Question

The rate of interest for a sum that becomes $\frac{729}{576}$ times itself in 2 years, when compounded annually, is

Answer 1

Principal = P

Time, t = 2 years

Amount, $A=\frac{729}{576}P$

n=1, [compounded annually]

$A=P[1+\frac{R}{n}{]}^{nt}$

$\frac{729}{576}P=P[1+\frac{R}{1}{]}^2$

$\frac{729}{576}=(1+R{)}^2$

Taking square root : $\sqrt{\frac{729}{576}}=1+R$

$\therefore \frac{27}{24}=1+R$

$\therefore R=\frac{27-24}{24}=\frac{3}{24}$

$\therefore$ Rate of interest = $\frac{1}{8}\%$

$\therefore R=\frac{1}{8}\%=0.125\%$