A firm anticipates a capital expenditure of Rs 50000 for a new equipment in 5 years. How much should be deposited quarterly in a sinking fund carrying 12% per annum compounded quarterly to provide for the purchase ?

₹1868

The correct answer is option (4) :₹1868

Given $A= ₹50, 000$

$r=\frac{12}{4}$% per quarter

$i = 0.03$

$n= 5×4=20$ quarters

Using formula

$A= R\left[\frac{(1+i)^n-1}{i}\right]$

$50000=R\left[\frac{(1.03)^{20}-1}{0.03}\right]$

Let $x= (1.03)^{20}$

Taking log on both sides we get

$log\, x = 20\, log 1.03$

$log\, x = 20×0.0128$

$log\, x = 0.256$

$x= antilog\, 0.256$

$x= 1.803$

$R=\frac{50000×0.3}{1.803-1}$

$R=\frac{1500}{0.803}$

$= 1867.99$

$R= ₹1868$