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.
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.