**Question:**

Sudershan deposited Rs 32000 in a bank, where the interest is credited quarterly. If the rate of interest be 5% per annum, what amount will he receive after 6 months?

**Solution:**

Let the principal amount be $P=$ Rs 32000 .

Annual rate of interest, $R=5 \%$

Rate of interest for a quarter year $=\frac{5}{4} \%$

Time, $n=6$ months $=2$ quarter years

Then the amount with the compound interest is given by

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

$=$ Rs. $32000 \times\left(1+\frac{5}{100 \times 4}\right)^{2}$

$=$ Rs. $32000 \times\left(\frac{400+5}{400}\right)^{2}$

$=$ Rs. $32000 \times\left(\frac{405}{400}\right)^{2}$

$=$ Rs. $32000 \times\left(\frac{81}{80}\right)^{2}$

$=$ Rs. $32000 \times\left(\frac{81}{80}\right) \times\left(\frac{81}{80}\right)$

$=$ Rs. $(5 \times 81 \times 81)$

$=$ Rs. 32805

Therefore, Sudershan will receive an amount of Rs. 32805 after 6 months.