A building fetches a rent of Rs. 10,000 annually. After repairing, it will last for 2 years. If the rate of interest on capital is 5% and the co-efficient of annual sinking fund is 0.05, then estimate the capitalized value of the building after 2 years.

Concept:

Capitalized value:

It is the amount of money whose annual interest at the highest prevailing rate of interest will be equal to the net income from the property.

To determine the capitalized value of a property, it is required to know the net income from the property and the highest prevailing rate of interest.

Capitalized value (V) of the property is given by:

V = Net annual income × Year purchase

Year’s purchase is defined as the capital sum required to be invested in order to receive an annuity of Rs. 1.00 at a certain rate of interest.

\({\rm{Yea}}{{\rm{r}}^{\rm{'}}}{\rm{s\;purchase}} = \frac{1}{{i \;+ \;s}}\)
1i+s

(Put i and S in decimals)

Where,

i = rate of interest

S = Sinking fund coefficient

Calculation:

Given: Net annual income = 10000, i = 5% = 0.05, s =0.05

\({\rm{Yea}}{{\rm{r}}^{\rm{'}}}{\rm{s\;purchase}} = \frac{1}{{0.05 \;+ \;0.05}}\)

⇒ Year's purchase = 10

V = 10000 × 10 = 100000