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 $Rs.\,8100$ . Find the time( in years ) of the recurring deposit account.

Answer 1

Hint: Here we are given instalment per month $P = Rs\,300$
Let the no of months be n and rate is $12\% $ p.a.
So simple interest is given by $SI = \left( {P \times \dfrac{{n\left( {n + 1} \right)}}{{2 \times 12}} \times \dfrac{r}{{100}}} \right)$
And maturity value $ = \left( {P \times n + SI} \right)$
And we are given that value of maturity is $Rs.\,8100$
Find out the value of n.

Complete step-by-step answer:
According to the question we are given that Mr. Gulati has a recurring deposit account of $Rs\,300$ that means instalment per month is given $Rs\,300$
Say P to be installed per month.
So $P = Rs\,300$
Rate is also given i.e. $12\% $ and also in the question the maturity value is given that is maturity value is $Rs.\,8100$
We know the formula for the simple interest of recurring deposit is
$SI = \left( {P \times \dfrac{{n\left( {n + 1} \right)}}{{2 \times 12}} \times \dfrac{r}{{100}}} \right)$
Here P represent instalment per month
Let n be the number of months.
And r is the given rate of interest. So we need to find n that is time of the recurring deposit account.
So we got
$SI = \left( {300 \times \dfrac{{n\left( {n + 1} \right)}}{{2 \times 12}} \times \dfrac{{12}}{{100}}} \right) = \dfrac{3}{2}n\left( {n + 1} \right)$
And we also know that maturity value is equal to $ = \left( {P \times n + SI} \right)$
And in question we are given the value of maturity value that is $Rs.\,8100$
So
$
  8100 = 300 \times n + \dfrac{3}{2}n\left( {n + 1} \right) \\
  16200 = 600n + 3n\left( {n + 1} \right) \\
  3{n^2} + 603n - 16200 = 0 \\
  {n^2} + 201n - 5400 = 0 \\
 $
Using splitting method
$
  {n^2} + 225n - 24n - 5400 = 0 \\
  n\left( {n + 225} \right) - 24\left( {n + 225} \right) = 0 \\
  \left( {n + 225} \right)\left( {n - 24} \right) = 0 \\
 $
So we get
$
  n + 225 = 0\,\,\,\,\,\,n = - 225 \\
  n - 24 = 0\,\,\,\,\,\,\,\,n = 24 \\
 $
As n cannot be negative so $\,\,n = 24$ or we can say n is equal to two years.

Note: Recurring deposit is a special kind of deposit offered by the bank which helps people to deposit a fixed amount every month into their recurring deposit account.