#### Question

Calculate the amount and compound interest on Rs 18000 for `2 1/2` years at 10% per annum compounded annually.

#### Solution

Principal (P) = Rs 18,000

Rate (R) = 10% annual

Number of years (*n*) = `2 1/2` year

The amount for 2 years and 6 months can be calculated by first calculating the amount for 2 years using the compound interest formula, and then calculating the simple interest for 6 months on the amount obtained at the end of 2 years.

Firstly, the amount for 2 years has to be calculated.

`A = Rs[18000(1 + 1/10)^2] = Rs (18000xx11/10xx11/10)` = Rs 21780

By taking Rs 21780 as principal, the S.I. for the next `1/2` year will be calculated.

S.I = Rs `((21780 xx 1/2 xx 10)/100)` = Rs 1089

∴ Interest for the first 2 years = Rs (21780 − 18000) = Rs 3780

And interest for the next `1/2` year = Rs 1089

∴ Total C.I. = Rs 3780 + Rs 1089 = Rs 4,869

A = P + C.I. = Rs 18000 + Rs 4869 = Rs 22,869