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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.?
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Solution
For the building:
`"V"_"n" = "V"_0 (1 - "r"/100)^"n"`
Vn = Rs 133100 `(1 - 10/100)^"n"`
Vn = Rs 133,100 x (0. 9)n
For the plot :
`"V"_"n" = "V"_0 (1 + "r"/100)^"n"`
Vn = Rs 72900 `(1 + 10/100)^"n"`
Vn = 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.
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