Question

Compute the compound interest on ${\text{Rs12000}}$ for $1\dfrac{1}{2}{\text{ years}}$ at the rate of $12\% $ per annum when the interest is compounded semi-annually.

Answer 1

Hint: We know that the amount formula for the compound interest is given as
$A = P{\left[ {1 + \dfrac{R}{n}} \right]^{nT}}$
Here $n = 2$ as the interest is compounded semi-annually and the rate is $12\% $ per annum and we need to find it for $1\dfrac{1}{2}{\text{ years}}$. So $T = 1\dfrac{1}{2}{\text{ years}}$
And $P$ is given as ${\text{Rs12000}}$
Put it in the formula we will get the answer.

Complete step-by-step answer:
Here we are given on ${\text{Rs12000}}$ for $1\dfrac{1}{2}{\text{ years}}$ at the rate of $12\% $ per annum, the interest is compounded semi-annually and we need to compute the compound interest.
So as we know that compound interest is addition of the interest to the principle sum of the loan or deposit and here we are given $P$ as ${\text{Rs12000}}$
Let us take an example where $P$ amount is invested at annual rate of $R$compounded $n$ times.
So the value of the investment after $T$ years will be $A = P{\left[ {1 + \dfrac{R}{n}} \right]^{nT}}$
Here A is the future amount of the investment and P is the principle investment value and R is the annual interest rate and n is the number of times that interest is compounded per unit t
T is the time the money is invested.
So we are given that
$P = {\text{Rs12000}}$, $R = 12\% $, $T = 1\dfrac{1}{2}{\text{ years}}$
So we will get
$A = P{\left[ {1 + \dfrac{R}{n}} \right]^{nT}}$
$A = 12000{\left[ {1 + \dfrac{{12}}{2}} \right]^{2\left( {\dfrac{3}{2}} \right)}}$
On simplifying, we get that $A = 12000{\left( {1 + 6} \right)^3}$
$A = 12000{(7)^3} = {\text{Rs 4116000}}$
Therefore compound interest$ = $amount $ - $ principal $
   = 4116000 - 12000 \\
   = {\text{Rs 4104000}} \\
 $

So after $1.5{\text{ years}}$ he got ${\text{Rs 4104000}}$ as compound interest.

Note: Simple interest is simply given by the formula $SI = \dfrac{{(P)(R)(T)}}{{100}}$ and amount is given by $A = P + SI$
And in case of compound interest amount is given by
$A = P{\left[ {1 + \dfrac{R}{n}} \right]^{nT}}$
Compound interest is given by $ = A - P$
Where A is the amount and P is the principle amount.