# Find the amount and the compound interest on Rs 10,000 for 1 1/2 years at 10% per annum, compounded half yearly.

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Find the amount and the compound interest on Rs 10,000 for 1 1/2 years at 10% per annum, compounded half yearly. Would this interest be more than the interest he would get if it was compounded annually?

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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.