Daniel’s Print Shop purchased a new printer for $35,000. Each year it depreciates at a rate of 5%. How much will the printer be worth in 8 years?

Answer 1

A = P(1-.05)^t Each year it's worth 95% of the previous year

A = 35,000(.95)^8 = $23,219.72

You might be tempted to multiply 5% by 8 = 40%

that would leave 60% of 35,000 = $21,000, but that takes off too much, by deducting 5% of 35,000 each year. You want 5% off the previous year each year. But $21,000 give you a lower bound.

.95 x 35K = 33.25 in one year

.95 x33.25 = 31.59 in 2 years

.95 x 31.59 =30 in 3

.95 x 30 = 28.5 in 4

.95 x 28.5 = 27.1 in 5

.95 x 27.1 = 25.7 in 6

.95 x 25.7 = 24.4 in 7

.95 x 24.4 = 23.2 in 8 years 23.2 is about $23,200 with rounding errors

do that 8 times with more decimal places and you get $23,219.72