Question

Rishabh has a recurring deposit account in a post office for $ 3 $ years at $ 10\% $ simple interest. If he gets $ {\rm{Rs }}9,990 $ as interest at the time of maturity. Find the amount of maturity.
(A) $ 33,300 $
(B) $ 33,000 $
(C) $ 33,333 $
(D) None of the above

Answer 1

Hint: This question is based on Simple Interest. Simple interest is defined as the interest generated on the principal amount at the end of the first year. The formula used to calculate the simple interest is given below-
 $ S.I. = \dfrac{{P \times R \times T}}{{100}} $
Here, $ S.I. $ is the simple interest generated at the end of a given time period,
 $ P $ is the original principal amount, also known as the amount of maturity
 $ R $ is the rate of interest applied
 $ T $ is the time period in years

Complete step-by-step answer:
The time period for which the amount has been deposited $ T = 3{\rm{ years}} $
The rate of interest $ R = 10\% {\text{ per year}} $
And, the simple interest at the end of the time period $ S.I. = {\rm{Rs }}9,990 $
Now applying the formula for the simple interest, we get,
 $ S.I. = \dfrac{{P \times R \times T}}{{100}} $
Substituting the values for each variable, we get,
 $ \begin{array}{c}
9990 = \dfrac{{P \times 10 \times 3}}{{100}}\\
P = \dfrac{{9990 \times 100}}{{10 \times 3}}
\end{array} $
Solving this we get,
 $ P = {\rm{ Rs }}33,300 $
Therefore, the amount of maturity is $ {\rm{Rs }}33,300 $ and the correct option is (A)
So, the correct answer is “Option A”.

Note: A recurring deposit is a type of deposit where a fixed amount is deposited into the account and interest is earned at the rate applied to the fixed deposit. That is why, we have calculated the simple interest at the end of $ 3 $ years because the interest was being generated at the end of each year on the fixed deposit amount also known as the amount of maturity.