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You bought your car for $12500 and it is depreciating at 13% per year. How long until it is only worth half of what you paid for it? What is your answer to the nearest year?

Respuesta :

nkirotedoreen46

Answer:

5 years

Step-by-step explanation:

We are given;

  • Initial value of the car = $12,500
  • Rate of Depreciation = 13% per year
  • New value (after depreciation) = $6,250 (half the initial value)

We are required to determine the time taken for the value of the car to depreciate to half the original value.

  • We need to know the depreciation formula;
  • New value = Initial value ( 1 - r/100)^n

Therefore;

$6,250 = $12,500(1 - r/100)^n

0.5 = (1 - 13/100)^n

0.5 = 0.87^n

Introducing log on both sides;

log 0.5 = n log 0.87

Therefore;

n = log 0.5 ÷ log 0.87

  = 4.977

  = 5 years

Therefore, it takes 5 years for the value of the car to depreciate to half the initial value.

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