Question
A sum of money amounts to Rs 6050 in 2 years and Rs 6655
in 3 years at compound interest, interest being compounded annually. What is the rate of interest per annum?Solution
ATQ, Let the principal be P and the rate be r% p.a. Amount after 2 years = P(1 + r/100)Β² = 6050 Amount after 3 years = P(1 + r/100)Β³ = 6655 Divide the second by the first: [ P(1 + r/100)Β³ ] / [ P(1 + r/100)Β² ] = 6655 / 6050 β 1 + r/100 = 6655 / 6050 Simplify 6655/6050: Divide numerator and denominator by 5: 6655 Γ· 5 = 1331 6050 Γ· 5 = 1210 So, 1 + r/100 = 1331/1210 Notice 1331 = 11Β³ and 1210 = 11 Γ 110 β 1331/1210 = 11/10 So, 1 + r/100 = 11/10 β r/100 = 1/10 β r = 10%
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