Question

PLEASE HELP

You buy a new motorcycle for $15,500. Its value depreciates by 8.5% each year. In how many years will it be worth only a tenth of what you paid for it?

a. 26
b. 27
c. 24
d. 25

Answer 1

a. 26

Explanation:

The formula for depreciation is given as

y = a(1 - r)^t

a = Initial value = $15,500

y = Current value = 1/10 of Initial value = $1,550

r = depreciation rate = 8.5% = 0.085

t = time in years = ?

Hence,

1550 = 15500(1 - 0.085)^t

1550 = 15500(0.915)^t

Divide both sides by 15500

1550/15500 =(0.915)^t

0.1 = (0.915)^t

Take the Logarithm of both sides

log 0.1 = log(0.915)^t

log 0.1 = t log (0.915)

Divide both sides by log 0.915

t = log 0.1/log 0.915

t = 25.920900964 years

Approximately Time t = 26 years

Option a is correct