A new car is purchased for 23400 dollars. The value of the car depreciates at 11.5% per year. To the nearest year, how long will it be until the value of the car is 12700 dollars?

Question

Aaron Donovan

Mathematics

24 April, 03:19

A new car is purchased for 23400 dollars. The value of the car depreciates at 11.5% per year. To the nearest year, how long will it be until the value of the car is 12700 dollars?

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Mcmillan · Answer 1

Answer: 5 years

Step-by-step explanation:

Using same formula as for Compound Interest:

12700 = 23400 (1-.115) ^t

12700 = 23400 x 0.885^t

0.885^t = 127/234

Convert decimal into fraction:

177/200^t = 127/234

Take logarithm of both sides of thr equation:

t = log 177/200 (127/234)

t = 5.00242