At what rate per cent per annum will Rs 640 amount to Rs 774.40 in 2 years when compounded annually?

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Solution

$Let the required rate be R % p . a . A = 774.40 P = 640 n = 2 years N o w, A = P {(1 + \frac{R}{100})}^{n} \Rightarrow 774.40 = 640 {(1 + \frac{R}{100})}^{2} \Rightarrow \frac{774.40}{640} = {(1 + \frac{R}{100})}^{2} \Rightarrow 1.21 = {(1 + \frac{R}{100})}^{2} \Rightarrow {(1.1)}^{2} = {(1 + \frac{R}{100})}^{2} \Rightarrow 1.1 - 1 = \frac{R}{100} \Rightarrow 0.1 = \frac{R}{100} \Rightarrow R = (0.1 \times 100) = 10 Hence, the required rate is 10 % p . a .$

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