Question

Rs.$8000$ became Rs.$9621$ in a certain interval of time at the rate of $5\% $per annum of C.I.
Find the time.

Answer 1

Hint: Use the formula for finding the amount after the n years, which is given as:

$A = P{\left( {1 + \dfrac{R}{{100}}} \right)^n}$, where A is the amount, P is the principal
amount, R is the interest rate and n is the time.
Substitute the values and get the desired result.

Complete step-by-step solution:
It is given in the problem that the amount Rs.8000 became Rs.9261 in a certain interval of time
at the rate of $5\% $per annum of C.I. Here, C.I. stands for compound interest, which means that the money is compounded per year.
We have to find the time taken during the increment of the money.
According to the given data, we have
Principle amount (P)$ = Rs.8000$
Amount (A)$ = Rs.9261$
Rate (R)$ = 5\% $per annum.
Assume that the time interval consumed in the increment of the money will be $n$years. Then
we know that the formula for finding the amount is given as:
$A = P{\left( {1 + \dfrac{R}{{100}}} \right)^n}$, where A is the amount, P is the principal
amount, R is the interest rate and n is the time.
Substitute the values, Principle amount (P)$ = Rs.8000$, Amount (A)$ = Rs.9261$, and Rate
(R)$ = 5\% $per annum, so the above equation becomes:
$9621 = 8000{\left( {1 + \dfrac{5}{{100}}} \right)^n}$
Solve the above equation for the value of$n$:
$ \Rightarrow \dfrac{{9621}}{{8000}} = {\left( {1 + \dfrac{5}{{100}}} \right)^n}$
$ \Rightarrow {\left( {\dfrac{{21}}{{20}}} \right)^3} = {\left( {1 + \dfrac{1}{{20}}}
\right)^n}$
$ \Rightarrow {\left( {\dfrac{{21}}{{20}}} \right)^3} = {\left( {\dfrac{{21}}{{20}}}
\right)^n}$
We know that:
${a^x} = {a^y}$, implies that$x = y$.
Therefore, the above equation gives:
$n = 3$

So, it will take 3 years to have an increment from Rs.$8000$ to become Rs.$9621$ at the rate of
$5\% $per annum of C.I.

Note: The simple interest is the cheaper option to take the loan because, in case of simple
interest, we only have to pay the interest on the principal amount but in case of compound
interest, we have to pay the interest on the principal amount as well as on the interest that
accumulates every period of time. In the given problem, the interest rate has the time period of a year after that we have to pay the interest of the previous year of interest too.