A new car costs $30,000, The value decreases by 15% each year. How do you find the car's value after 4 years?

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A new car costs $30,000, The value decreases by 15% each year. How do you find the car's value after 4 years?

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Answer 1 · 2015-10-19T18:36:57

After 4 years the car is worth $$15,660.19$

Explanation:

Let $a_1=30,000$ be the car's initial value, We knwo, that every year the new value can be calculated as:

$a_{n+1}=a_n*(1-0.15)=0.85a_n$

From this we know, that the consecutive values form a (decreasing) geometric sequence with: $a_1=$30,000$ , $q=0.85$ , and every term $a_i$ (for $i>=2$ ) is the car's value after year number $i-1$ , so the value we are looking for is $a_5$

$a_5=a_1*q^(5-1)=a_1*q^4=30,000*(0.85)^4 ~~15,660.19$

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A new car costs $30,000, The value decreases by 15% each year. How do you find the car's value after 4 years?

1 Answer

Explanation:

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