Question

What sum will amount to $Rs4,913$ in $1\frac{1}{2}$ years if the rate of interest is $12.5$ per annum compounded half-yearly?

Answer 1

Given:-

Amount, $A=Rs.4913$

Time $=1\frac{1}{2}$ years.

Rate of interest $=12.5=12\frac{1}{2}\%$ per annum

Since the interest is compounded half-yearly.

Therefore,

n $=$ no. of times interest added in one and half years $=3$

R @ half yearly $=\frac{12.5}{2}=12\frac{1}{2}÷2=\frac{25}{2}÷2=\frac{25}{4}\%$

As we know that amount is given by the formula

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

$\Rightarrow 4913=P{(1+\frac{\frac{25}{4}}{100})}^3$

$\Rightarrow 4913=P{(1+\frac{25}{400})}^3$

$\Rightarrow 4913=P{\left(\frac{425}{400}\right)}^3$

$\Rightarrow 4913=P{\left(\frac{17}{16}\right)}^3$

$\Rightarrow P=\frac{4913\times 16\times 16\times 16}{17\times 17\times 17}$

$\Rightarrow P=\frac{4913\times 4096}{4913}=Rs.4096$

Hence the sum will be $Rs.4096$