Question

Mrs. Rita deposits ₹1600 every month in recurring deposit account at 9% p.a. simple interest. She receives ₹65,592 at the time of maturity. What is the total time for which the account was held?

• A. 16 months
• B. 24 months
• C. 47 months
• D. 36 months

Answer 1

The correct option is D

36 months

Let the time of the recurring deposit in month be n

Monthly installment = ₹1600

Amount Deposited = 1600 x n = 1600n

Rate of Interest = 9%

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

= 1600 $\times$ $\frac{n\times (n+1)}{2\times 12}$ $\times$ $\frac{9}{100}$

= 6 $\times$n $\times$ (n+1)

= 6 $n^2$ + 6 n

Given Maturity Value = 65592

Maturity Value = Amount Deposited + Interest

65592 = 1600n + 6 $n^2$ + 6 n

65592 = 1606n + 6 $n^2$

6 $n^2$ + 1606 n - 65592 = 0

(n-36)(3n+911) = 0

n = 36 and n = -911/3 (neglecting -911/3 as n cannot be negative as it time period)

Therefore, the time for which he held the account = 36 months or 3 years.