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

Hint: The depositor is paid maturity value that is a lump sum amount of amount deposited and interest compounded at a fixed rate at the end of the period of recurring deposit
Interest received at the end of the maturity = Total amount received – Amount deposited
Use the formula of calculating the interest at the end to find out the time period.

Complete step-by-step answer:
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 \times \dfrac{{n(n + 1)}}{{24}} \times \dfrac{r}{{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 = 300 \times \dfrac{{n(n + 1)}}{{24}} \times \dfrac{{12}}{{100}} \\
  8100 - 300n = \dfrac{{3n(n + 1)}}{2} \\
  16200 - 600n = 3{n^2} + 3n \\
  3{n^2} + 603n - 16200 = 0 \\
   \Rightarrow {n^2} + 201n - 5400 = 0 \;
  $
Factorizing the above equation, we get –
 $
  {n^2} + 225n - 24n - 5400 = 0 \\
  n(n + 225) - 24(n + 225) = 0 \\
  (n - 24)(n + 225) \\
   \Rightarrow n = 24,\,n = - 225 \;
  $
Now, the time period cannot be negative, so the total time for which the account was held is 24 months or 2 years.
So, the correct answer is “24 months or 2 years”.

Note: A special kind of term deposit offered by the banks is known as a recurring deposit. People earn interest at the rate applicable to the fixed deposits by depositing a fixed amount every month into their recurring deposit account. The time period of recurring deposits varies from 3 months to 10 years.