Question

Find the amount when Rs. 10,000 is invested for $2\frac{1}{2}$ years at 10% interest compounded yearly.

Answer 1

First of all find the amount in 2 years.
Amount in 2 years $=Rs.10000{(1+\frac{10}{100})}^2=Rs.12100$
After two years, Rs. 12,100 is the principal for the remaining half year and so :
$A=P{(1+\frac{r}{2\times 100})}^{n\times 2}$
$=Rs.12100{(1+\frac{10}{2\times 100})}^{\frac{1}{2}\times 2}=Rs.12705$
Amount in $2\frac{1}{2}$ years = Rs.12705
Note: For the example given above, we can directly use the formula :
$A=P{(1+\frac{r}{100})}^2{(1+\frac{r}{2\times 100})}^{\frac{1}{2}\times 2}$
Amount in $2\frac{1}{2}$ years
$=Rs.10000{(1+\frac{10}{2\times 100})}^2(1+\frac{10}{2\times 100})=Rs.12705$