Price Increases and Decreases

Question

Suppose that 9 years ago, Miranda bought a $17547 car. Each year the car's value decreased by 13%. If she sold the car today for 197% of its (current) value, how much did she make in the sale?

Answer 1

Let V be the value of the car after 9 years of depreciation.

C = $17,549 is the amount Miranda paid for the car.

r = -0.13 is the annual rate of depreciation.

t = 9 years

V = C(1+r)^t

Plug in the numeric values to see that after 9 years Miranda's car is worth

V = 17,549(1-0.13)⁹ = 17,549(0.87⁹) = $5011.01

Miranda sold her car for 197% or 1.97 x V

She sold it for 1.97($5011.01) = $9871.70

Her profit from the sale was $9871.70 - 5011.01 = $4860.69.