**Question:**

Find the amount of Rs 8000 for 2 years compounded annually and the rates being 9% per annum during the first year and 10% per annum during the second year.

**Solution:**

Principal amount, $P=$ Rs. 8000

Rate of interest for the first year, $p=9 \%$ p. a.

Rate of interest for the second year, $q=10 \%$ p. a.

Time, $n=2$ years.

Formula for the amount including the compound interest for the first year:

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

$=$ Rs. $\left\{8000 \times\left(1+\frac{9}{100}\right) \times\left(1+\frac{10}{100}\right)\right\}$

$=$ Rs. $\left\{8000 \times\left(\frac{109}{100}\right) \times\left(\frac{110}{100}\right)\right\}$

$=$ Rs. $\{8000 \times(1.09) \times(1.1)\}$

$=$ Rs. 9592

i.e., the amount including the compound interest for first year is Rs 9592 .