A person constructed a warehouse at a cost of Rs. 4,00,000, excluding the cost of land. The warehouse will become obsolete after 10 years. Find the amount of sinking fund to be annually deposited at the rate of 5% compound interest. The scrap value of the warehouse is 10% of the cost of purchase. 

Concept:

Sinking fund:

• It is a fund that is built up for the sole purpose of replacement or reconstruction of the property when it loses its utility at the end of its useful life.
• The fund is regularly deposited in a bank or with an insurance agency so that on the expiry of the period utility of the building, a sufficient amount is available for its replacement.
• It is given as,
• Annual installment of sinking fund, Sc = \(\frac{S\times i}{(1+i)^{n}-1}\) = \(\frac{(Original\:cost-Scrap\:value)\times i}{(1+i)^{n}-1}\) 

Where,

S = Total amount of Sinking fund accumulated at the end of utility period = Original cost - Scrap value

i = rate of interest

n = utility period

Given,
Original cost = Rs. 4,00,000 

i = 5% = 0.05

n = 10 years 

Scrap value = 10% of purchase cost

∵ We know that, S = Purchase cost - Scrap value =  400000 - 0.1 × 400000 = 0.9 x 400000

Annual installment of sinking fund, Sc = \(\frac{0.9\times 400000\times 0.05}{(1+0.05)^{10}-1}\) = 28,621.64 ≈ 28,571 Rs
∴ Sc = 28,571 Rs