Question

By using the formula, find the amount and compound interest on:

$Rs.62500$ for $2$ years $6$ months at $12\%$ per annum compounded annually.

Answer 1

$\text{Principal (P)}=Rs.62500\text{Rate (R)}=12\%p.a.\text{Period (n) = 2 years 6 months}=2\frac{1}{2}\text{years}$
Here for first $2$ years, we apply the compound interest formula and next $6$ months, we apply simple interest formula.

The amount for $2$ years is
$\therefore \text{Amount (A)}=P{(1+\frac{R}{100})}^n=Rs.62500{(1+\frac{12}{100})}^2=Rs.62500\times {\left(\frac{28}{25}\right)}^2\times \frac{53}{50}=Rs.62500\times \frac{28}{25}\times \frac{28}{25}100\times 784=Rs.78400$
The amount for next $6$ months:
$78400\times (1+\frac{12\times 1}{100\times 2})$
$=78400\times \frac{53}{50}$
$=83104$
Therefore, amount after $2\frac{1}{2}$ years is $Rs.83104$

$\therefore \text{C.I = A- P}=Rs.83104-Rs.62500=Rs.20604$