Question

At what rate of compound interest will the interest $Rs.8000$ for $3$ years be $Rs.1261$, when the interest is payable annually?

Answer 1

$P=Rs.8000$

$C.I.=Rs.1261$

$n=3$ years

$A=P+C.I.=Rs.(8000+1261)=Rs.9261$

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

$9261=8000{(1+\frac{R}{100})}^3$

$\Rightarrow \frac{9261}{8000}={(1+\frac{R}{100})}^3$

$\Rightarrow {\left(\frac{21}{23}\right)}^3={(1+\frac{R}{100})}^3$

$\because$ Exponents are equal, bases are also equal.

$\therefore \frac{21}{20}=1+\frac{R}{100}$

$\Rightarrow \frac{R}{100}=\frac{21}{20}-1$

$\Rightarrow \frac{R}{100}=\frac{21-20}{20}=\frac{1}{20}$

$\Rightarrow R=\frac{1}{20}\times 100=5$%