A company purchased a machine for Rs. 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 Rs. 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: \((1.05)^{10}=1.629\)]
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → Rs. 1,00,000
The sinking fund must provide the cost of a new machine less the scrap value of the old one:
\( A = 15{,}00{,}000 - 2{,}42{,}000 = 12{,}58{,}000 \)
The fund receives R at the end of every year for n = 10 years at i = 0.05, so A is the amount of an ordinary annuity:
\( \displaystyle A = R\left[\frac{(1+i)^n - 1}{i}\right] \)
\( \displaystyle 12{,}58{,}000 = R\left[\frac{1.629 - 1}{0.05}\right] \)
\( 12{,}58{,}000 = 12.58R \)
\( \displaystyle R = \frac{12{,}58{,}000}{12.58} = 1{,}00{,}000 \)
So the company should set aside Rs. 1,00,000 every year.