Question

A building worth Rs 1, 33,100 is constructed on a plot of land worth Rs 72,900. After how many years will the values of both be same, if the land appreciates at 10% p.a. and the building depreciates at 10% p.a.?

Answer 1

For the building: 

`"V"_"n" = "V"_0  (1 - "r"/100)^"n"`

V_n = Rs 133100 `(1 - 10/100)^"n"`

V_n = Rs 133,100 x (0. 9)ⁿ

For the plot :

`"V"_"n" = "V"_0  (1 + "r"/100)^"n"`

V_n = Rs 72900 `(1 + 10/100)^"n"`

V_n = Rs 72900 × (1.1)ⁿ

Since, value becomes same: 

1,33,100 x (0.9)ⁿ = 72, 900 x (1.1)ⁿ `lim_(x -> ∞)`

`(1.1)^"n"/(0.9)^"n" = 133100/72900`

`(1.1)^"n"/(0.9)^"n" = 1331 /729 = 11^3/9^3`

t = 3

Hence, after 3 years value of both will be same.