Question

Find the sum invested for $1\frac{1}{2}$ years compounded half-yearly at the rate of $8\%$ per annum. that will amount to $\text{Rs.}17576$.

Answer 1

Given:-

Time period, $t=1\frac{1}{2}$ years $=\frac{3}{2}$ years.

Rate of interest, $r=8\%$

Amount, $A=\text{Rs.}17576$

As the interest is compounded half yearly interest will become half and time period will becomes double in this case so,

$A=P{(1+\frac{r}{100})}^t$

$\Rightarrow 17576=P{(1+\frac{4}{100})}^3$

$\Rightarrow 17576=P{(1+0.04)}^3$

$\Rightarrow 17576=P{\left(1.04\right)}^3$

$\Rightarrow P=\frac{17576}{(1.04{)}^3}$

$\Rightarrow P=\text{Rs.}15625$

Hence the sum invested is $\text{Rs.}15625.$