The present worth of a bill of Rs. 1764 due f | vedclass

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Question

(C) The formula for the present worth $(P.W.)$ when the amount $(A)$ is due after $n$ years at a rate of $r\%$ per annum compounded annually is given

Vedclass · Accepted Answer

$1600$

Vedclass · Answer

(C) The formula for the present worth $(P.W.)$ when the amount $(A)$ is due after $n$ years at a rate of $r\%$ per annum compounded annually is given by: $P.W. = \frac{A}{(1 + \frac{r}{100})^n}$ Given: $A = Rs. 1764$,$r = 5\%$,$n = 2$ years. Substituting the values: $P.W. = \frac{1764}{(1 + \frac{5}{100})^2}$ $P.W. = \frac{1764}{(1 + 0.05)^2} = \frac{1764}{(1.05)^2}$ $P.W. = \frac{1764}{1.1025} = 1764 	imes \frac{10000}{11025}$ Alternatively,$P.W. = 1764 	imes (\frac{20}{21})^2 = 1764 	imes \frac{400}{441}$ $P.W. = 4 	imes 400 = Rs. 1600$.

The present worth of a bill of $Rs. 1764$ due for $2$ years at $5\%$ compound interest is (in $Rs.$)

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