Question

A machine costs Rs. $60,000$ and its effective life is estimated to be $25$ years. A sinking fund is to be created for replacing the machine at the end of its life time when its scrap value is estimated as Rs. $5,000$. The price of the new machine is estimated to be $100\%$ more than the price of the present one. Find the amount that should be set aside at the end of each year, out of the profits, for the sinking fund if it accumulates at an interest of $6\%$ per annum compounded annually.

Answer 1

Amount needed for buying a new machine $=2\times 60000=1,20,000$

Cost of scrap $=5,000$

So effective amount needed $=1,20,000-5,000=1,15,000$

Rate of intersest $=6\%$

Time $=25$ years

$A=P{(1+\frac{r}{100})}^t\Rightarrow 120000=P{(1+\frac{6}{100})}^{25}\Rightarrow 120000=P{\left(1.06\right)}^{25}\Rightarrow P=\frac{120000}{{\left(1.06\right)}^{25}}=\frac{120000}{4.291}=27965$

So an amount of Rs. $27,965$ must be kept aside