A new car begins to decrease in value or depreciate from the

A new car begins to decrease in value, or depreciate, from the moment it is purchased. Suppose a new car purchased for $25,000 in July 2013 depreciates by 17% each year. When the value reaches $500, depreciation stops and the car is worth $500 from then on. In what year will the value of the car reach $500? Find the rate of depreciation for a car that takes 7 years to lose two-thirds of its value. Give your answer to the nearest tenth of a percent. In 2015, Sarah\'s truck, which she bought used in 2009 for $13,995.36, is worth $4477.31. Find the price paid by the original owner in 2004 to the nearest thousand dollars.

Solution

24. Cost of car = $25000

Depriciate at the rate of 17% each year

A = $500

A = P( 1- R/100)ⁿ

500 = 25000 ( 1- 17/100)ⁿ

1/50 = (1- 0.17)ⁿ

1/50 = (0.83)ⁿ

log(1/50) = n log 0.83

-1.69 = n (-0.081)

n = 1.69/0.081

n = 21 years

25. n = 7

A = 2/3 P

A = P( 1- R/100)ⁿ

2/3P = P (1- R/100)⁷

2/3 = (1- R/100)⁷

(0.67)^1/7 = 1- R/100

0.93 = 1- R/100

R/100 = 1-0.93

R/100 = 0.07

R = 7%

26. In 2015 cost of truck = $4477.31

In 2009 cost of truck = $13995.36

A = P(1-R/100)ⁿ

4477.31 = 13995.36 (1-R/100)⁶

4477.31/13995.36 = (1-R/100)⁶

0.32 = (1-R/100)⁶

(1-R/100) = 0.82

R/100 = 1-0.82

R/100 = 0.18

R = 18%

Cost of truck in 2004 =

A = P(1-R/100)ⁿ

A = 13995.36(1 - 18/100)¹¹

A = 13995.36*(0.82)¹¹

A = 1577.38 + 13995.36 = $15772.74 = $16000