Find the amount and the compound interest on Rs 8000 for 1 year

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