Question

Ahmed has a recurring deposit account in a bank. He deposits Rs.2500 per month for 2 years. If he gets Rs.66,250 at the time of maturity. Find the rate of interest.

Answer 1

Hint: Here, in the question we have given the monthly instalment value and the amount he receives after the time of maturity. So, first of all we will find the interest paid by the bank and then find the rate of the interest.

Formula used: Interest paid by bank= matured amount- amount paid
Principal amount of one month$ = \dfrac{{P \times n(n + 1)}}{2}$, Rate of interest$ = \dfrac{{I \times 100}}{{P \times T}}$

Complete step-by-step answer:
Here, first of all we found the amount deposited by the Ahmed in 2 years (i.e. 24 months)
∴amount paid
$ = 2400 \times 25$
$ = 60,000$
Now the interest paid by the bank is given by the= matured amount received – amount paid
$
   = 66250 - 60000 \\
   = 6250 \\
 $
Therefore, the interest paid by bank Rs6250.
Now, the principal amount for one month
$
   = \dfrac{{P \times n(n + 1)}}{2} \\
   = \dfrac{{2500 \times 24 \times 25}}{2} \\
   = Rs750000 \\
 $
Rate of interest$ = \dfrac{{I \times 100}}{{P \times T}}$
$
   = \dfrac{{6250 \times 100 \times 12}}{{750000 \times 1}} \\
   = 10\% \\
 $
Therefore, the rate of interest received by Ahmed $ = 10\% $
Note: To find the interest rate paid by the bank we have to first find the interest amount paid the bank. In the simple interest the interest is given on the amount paid in one period and then multiply by the no. of time period while in the compound interest the interest is count on one period and in the second period the interest is given on the sum of the amount in period and the interest receive on the first period.