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Question
Calculate the sum of money on which the compound interest (payable annually) for 2 years be four times the simple interest on Rs. 4,715 for 5 years, both at the rate of 5% per annum.
Solution
Given : Principal = Rs.4,715; time = 5 years and rate= 5% p.a.
∴ S.I. = `[ "P" xx "R" xx "T" ]/100 = [ 4715 xx 5 xx 5 ]/100 = Rs. 1,178.75`
Then C.I. = Rs.1,178.75 x 4 = Rs. 4,715
Time = 2 years and rate = 5%
∴ C.I. = P`[( 1 + r/100)^n - 1 ]`
⇒ 4,715 = P`[( 1 + 5/100)^2 - 1 ]`
⇒ 4,715 = P`[41/400]`
⇒ P = Rs. `[ 4,715 xx 400 ]/41` = Rs. 46,000.
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