At what rate per cent per annum will 5000 amount to Rs. 5832 in 2 years, compounded annually?

Present value, P = Rs.5000


Amount, A = Rs.5832


Time, n = 2 years


Now,


Amount (A) = P (1 + R/100)n [Where, A = Amount with compound interest


P = Present value


R = Annual interest rate


n = Time in years]


∴ Amount (A) = P (1 + R/100)n


⇒ 5832 = 5000 (1 + R/100)2


⇒ (1 + R/100)2 = 5832/5000


⇒ (1 + R/100)2 = 2916/2500


⇒ (1 + R/100)2 = (54/50)2


⇒ 1 + R/100 = 54/50


⇒ R/100 = (54/50) - 1


⇒ R/100 = (54 – 50)/50


⇒ R/100 = 4/50


⇒ R = 400/50


⇒ R = 8


∴ Rate = 8 %.

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