SOLUTION: Hi would you please help me with my homework. Suppose that an automobile loses 1/5 of its value each year; that is at the end of a given year the value is 4/5 of the value at th

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Question 930749: Hi would you please help me with my homework.
Suppose that an automobile loses 1/5 of its value each year; that is at the end of a given year the value is 4/5 of the value at the beginning of that year. If a car costs $24,000 new, What is the value at the end of five years?
My professor said that the answer is $7864.
Would you please show me the steps on how to solve this problem. Thank you.
Found 2 solutions by jim_thompson5910, josgarithmetic:
Answer by jim_thompson5910(35256) (Show Source):
You can put this solution on YOUR website!
an = a*(r)^(n-1)

an = 24000*(4/5)^(n-1)

a6 = 24000*(4/5)^(6-1) ... plug in n = 6 (to make sure you get to the end of year 5)

a6 = 7,864.32 ... use a calculator here

That rounds to $7,864
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Answer by josgarithmetic(39618) (Show Source):
You can put this solution on YOUR website!
This works just like your other question. v for value after any given t number of years, . What is v when t=5? You could if you wish, compute for each the the five successive years, year by year.

The sophisticated way is to either use a calculator or table of logarithms and algebra.

The long way:
Year_________________Value
0_____________________24000
1_____________________19200
2_____________________15360
3_____________________12288
4______________________9830
5______________________7863