Find the amount and the compound interest on Rs 12800 for 1 year
Question:

Find the amount and the compound interest on Rs 12800 for 1 year at $7 \frac{1}{2} \%$ per annum, compounded semi-annually.

Solution:

Principal, $P=$ Rs. 12800

Annual rate of interest, $R=\frac{15}{2} \%$

Rate of interest for a half year $=\frac{1}{2}\left(\frac{15}{2}\right) \%=\frac{15}{4} \%$

Time, $n=1$ year $=2$ half years

Then the amount with the compound interest is given by

$A=P \times\left(1+\frac{R}{100}\right)^{n}$

$=12800 \times\left(1+\frac{\frac{15}{4}}{100}\right)^{2}$

$=12800 \times\left(1+\frac{15}{100 \times 4}\right)^{2}$

$=12800 \times\left(\frac{400+15}{400}\right)^{2}$

$=12800 \times\left(\frac{415}{400}\right)^{2}$

$=12800 \times\left(\frac{83}{80}\right) \times\left(\frac{83}{80}\right)$

$=(2 \times 83 \times 83)$

$=$ Rs 13778

Therefore, compound interest $=$ amount $-$ principal $=\mathrm{Rs}(13778-12800)=$ Rs 978