Question

What is the compound interest on ₹ 2000 for 9 months at 8% per annum being given when the interest is reckoned quarterly?

Answer 1

$P=₹2000,R=8\%p.a,t=9months=\frac{9}{12}=\frac{3}{4}year$
Since the principal is compounded quartely, r = R/4 % = $\frac{8}{4}\%$ and n = $4\times \frac{3}{4}$

Now, C.I. = Amount - Principal

C.I. = $P[1+\frac{r}{100}{]}^n-P$

$⟹C.I.=P[{(1+\frac{r}{100})}^n-1]$
$C.I=2000[{(1+\frac{8}{100\times 4})}^{4\times \frac{3}{4}}-1]$
$=2000[{\left(\frac{102}{100}\right)}^3-1]=₹122$
$\therefore$ the compound interest is ₹ 122