Q15 of 74 Page 154

At what rate per cent per annum will a sum of Rs. 7500 amount to Rs. 8427 in 2 years, compounded annually?

Present value, P = Rs.7500


Amount, A = Rs.8427


Time, n = 2 years


Now,


Amount (A) = P (1 + R/100)n


⇒ 8427 = 7500 (1 + R/100)2


⇒ (1 + R/100)2 = 8427/7500


⇒ (1 + R/100)2 = (53/50)2


⇒ (1 + R/100) = (53/50)


⇒ R/100 = 53/50 – 1


⇒ R/100 = (53 – 50)/50


⇒ R = 3/50 × 100


⇒ R = 6


∴ Rate = 6%

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