Question

A recurring deposit account of $Rs.1,200$ per month has maturity value of $Rs.12,440$. If the rate of interest is $8$ and the interest is calculated at the end of every month, find the time (in months) of this Recurring Deposit Account.

Answer 1

Installment(P) per month = Rs 1200

number of months = n

let rate of interest = 8% per annum

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

$=\frac{1200\times n(n+1)\times 8}{2\times 12\times 100}$

$=4n(n+1)$

Maturity value $=(1200\times n)+4n(n+1)=1200n+4n^2+4n$

Given Maturity value = Rs 12440

Then,

$12440=1200n+4n^2+4n$

$4n^2+1204n-12440=0$

On solving the equation, we get n = 10 months and n = -311 months (not possible)

Therefore, number of months = 10