Question

Mr. Gulati has a Recurring Deposit Account of Rs. 300 per month. If the rate of interest is 12% and the maturity value of this account is Rs. 8,100; find the time (in years) of this Recurring Deposit Account.

Answer 1

Let n be the maturity period, P be the money deposited every month and R be the rate of interest per annum. The interest received at the end of the maturity is given by,

`I = P xx (n(n + 1))/24xxr/100`

In the question, we are given that the amount deposited every month is

Rs. 300,

P = Rs. 300

Rate of interest per annum, R = 12%

Now, Mr. Gulati receives Rs. 8,100 at the time of maturity, so

I = 16220 − 400n

On putting the known values in the above equation, we get-

`8100 - 300n = 300xx(n(n + 1))/24 xx 12/100`

`8100 - 300n = (3n(n + 1))/2`

16200 − 600n = 3n² + 3n

3n² + 603n − 16200 = 0

⇒ n² + 201n − 5400 = 0

Factorizing the above equation, we get,

n² + 225n − 24n − 5400 = 0

n(n + 225) − 24(n + 225) = 0

(n − 24)(n + 225)

⇒ n = 24, n = −225

Now, the time period cannot be negative; the total time the account was kept is 24 months or 2 years.