Question

Find the amount and the compound interest on $INR10,000$ for $1\frac{1}{2}$ years at $10\%$ per annum, compounded half yearly. Would this interest be more than the interest he would get if it was compounded annually?

Answer 1

For interest compounded half-yearly,

$r=\frac{10\%}{2}=5\%,n=\left(3/2\right)\times 2=3$

$CI=P\left[\right(1+\frac{r}{100}{)}^n-1]$

$CI=Rs.10,000\left[\right(1+\frac{5}{100}{)}^3-1]=Rs.1,576.25$

For interest compounded annually,

$r=10\%,n=\frac{3}{2}$

$CI=P\left[\right(1+\frac{r}{100}{)}^n-1]$

$CI=Rs.10,000\left[\right(1+\frac{10}{100}{)}^{\left(3/2\right)}-1]=Rs.1,536.9$

Hence interest compounded half yearly ism greater then interest compounded annually.