Question

Rohan has a recurring deposit account in State Bank of India of ₹2000 per month at the rate of 10% per annum. He receives ₹83100 at the time of maturity. What was the time period for which he held the account?

• A. 36 months
• B. 16 months
• C. 24 months
• D. 30 months

Answer 1

The correct option is A

36 months

Let the number of installments be n

Monthly installment = ₹2000

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

Interest = 2000 $\times$ $\frac{n(n+1)}{2}$ $\times$ $\frac{1}{12}$ $\times$ $\frac{10}{100}$

Maturity Amount = Amount Deposited + Interest

2000n + 2000 $\times$ $\frac{n(n+1)}{2}$ $\times$ $\frac{1}{12}$ $\times$ $\frac{10}{100}$= 83100

$n^2+241n–9972=0$

$(n-36)(n+277)=0$

n = 36 and n = -277 (neglecting -277 as n cannot be negative as it time period)

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