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?

Answer 1

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