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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 payment
Then, 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.5040

1245563_1509401_ans_74ae8ca9ec8242a681eeebf46a3b9826.PNG

Mathematics

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