A new car is purchased for 17900 dollars. The value of the car depreciates at 12.25% per year. What will the value of the car be, to the nearest cent, after 10 years?

Answer 1

We can use the formula Final Value=Initial Value * (1-Depreciation Rate)^{Number of Time Periods}

The initial value is 17900, the depreciation rate is 12.25% (which is plugged in as 0.1225 in the formula), and this occurs over 10 years.

Therefore we can set this up as V=$17900*(1-0.1225)¹⁰, and V=$4845.34.

If you look at the formula, it is the same as the compound interest formula Final Value=Initial Value * (1+Interest Rate)^{Number of Time Periods}, except in the case of depreciation, the rate is subtracted from 1 instead of added.

Answer 2

17900(.8775)^10

=17900(.2706895012)

=4,845.340282

=$4,845.34 rounded off to nearest cent

depreciating 12.25% = retaining 87.75% of the value annually

this assumes the car keeps a constant value all year and depreciates in one micro second, instantaneously, at the end of the year. the formula is the annual compounding formula Po(1-r/n)^nt where n=number of compounding periods per year, t= time in years, r = the interest rate, Po=initial value. if n=1, then the formula becomes Po(1-r)^t. for continuous depreciation, n approaches infinity and the formula becomes Po(e^-rt) where e=an irrational number=about 2.71828...= base of the natural log. 17900(e^-.1225(10))= $5,258.26 rounded to nearest cent

Answer 3

These responses are good. I would strongly not focus on memorizing that formula. Think about this simple example:

You bought a car for 100000 and it depreciates 20% each year (yeah cars are depreciating assets, so good real world example). So after year 1, the car's value is 80% of the original amount and then after year 2, the car's value is 80% of the year 1 value. Repeated multiplication pretty much, which is another word for exponent!

so, value is 17900*(1-0.1225) ^ 10

Answer 4

Use the formula A = P * (1-r)^t

where A is the amount left after t years, t is in years, r is the rate of depreciation in decimals (not in percent)

Therefore,

A = 17900 * (1 - 12.25/100)¹⁰

^{Note: If the problem had asked for appreciation value after t years, you should use (1+r) instead of (1-r)}

Answer 5

P = 17900(1 - 0.1225)¹⁰ = $4845.34