \\[1em] \Rightarrow n = 36 \text{ or } n = -37.$

Since, months cannot be negative.

∴ n = 36.

Hence, no. of installments paid = 36.