Chapter 5.R, Problem 49RE

Salvage Value The number of years n for a piece of machinery to depreciate to a known salvage value can be found using the formula

$n\text{ = }\frac{\log s-\log i}{\log \left(1-d\right)}$

where s is the salvage value of the machinery, i is its initial value, and d is the annual rate of depreciation.

(a) How many years will it take for a piece of machinery to decline in value from $\$90,000$ to $\$10,000$ if the annual rate of depreciation is $0.20\left(20\%\right)$?

(b) How many years will it take for a piece of machinery to lose half of its value if the annual rate of depreciation is $15\%$?