A new car is purchased for 22300 dollars. The value of the car depreciates at 10.25% per year. What will the value of the car be, to the nearest cent, after 6 years?
Question
A new car is purchased for 22300 dollars. The value of the car depreciates at 10.25% per year. What will the value of the car be, to the nearest cent, after 6 years?
Solution
To solve this problem, we will use the formula for exponential decay, which is:
V = P * (1 - r)^t
where:
- V is the final value of the car
- P is the initial value of the car
- r is the rate of depreciation
- t is the time in years
Given in the problem: P = $22,300 r = 10.25% = 0.1025 (as a decimal) t = 6 years
Substitute these values into the formula:
V = 22300 * (1 - 0.1025)^6
First, calculate the value inside the parentheses:
1 - 0.1025 = 0.8975
Then, raise this result to the power of 6:
0.8975^6 = 0.558405
Finally, multiply this result by the initial value of the car:
V = 22300 * 0.558405 = $12452.63
So, the value of the car after 6 years, to the nearest cent, will be approximately $12,452.63.
Similar Questions
A new car is purchased for $25,000. The value of the car depreciates by 10% in the first year and 10% in the next. What is the value of the car after two years?$19,500$19,750$20,000$20,250$20,500
A car is purchased for $31,000. Each year it loses 25% of its value. After how many years will the car be worth $6400 or less?
A car's value depreciates by 20% each year. If the current value of the car is $15,000, what will be its value after one year?
Kyle buys a car for $58,000. His car immediately starts depreciating, losing 23% of its value every year. How much will the car be worth in 12 years?If necessary, round your answer to the nearest cent.
A car is purchased for US$24.000. After each year, the resale value decreases by 20%. What will the resale value be after 4 years?
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.