Rs. 17000 is lent at compound interest at an annual rate of 22 percent for 1 year (compounding annually). If the compounding of interest is done half yearly, then how much more interest will be obtained?

When interest is compounded half-yearly, the annual rate is divided by 2 and the time period (in years) is doubled.

Compound Interest (CI):

​$$A = P \times \left(1 + \frac{R}{100}\right)^n$$​​

where A is the amount, P is the principal, R is the interest rate per period, and n is the number of periods.

Calculating CI with annual compounding:

​$$A_{\text{annual}} = 17000 \times \left(1 + \frac{22}{100}\right) \\ \ \\= 17000 \times 1.22 = 20740 \\ \ \\\text{CI (annually)} = A_{\text{annual}} - P = 20740 - 17000 = 3740$$​​

Calculating CI with half-yearly compounding:

​$$A_{\text{half-yearly}} = 17000 \times \left(1 + \frac{11}{100}\right)^2\\ \ \\ = 17000 \times 1.11^2 = 17000 \times 1.2321 = 20945.7 \\ \ \\\text{CI (half-yearly)} = A_{\text{half-yearly}} - P = 20945.7 - 17000 = 3945.7$$​​

Now, Difference in Interest = 3945.7− 3740 = 205.7

Thus, The additional interest obtained with half-yearly compounding is Rs. 205.7.