Help please!!!!

Question

A car is purchased for $17,000. After each year, the resale value decreases by 35%. What will the resale value be after 3 years? Use a calculator and round your answer to the nearest dollar.

Answer 1

If the value of the car decreases by 35% each year, then the remaining value is 65% (because 100-35=65). After one year the value is $17000 x 0.65 or $11050. After 2 years the value is $11050 x 0.65, or $7182.50. After 3 years the value is $7182.5 x 0.65 or $4668.62. Round that up to $4669.

Answer 2

Value in t years = V(t) = 17000(1 - 0.35)^t

So, value in 3 years = V(3) = 17000(0.65)³

Answer 3

FV = 17000e^.-35(3)

= 17000/e^1.05

= about $5959 rounded to nearest dollar

if you assume continuous depreciation, which is practical reality

but the problem suggests compounding decay once a year

FV = 17K(1-.35)^3 = 17000(.65)^3 = $4,669

year 0 17K

end of year 1, .65(17K) = 11050

year 2: .65(11050) = 7182.5

year 3 .65(7182.5) = 4668.63

decay compounding 12 times a year for 3 years

FV = 17K(1-.35/12)^12(3) = 5857

compounding twice annually for 3 years

FV = 17K(1-.35/2)^2(3) = 17K(.825)^6 = 5360

Answer 4

This is known as depreciation. When it is increasing it is known as compounding...

There is a way to solve this year by year, and there is a way to solve this by all 3 years.

The remaining value after the first year is 65% or .65. After the next year, it is .65 of that, so .65^2. Then on the third year, it is .65 that value, so it is .65^3 x original value.

The simple way is, it depreciates over three years by 35%. 100-35=65% so the remaining value is .65 per year. .65^3 x original value. The results are the same, but instead of going year by year, you solve it in one step.

So:

.65^3=0.274625 x 17,000 = 4,668.625 Rounding up tp the nearest dollar means no cents. $4,669 or depending on country 4 669$