₹20000 is invested on compound interest (compounded half-yearly) at the rate of 20% per annum, then what will be the interest after two years?

As per the information given in the question, interest is compounded on a half-yearly basis. Then the rate of interest will be half and the time will be double.

₹20000 is invested on compound interest (compounded half-yearly) at the rate of 20% per annum.

P = principal amount = ₹20000

R = rate of interest = $$\left(\frac{20}{2}\right)\%$$ = 10% per half-year

T = time = $$2\times2$$ = 4 (actual time is 2 years. But becasue of the half-yearly interest calculation it was happened.)

Interest after two years = $$P\left(1+\frac{R}{100}\right)^T\ -\ P$$

= $$20000\left(1+\frac{10}{100}\right)^4\ -\ 20000$$

= $$20000\left(\frac{11}{10}\right)^4\ -\ 20000$$

= $$20000\times\ \frac{14641}{10000}-\ 20000$$

= $$2\times14641-\ 20000$$

= 29282 - 20000

= ₹9282