Question

# A sum of Rs.$$8400$$ was taken as a loan.This is to be repaid in to two equal annual installments.If the rate of interest is $$20\%$$ compounded annually then find the value of each installment?

Solution

## Let x be the annual paymentThen, present worth of x due 1 year hence + present worth of x due 2 year hence = Rs. 8400$$\frac{x}{(1+\frac{20}{100})}+\frac{x}{(1+\frac{20}{100})^{2}}= 8400$$$$\Rightarrow \frac{x}{\frac{120}{100}}+\frac{x}{(\frac{120}{100})^{2}}=8400$$$$\Rightarrow \frac{10x}{12}+\frac{100x}{144}=8400$$$$\Rightarrow 120x+100x=8400\times 144$$$$\Rightarrow x=\frac{8400\times 144}{240}=5040$$$$\therefore$$ Annual payment = Rs.5040Mathematics

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