Question

Mr. Ravi has a recurring deposit amount of Rs.400 per month at 10% per annum. If he gets Rs.16220. At the time of maturity, find the total time for which the account was held.

Answer 1

Hint: At the end of the period of recurring deposit, the depositor is paid a maturity value that is a lump sum amount of the amount deposited and interest compounded at a fixed rate.
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,
 $ \Rightarrow 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.400, $ P = Rs.400 $
Rate of interest per annum, $ R = 10\% $
Now, Ravi receives Rs.16220 at the time of maturity, so $ I = 16220 - 400n $
Putting these values in the above equation, we get –
 $
\Rightarrow 16220 - 400n = 400 \times \dfrac{{n(n + 1)}}{{24}} \times \dfrac{{10}}{{100}} \\
\Rightarrow 16220 - 400n = n(n + 1)\dfrac{5}{3} \\
\Rightarrow n(n + 1) = \dfrac{3}{5}(16220 - 400n) \\
\Rightarrow n(n + 1) = 9732 - 240n \\
\Rightarrow {n^2} + n + 240n - 9732 = 0 \\
\Rightarrow {n^2} + 241n - 9732 = 0 \;
  $
Solving the above equation, we get –
 $ \Rightarrow n = - 276.235 $ and $ n = 35.235 $
Now, the time period cannot be negative, so the total time for which the account was held is 35.235 months.
So, the correct answer is “35.235 months”.

Note: A recurring deposit is a special kind of term deposit offered by the banks. 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.