Rs. 20000 is lent at compound interest at an annual rate of 18 percent for 1 year (compounding annually). If the compounding of interest is done half yearly, then how much more interest will be obtained?

Principal (P) = Rs. 20,000

Annual Interest Rate (r) = 18

Time (t) = 1 year

Compounding Frequency: Half-yearly

When compound interest is compounded more frequently than annually, the effective rate changes according to the frequency.

For half-yearly compounding, the annual rate is divided by 2, and the time period is doubled.

The formula for compound interest is:

​$$A=P(1+\frac{r}{100})^n$$

Calculate interest with annual compounding (once per year):

$$A=2000(1+\frac{18}{100})^1\\ \ \\ =2000\times1.18\\ \ \\ =23600 \\ \ \\ \text{Intrest annual} = 23600 - 20000=3600\\ \ \\ \text{Calculate interest with half-yearly compounding (twice per year):}\\ \ \\A= 2000(1+\frac{9}{100})^2\\ \ \\ 2000\times(1.09)^2= 2000\times(1.1881)= 23762 \\ \ \\ \text{Intrest half yearly}= 23762-2000= 3762$$​​