Question

A machine purchased at a cost of Rs.10,000 has a useful life of two years. The amount which is to be set aside annually as sinking fund at the rate of 10% compound interest will be
1. Rs. 1000/ 0.10
2. Rs. 1000/ 0.31
3. Rs. 1000/ 0.21
4. Rs. 1000/ 1.10

Answer 1

Correct Answer - Option 3 : Rs. 1000/ 0.21

Concept: 

Sinking fund:

(i) 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,

\(\text{Annual installment of sinking fund}, S_c = \frac{SR}{(1 \;+ \;R)^n - 1}​​\)

Where,

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

R = rate of interest and n = utility period

Calculation:

Given: R = 10%, n = 2 years, S = 10000

\(\text{Annual installment of sinking fund}, S_c = \frac{10000 ~\times~ 0.1}{(1\; +\;0.1)^2- 1}\)

\(\text{Annual installment of sinking fund}, S_c = \frac{1000}{0.21}\)

⇒ S_c = 1000/0.21