Question

A man deposited a sum of Rs 400 every month is a recurring deposit account at an interest rate of 8$\%$ per annum. If he gets a maturity amount Rs 5008 after the end of maturity period, then the period for which he deposited the amount is ________

• A. 2 years
• B. 1.5 years
• C. 1 year
• D. 2.5 years

Answer 1

The correct option is C

1 year

Given P = Rs 400

r = 8$\%$

Let number of month he deposited money be n

Then Amount deposited = 400 m

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

I = $\frac{p\times n(n+1)}{2\times 12}\left(\frac{8}{100}\right)=\frac{4}{3}n(n+1)$

Maturity Value = Amount deposited + Interest

5008 = 400 n + $\frac{4}{3}n(n+1)$

15024 = 1200n+$4n^2+4n$

3756 = 300n+$n^2$ +n

$n^2$+301n-3756=0

$n^2$+313n-12n-3756=0

n(n+313)-12(n+313)=0

(n-12)(n+313)=0

n=12 or -313 ( Month cannot be -ve hence -313 is not possible)

n = 12 months = 1 year