P = Rs 10,000
Rate = 10% per annum = 5% per half year
n = 1 1/2 years
There will be 3 half years in 1 1/2 years.
C.I. = A − P
= Rs 11576.25 − Rs 10000 = Rs 1,576.25
The amount for 1 year and 6 months can be calculated by first calculating the amount for 1 year using the compound interest formula, and then calculating the simple interest for 6 months on the amount obtained at the end of 1 year. The amount for the first year has to be calculated first.
By taking Rs 11,000 as the principal, the S.I. for the next 1/2 year will be calculated.
∴ Interest for the first year = Rs 11000 − Rs 10000 = Rs 1,000
∴ Total compound interest = Rs 1000 + Rs 550 = Rs 1,550
Therefore, the interest would be more when compounded half yearly than the interest when compounded annually.