Question:
Find the amount and the compound interest on Rs 8000 for 1 year at 10% per annum, compounded half-yearly.
Solution:
Principal, $P=$ Rs. 8000
Time, $n=1$ year $=2$ half years
Rate of interest per annum $=10 \%$
Rate of interest for half year, $R=\frac{10 \%}{2}=5 \%$
The amount with the compound interest is given by
Amount $=$ Rs. $P \times\left(1+\frac{R}{100}\right)^{2}$
$=$ Rs. $8000 \times\left(1+\frac{5}{100}\right)^{2}$
$=$ Rs. $8000 \times\left(\frac{105}{100}\right)^{2}$
$=$ Rs. $8000 \times\left(\frac{21}{20}\right)^{2}$
$=$ Rs. $8000 \times\left(\frac{21}{20}\right) \times\left(\frac{21}{20}\right)$
$=$ Rs. $(20 \times 21 \times 21)$
$=$ Rs. 8820
$\therefore$ Compound interest $=$ amount $-$ principal $=$ Rs. $(8820-8000)=$ Rs. 820