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Automobiles start losing value, or depreciating, as soon as they leave the car dealership. Five years ago, a family purchased a new car that cost $16,490. If the car lost 13% of its value each year, what is the value of the car now?

Respuesta :

arokoyuola

Answer:

$8,218.96

Step-by-step explanation:

At the end of the 1st year, 16,490 - (16,490 *13/100) = $14,346.3

At the end of the 2nd year, 14,346.3 - (14346.3*13/100) = $12,481.28

At the end of the 3rd year, 12481.28 - (12481.28*13/100) = $10,858.71

At the end of the 4th year, 10858.71 - (10858.71*13/100) = $9,447.08

At the end of the 5th year, 9447.08 - (9447.08*13/100) = $8,218.96

The value depreciation is compounding each year at 13% rate.

The value of the car currently is $8218.96

Given that:

  • The car was brought five years ago.
  • The rate of depreciation is 13%
  • The cost of car was $16,490

To find:

The resultant cost of car now.

The formula for resultant amount after depreciation with rate R% annually after time T years at initial price P is:

[tex]A = P(1-\dfrac{R}{100}})^T[/tex]

( i used same Compound interest formula to find final amount but the rate is negative here since it is depreciation)

Since R = 13, T = 5, and P = $16,490, thus we have:

[tex]A = 16490(1-\dfrac{13}{100})^5= 16490 \times (0.87)^5 \approx 0.49842 \times 16490 \approx 8218.96[/tex]

Thus, the final price of car would be approx  $8218.96

Learn more about depreciation here:

https://brainly.com/question/7279545

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