SOLUTION: Barry says a friend told him, "my car has lost 20% of it's value each year, and I've had it for 4 years, so it's only worth 20% of what I paid for it. I'll sell it to you for that

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Question 540067: Barry says a friend told him, "my car has lost 20% of it's value each year, and I've had it for 4 years, so it's only worth 20% of what I paid for it. I'll sell it to you for that amount." An independent mechanic tells Barry that the car is in great condition. Would you advise Barry to purchase the car? Explain

Answer by jpg7n16(66) About Me  (Show Source):
You can put this solution on YOUR website!
Yes. He should buy the car. Here's why: the value of the car at the end of each year is 20% less than it was the year before. NOT 20% less of the original value. His friend did the WRONG math of
100%-(4*20%)=20%
The correct math is to say that each year the car is worth 20% less than the previous year. 100%-20%=80% of the previous year. So the true value of the car is not 20% but rather:
100%28%28.8%29%5E4%29% or 40.96% of the original value.
Let's put some numbers to that so you can see what that means. Say the car originally cost $20,000. Barry's friend is selling it for 20% of that amount:
20000%2A0.20=4000
When the true value of that car is 40.96% of the original amount:
20000%2A.04096=8192
Would you pay $4,000 for a car worth $8,192? I would!