Question

Find the compound interest on Rs.$1000$ for $1\frac{1}{2}$ yrs at the rate of $10\%$ p.a. compounded half-yearly.

Answer 1

Given, Principal $P=Rs.1000$

Rate $R=10\%$ p.a$=\frac{10\%}{2}$ half yearly$=5\%$ half yearly

Time $n=1\frac{1}{2}$ years$=3$ half years

Amount $=P{(1+\frac{R}{100})}^n$

$=Rs.1000{(1+\frac{5}{100})}^3$

$=Rs.1000{(1+\frac{1}{20})}^3$

$=Rs.1000{\left(\frac{21}{20}\right)}^3$

$=Rs.1000\times \frac{9261}{8000}$

$=Rs.1157.625$

$=Rs.1157.63$

Compound interest $=Rs.(1157.63-1000)=Rs.157.63$.