What is the compound interest on ₹5000 in 2 years at the rate of 20% per annum?(interest compounded half-yearly)

Here the interest compounded half-yearly. but the rate of interest is given yearly. So make it half-yearly, we need to divide it by 2.

Similarly the given time is multiplied by 2.

compound interest = $$P\left(1+\frac{R}{100}\right)^n\ -P$$

= $$5000\left(1+\frac{\frac{20}{2}}{100}\right)^{2\times\ 2}\ -5000$$

= $$5000\left(1+\frac{10}{100}\right)^4\ -5000$$

= $$5000\left(1+\frac{1}{10}\right)^4\ -5000$$

= $$5000\left(\frac{11}{10}\right)^4\ -5000$$

= $$5000\left(\frac{14641}{10000}\right)\ -5000$$

= $$5000\left(\frac{14641}{10000}-1\right)$$

= $$5000\left(1.4641-1\right)$$

= $$5000\times0.4641$$

= ₹2320.50