**Question:**

Shubhalaxmi took a loan of Rs 18000 from surya Finance to purchase a TV set. If the company charges compound interest at $12 \%$ per annum during the first year and $12 \frac{1}{2} \%$ per annum during the second year, how much will she have to pay after 2 years?

**Solution:**

Principal amount, $P=$ Rs. 18000

Rate of interest for the first year, $p=12 \%$ p. a.

Rate of interest for the second year, $q=12 \frac{1}{2} \%$ p.a.

Time, $n=2$ years

The formula for the amount including the compound interest for the first year is given below:

$A=\left\{P \times\left(1+\frac{p}{100}\right) \times\left(1+\frac{q}{100}\right)\right\}$

$=$ Rs. $\left\{18000 \times\left(1+\frac{12}{100}\right) \times\left(1+\frac{25}{100 \times 2}\right)\right\}$

$=$ Rs. $\left\{18000 \times\left(\frac{100+12}{100}\right) \times\left(1+\frac{25}{200}\right)\right\}$

$=$ Rs. $\left\{18000 \times\left(\frac{100+12}{100}\right) \times\left(1+\frac{1}{8}\right)\right\}$

$=$ Rs. $\left\{18000 \times\left(\frac{100+12}{100}\right) \times\left(\frac{8+1}{8}\right)\right\}$

$=$ Rs. $\left\{18000 \times\left(\frac{112}{100}\right) \times\left(\frac{9}{8}\right)\right\}$

$=$ Rs. $\{18000 \times(1.12) \times(1.125)\}$

$=$ Rs. 22680

$\therefore$ Shubhalaxmi has to pay Rs 22680 to the finance company after 2 years.