Question

Mrs. Rita deposits Rs 1600 every month in recurring deposit account at 9% p.a. simple interest. She receives Rs 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 number of installments be x

Monthly installment = Rs 1600

Equivalent principal for 1 month =1600 $\times$ $\frac{x(x+1)}{2}$

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

$1600x+1600\times \frac{x(x+1)}{2}\times \frac{1}{12}\times \frac{9}{100}=65,592$

$3x^2+803x–32796=0$

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

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

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