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Calculate the amount and compound interest on(a) Rs 10800 for 3 years at 12 1/2% per annum compounded annually.(b) Rs 18000 for 2 1/2 years at 10% per annum compounded annually. |
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Answer» (a) Principal (P) = Rs 10, 800 Rate (R) 12 1/2% = 25/2% ( annual ) Number of years (n) = 3 Amount, A = p( 1 + R/100 )n = Rs [10800 (1 + 25/200)3] = Rs [10800(225/200)3] = Rs ( 10800 x 225/200 x 225/200 x 225/200 ) = Rs 15377.34375 = Rs 15377.34 (approximately) C.I. = A − P = Rs (15377.34 − 10800) = Rs 4,577.34 (b) Principal (P) = Rs 18,000 Rate (R) = 10% annual Number of years (n) = 2 1/2 years 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 (18000 x 11/10 x 11/10) = Rs 21780 By taking Rs 21780 as principal, the S.I. for the next 1/2 year will be calculated. S.I = Rs (21780 x 1/2 x 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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