Question

An old building has a future life of 15 years. The rate of interest on capital is 7%. If the coefficient of annual sinking fund is 0.43, then what will be value of year's purchase?
1. 3
2. 4
3. 2
4. 2.36

Answer 1

Correct Answer - Option 3 : 2

Concept:

Sinking Fund Method:

It is a technique for depreciating an asset while generating enough money to replace it at the end of its useful life. The sinking Fund coefficient(S) for n years is given below the formula

\(S = {i \over {(1+i_s)^n-1}}\)

Where i_s = interest rate of sinking fund, i = rate of interest, and S = Sinking fund coefficient

Year's Purchase(YP):

It is defined as the capital sum required to be invested in order to receive an annuity of Re 1.00 at a certain rate of interest.

\(YP = {1 \over (i+S)}\)

Where  i = rate of interest, and S = Sinking fund coefficient

Calculation:

Given Data

Rate of interest(I) = 7% = 0.07

Coefficient of annual sinking fund(S) = 0.43

So, Year's Purchase(YP)

\(YP = {1 \over (i+S)} = {1 \over (0.07+0.43)} = {1 \over (0.50)}\) = 2