Calculate years purchase for a property of useful life of 30 years and rate of interest of 5% per annum. The rate of interest for sinking fund is 3%.

12.5 14 17 22

Concept:

Year’s purchase 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.

Sinking Coefficient = $S = \frac{i_{s}}{(1 + i_{s})^{n} - 1}$

Year’s purchase = $\frac{1}{i + s}$ (Put i and s in decimals)

Where,

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

Calculation:

i_s = 0.03

Sinking Coefficient (s) = $S = \frac{i_{s}}{(1 + i_{s})^{n} - 1} = \frac{0.03}{(1 + 0.03)^{30} - 1} = 0.021$

i = 0.05

Year's Purchase = $\frac{1}{i + s} = \frac{1}{0.05 + 0.021}$ = 14.08 ≈ 14

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