Answer:
The value of the car after 10 years will be $32669.74
Step-by-step explanation:
The value of the car was $38,000 in 2007. Its value depreciated by 1.5% every year.
To find its value after T years, we use the formula of compound interest (with decreasing rate):
[tex]A = P(1 - R)^T[/tex]
where A = value after T years
P = Principal (initial value of car)
R = rate of decrease of value = 1.5% = 0.015
Therefore, the value of the car after 10 years (2017) is:
[tex]A = 38000(1 - 0.015)^{10}\\\\A = 38000(0.985)^{10}\\\\A = 38000 * 0.85973\\\\[/tex]
=> A = $32669.74
The value of the car after 10 years will be $32669.74.
Based on the amount the car is depreciating by and its value in 2007, in 2017, the car would be worth $32,669.76.
The worth of the car can be calculated using the future value formula:
= Amount x ( 1 + rate) ^ number of years
As the value is decreasing, the rate will be negative.
The number of years is:
= 2017 - 2007
= 10 years
Solving would give:
= 38,000 x (1 - 1.5%) ¹⁰
= $32,669.76
In conclusion, the car would be valued at $32,669.76 in 2017.
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