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10. Mr. Gulati has a Recurring Deposit Account of300 per month. If the rate of interest is 12%and the maturity value of this account is* 8.100; find the time in years) of thisRecurring Deposit Account |
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Answer» P = Rs 300 r = 12% per annum = 1% per monthSum on maturity= Rs 8,100. let n be number of months after which the amount become mature. the first installment earns interest for n months, the second one for n-1 months, and the last installment earns interest for 1 month. The sum is a geometric series with ratio 1+r/100. Sum = P (1 + r/100)^n + P (1+r/100)^n-1 + P(1+r/100)^n-2+......+P(1+r/100)^18,100 = 300 [ 1.01^n + 1.01^n-1 + 1.01^n-2 +.... + 1.01^2 + 1.01 ]27 = 1.01 [ 1.01^(n+1) - 1 ] / [ 1.01 - 1] 27 = 101 [ 1.01^(n+1) - 1 ] 1.01^(n+1) = 1 + 27/101 = 128/101 (n+1) Log 1.01 = Log 128/101 n+ 1 = [ log 128/101 ] / Lo g 1.01 = 23.81 n = 22.81 months or, 1.984 years is the correct answer |
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