A man borrows Rs. 5100 to be paid back with c | vedclass

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(A) Let the value of each equal annual instalment be $P$.The formula for the present value of instalments paid at the end of each year under compound

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$2704$

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(A) Let the value of each equal annual instalment be $P$.The formula for the present value of instalments paid at the end of each year under compound interest is:$P 	imes (1 + r/100)^{-1} + P 	imes (1 + r/100)^{-2} = 	ext{Principal}$Given,Principal = $5100$,Rate $(r)$ = $4 \%$,Time = $2$ years.$\Rightarrow \frac{P}{(1 + 4/100)} + \frac{P}{(1 + 4/100)^2} = 5100$$\Rightarrow \frac{P}{(26/25)} + \frac{P}{(26/25)^2} = 5100$$\Rightarrow \frac{25P}{26} + \frac{625P}{676} = 5100$Taking $676$ as the common denominator:$\Rightarrow \frac{25 	imes 26 	imes P + 625P}{676} = 5100$$\Rightarrow \frac{650P + 625P}{676} = 5100$$\Rightarrow \frac{1275P}{676} = 5100$$P = \frac{5100 	imes 676}{1275}$$P = 4 	imes 676 = 2704$Thus,each instalment is $Rs. 2704$.

$A$ man borrows $Rs. 5100$ to be paid back with compound interest at the rate of $4 \%$ p.a. by the end of $2$ years in two equal yearly instalments. How much (in $Rs.$) will be each instalment?

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