Find the amount and the compound interest on Rs 31250 for
Question:

Find the amount and the compound interest on Rs 31250 for $1 \frac{1}{2}$ years at $8 \%$ per annum, compounded half-yearly.

Solution:

Principal, $P=$ Rs. 31250

Annual rate of interest, $R=8 \%$

Rate of interest for a half year $=\frac{1}{2} \times 8 \%=4 \%$

Time, $n=1 \frac{1}{2}$ years $=3$ half years

Then the amount with the compound interest is given by

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

$=31250 \times\left(1+\frac{4}{100}\right)^{3}$

$=31250 \times\left(1+\frac{1}{25}\right)^{3}$

$=31250 \times\left(\frac{25+1}{25}\right)^{3}$

$=31250 \times\left(\frac{26}{25}\right)^{3}$

$=31250 \times\left(\frac{26}{25}\right) \times\left(\frac{26}{25}\right) \times\left(\frac{26}{25}\right)$

$=$ Rs $2 \times 17576$

$=$ Rs 35152

Therefore, compound interest $=$ amount $-$ principal $=$ Rs $(35152-31250)=$ Rs 3902