#### Question

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?

#### Solution

P = Rs 10,000

Rate = 10% per annum = 5% per half year

n = `1 1/2` year

There will be 3 half years in `1 1/2` years.

A = Rs `[10000(1 + 5/100)^3] = Rs[10000(1 + 1/20)^3]`

= Rs `(10000 xx 21/20 xx 21/20 xx 21/20)` = Rs 11576.25

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

A = Rs `[10000(1 + 10/100)^1] = Rs[10000(1 + 1/10)]`

= Rs `(10000 xx 11/10)`= Rs 11000

By taking Rs 11,000 as the principal, the S.I. for the next `1/2` year will be calculated.

S.I. = Rs `((11000xx10xx1/2)/100)` = Rs 550

∴ 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.