SOLUTION: A vehicle purchase for $25,000 depreciates at a constant rate of 8% determine the approximate value of the vehicle 14 years after purchase round to the nearest whole dollar

Question 1167807: A vehicle purchase for $25,000 depreciates at a constant rate of 8% determine the approximate value of the vehicle 14 years after purchase round to the nearest whole dollar
Found 2 solutions by Boreal, Theo:
Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
This is A=Ao(1-x)^14
or A=25000(0.92)^14
=$7779.82 or $7780.
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
the vehicle is purchased for 25,000 dollars.

it loses 8% of value each year.

the formula to use is f = p * (1 + r) ^ n

f is the future value
p is the present value
r is the rate of growth each year
n is the number of years.

the rate of growth per year is equal to the percent growth each year / 100.

therefore, a percent growth of -8% each year equals a rate of growth each year of -.08.

when p = 25,000 and r = -.08 and n = 14, the formula becomes:

f = 25,000 * (1 - .08) ^ 14 = 7779.820763.

the value of the car after 14 years is 7780 dollars.

this can be seen on a graph.

let y = the value of the car.

the equation is y = 25000 * (1 - .08) ^ x = 25000 * .92 ^ x

this is what the graph looks like.

the coordinate points on the graph are in (x,y) format.

x is the number of years.
y is the value of the car.

on the graph, when x = 14, y = 7779.821.

round y to the nearest integer to get y = 7780.

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