At what rate per cent per annum willl $R s 640$ amount to $R s 774.40$ in $2$ years, interest being compound annually?

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Solution

Since, interest is compounded anvally
$A = P {(1 + \frac{R}{100})}^{T}$
$794.40 = 640 {(1 + \frac{R}{100})}^{2}$
$\Rightarrow {(1 + \frac{R}{100})}^{2} = \frac{774.40}{640} = \frac{7744}{6400}$
$\Rightarrow 1 + \frac{R}{100} = \frac{\sqrt{7744}}{\sqrt{6400}} = \frac{88}{80}$
$\Rightarrow 1 + \frac{R}{100} = \frac{110}{100}$
$\Rightarrow \frac{R}{100} = \frac{110 - 100}{100}$
$\Rightarrow R = 10$
$∴$ Rate is $10 %$ per annum.

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