Question

Jason bought new truck for $25,000. The truck depreciates 15% of its value each year. How much is it worth after 5 years?

Answer 1

Answer:

Step-by-step explanation:

After 2 months, it will have depreciated again by the same percentage. So the amount it was at the beginning of that month will have also been multiplied by (1 - y/100), so the amount after two months is A(1 - y/100)2.

 

After 12 months, we should get that the car has depreciated to become worth A(1 - y/100)12. But we also know what the yearly depreciation rate is: 12.4%.

 

So the car after a full year is worth A(1 - 0.124) = 0.876A.

 

Now we have two expressions that both represent the value of the car:

 

A(1 - y/100)12 = 0.876A

 

So the initial value of the car really doesn't matter at all if we're trying to find the monthly depreciation rate. We can divide both sides by A to get:

 

(1 - y/100)12 = 0.876

 

To get what y is, take the 12th root of both sides. If your calculator sucks, you can take the square root of 0.876 twice and the cube root once.  

 

1 - y/100 = (0.876)1/12

 

y/100 = 1 - (0.876)1/12

 

Multiply by 100 to get y%.

 

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I'm not very strong at these. I'm assuming that "the value depreciates each year at the rate of 12.4%" means that at the end of the year the value of the car is 87.6% of what it was at the beginning of the year.  

 

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I get y to be 1.1% when I round to the nearest tenth.

Answer 2

Given:

Jason bought new truck for $25,000. The truck depreciates 15% of its value each year.

To Find:

How much is it worth after 5 years?

Solution:

Original price of truck = $25000

The truck depreciates 15% of its value each year.

So, Price of truck after t years = $P(1-r)^t$

So, Price of truck after 5 years =$25000(1-0.15)^5=11092.63$

Hence It is worth $11092.63 after 5 years