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