A person constructed a warehouse at a cost of Rs. 4,00,000, excluding cost of land. The warehouse will become obsolete after 10 years. Find amount of sinking fund to be annually deposited at rate of 5% compound interest. The scrap value of warehouse is 10% of 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 = $\frac{S\times i}{(1+i{)}^n-1}$ = $\frac{(Originalcost-Scrapvalue)\times i}{(1+i{)}^n-1}$ 

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