Question

Calculate the compound interest on : Rs. $8,000$ in $2\frac{1}{2}$ years at $15$% per annum.

Answer 1

We first calculate the C.I. for first $2$ years and then the S.I. next $\frac{1}{2}$ year.
For ,
$N=2years$
$R=15$ %
$=>P=Rs8,000$
And on interest being compounded we have,
$Amount=P{(1+\frac{R}{100})}^N=8,000\times {(1+\frac{15}{100})}^2=8,000\times {1.15}^2=Rs10,580$
So, $C.I$ for first $2$ years $=.=A-P=Rs10,580=Rs8,000=Rs2,580$
This, $Rs10,580$ is the principal for the next $\frac{1}{2}$ year.
So, $S.I.=\frac{PNR}{100}=\frac{10,580\times \frac{1}{2}\times 15}{100}=Rs793.5$
Thus, total interest $=Rs2,580+Rs793.5=Rs3,373.50$
And Amount $=Rs8,000+Rs3,373.50=Rs11,373.50$