**Question:**

Swati borrowed Rs 40960 from a bank to buy a piece of land. If the bank charges $12 \frac{1}{2} \%$ per annum, compounded half-yearly, what amount will she have to pay after $1 \frac{1}{2}$ years? Also, find the interest paid by her.

**Solution:**

Principal, $P=$ Rs. 40960

Annual rate of interest, $R=\frac{25}{2} \%$

Rate of interest for half year $=\frac{25}{4} \%$

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

Then the amount with the compound interest is given by

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

$=40960 \times\left(1+\frac{25}{100 \times 4}\right)^{3}$

$=40960 \times\left(\frac{400+25}{400}\right)^{3}$

$=40960 \times\left(\frac{425}{400}\right)^{3}$

$=40960 \times\left(\frac{17}{16}\right) \times\left(\frac{17}{16}\right) \times\left(\frac{17}{16}\right)$

$=(10 \times 17 \times 17 \times 17)$

$=\operatorname{Rs} 49130$

Therefore, compound interest $=$ amount $-$ principal $=$ Rs $(49130-40960)=$ Rs 8170

Therefore, Swati has to pay Rs. 49130 , which includes an interest of Rs. 8170 , to the bank after $1 \frac{1}{2}$ years.