A company purchased a machine for ₹15,00,000 and its effective life is estimated to be 10 years. A sinking fund is created for replacing the machine at the end of its effective life when its scrap value is ₹2,42,000. What amount company should provide at the end of every year out of profits for the sinking fund if it accumulates an interest of 5% per annum? [Given:$(1.05)^{10}=1.629$]

₹1,00,000

The correct answer is Option (2) → ₹1,00,000 **

Replacement requirement = purchase price − scrap value = ₹1500000 − ₹242000 = ₹1258000.

Let annual sinking fund deposit = $R$, interest $i=0.05$, period $n=10$, and $(1+i)^n=1.629$.

Future value of annual deposits: $R\displaystyle\frac{(1+i)^n-1}{i}=1258000$.

Hence $R=1258000\cdot\frac{i}{(1+i)^n-1}=1258000\cdot\frac{0.05}{1.629-1}$.

$1258000\cdot0.05=62900$ and $1.629-1=0.629$, so $R=\frac{62900}{0.629}=100000$.

Required annual provision = ₹100000