Question

At what time will Rs.16800 amount to Rs. 23782.50 at $8\dfrac{3}{4}\%$ p.a ?

Answer 1

Hint: In this question, we need to find the time period . As there is no direct formula to find the time period ,we will use a simple interest formula to find the time. Simple interest is the method of calculating interest charged on the amount invested in the fixed deposit.
Formula used :
Simple interest, \[\S.I = \dfrac{\ P \times R \times T}{100}\]
Where,
\[P\] is principal amount
\[T\] is time period
\[R\] is rate of interest
From this formula,
\[T = \dfrac{S.I \times 100}{P \times R}\]

Complete step-by-step solution:
Given, \[A\ = \ Rs.23782.50\]
 \[P = \ Rs.16800\]
 \[\text{Interest} = A – P\]
=\[\ Rs.23782.50\ - \ Rs.16800\]
By subtracting,
We get,
\[I = \ Rs.\ 6982.50\]
Also given,
\[\ R\ = \ 8\dfrac{3}{4}\%\]
By converting the mixed fraction,
We get,
 =\[\dfrac{35}{4}\%\]
Now substituting the known values in the formula,
\[T = \dfrac{\left({S.I} \times 100 \right)}{P \times R}\]
=\[\dfrac{6982.50 \times 100}{16800 \times \dfrac{35}{4}}\]
=\[\dfrac{6982.50 \times 100 \times 4}{16800 \times 35}\]
By simplifying,
We get,
\[T\ = \ 4.75\ years\ \]
In order to convert the time period in years to months multiply with \[12\]
We get,
\[T\ = 4\ years(\dfrac{75}{100} \times 12){months}\]
By converting,
We get,
\[T\ = \ 4\ years\ 9\ months\ \]
Final answer :
The time period for \[Rs.16800\] amount to \[Rs.23782.50\] is \[4\text{years }9 \text{months}\]

Note: We can also convert the time period to mixed fraction also. By converting to mixed fraction, we get the time period will be \[4\dfrac{3}{4}\ {years}\]. Simple interest is determined by multiplying the daily interest rate by the principal by the number of days that elapse between payments. With the use of simple interest, we can calculate the interest without any error by saving time and effort.