. . A new car depreciates at a rate of 15% per year. What is the expected value of a $25,000 car after 5 years (rounded to nearest whole dollar)? . . . . . . . . . . . . A). $20750 . . B). $11093 . . C). $9429 . . D). $6250 . .

Respuesta :

The answer to the question above is letter B. The new car depreciates at the rate of 15% per year. The expected value of the car after 5 years is $11,093. to explain the calculation of the answer :

year       amount      %      interest        total
  1          25000       0.15     3750         21250
  2          21250       0.15     3187.5      18062.5
  3         18062.5     0.15     2709.375  15353.13
  4         15353.13   0.15     2302.969  13050.16
  5         13050.16   0.15    1957.523   11092.63
You might have lacking given information so you can re-check the given.
You are lacking the value of L (life of the car in years).

There are several types of depreciation formulas. The straight-line method, sinking fund method, declining balance and double-declining balance. For the other methods you can search it up.

I used the sinking fund method for this case:

d = \frac{(25000 - 0)*0.15}{(1+0.15)^{L} -1

where d is the annual cost of depreciation
Co is the original cost,
[tex] C_{L} [/tex] is the value at the end of the life of object or salvage value
L is useful life of the property
and i is the interest rate.

The salvage value can be assumed as zero in this case, therefore,
[tex]d = \frac{(25000 - 0)*0.15}{(1+0.15)^{L} -1}[/tex] 

In solving for the expected depreciation one can use this formula:
[tex] D_n = d*\frac{(1 + i)^{n}-1 }{i}[/tex]
where n is the number of years of the expected depreciation
D_n is the depreciation up to the number of years (n)