Question
Rama and Dipak each invested a sum of ₹8000 for a
period of two years at 15% compound interest per annum. However, while for Rama the interest was compounded annually, for Dipak it was compounded every eight months. How much more will Dipak receive as interest compared to Rama at the end of the two years?Solution
When the rate of interest is compounded eight months of Dipak = (15 × 8/12) %=10% Time for Dipak = (2 × 12/8) = 3 years Now, CI for Rama is. A = P (1 + r/100) t =8000(1+15/100)2 (8000 × 23/20 × 23/20) = (8000 × 529/400) =20×529 = 10580 Interest = A – P = (10580– 8000) Rs. = 2580 Rs. Now, CI for Dipak is. A = P (1 + r/100) t A = 8000(1 + 10/100)3 = 8000(1 + 1/10)3 = 8000(11/10)3 = 8×1331=10648 Interest = A – P = (10648– 8000) =2648Rs. Now, Dipak receives as much interest as compared to Rama at the end of the two-year period = Rs. (2648 – 2580) = 68 Rs.
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