**Question:**

Mohd. Aslam purchased a house from Avas Vikas Parishad on credit. If the cost of the house is Rs 125000 and the Parishad charges interest at 12% per annum compounded half-yearly, find the interest paid by Aslam after a year and a half.

**Solution:**

Let the principal amount be $P=$ Rs. 125000 .

Annual rate of interest, $R=12 \%$

Rate of interest for a half year $=6 \%$

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

Then the amount with the compound interest is given by

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

$=$ Rs. $125000 \times\left(1+\frac{6}{100}\right)^{3}$

$=$ Rs. $125000 \times\left(\frac{100+6}{100}\right)^{3}$

$=$ Rs. $125000 \times\left(\frac{106}{100}\right)^{3}$

$=$ Rs. $125000 \times\left(\frac{53}{50}\right) \times\left(\frac{53}{50}\right) \times\left(\frac{53}{50}\right)$

$=$ Rs. $(53 \times 53 \times 53)$

$=$ Rs. 148877

Now, $C I=A-P=$ Rs. $(148877-125000)=$ Rs. 23877

Therefore, Aslam has to pay an interest of Rs. 23877 to the bank after $1 \frac{1}{2}$ years.