Question

Find the compound interest on Rs.8,000 for the period of $1\dfrac{1}{2}$ years at the rate of interest 10% per annum, if the interest is compounded half yearly.

Hint: First calculate the amount by making use of the formula and then calculate the compound interest.

Given that the principal=Rs.8,000
Time period=$1\dfrac{1}{2}$ years=$\dfrac{3}{2}$ years
But, it is given that the interest is compounded half yearly
So,
t=$\dfrac{3}{2} \times 2 =$ 3years
Rate of interest=10%
Make use of the formula of amount
$A = P{\left( {1 + \dfrac{R}{{100}}} \right)^t}$
$A = 8000{\left( {1 + \dfrac{{10}}{{100}}} \right)^3} \\ A = 8000{\left( {\dfrac{{110}}{{100}}} \right)^3} \\ A = 8000 \times {(1.1)^3} \\ A = 8000 \times 1.331 \\ A = Rs.10648 \\$
So, the amount =Rs.10648
We know that the compound interest is calculated by
Compound Interest=Amount-Principal
Compound Interest=10648-8000
Compound Interest=Rs.2648

Note: Whenever we are solving these types of problems related to compound interest, it is always recommended to first find out the amount using the formula and from this calculate the compound interest and also note that in this problem the interest is compounded half yearly and not annually.