A new car is purchased for 20800 dollars. The value of the car depreciates at 10.75% per year. What will the value of the car be, to the nearest cent, after 13 years?
Question
A new car is purchased for 20800 dollars. The value of the car depreciates at 10.75% per year. What will the value of the car be, to the nearest cent, after 13 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 = $20,800 r = 10.75% = 0.1075 (as a decimal) t = 13 years
Substitute these values into the formula:
V = 20800 * (1 - 0.1075)^13
Now, calculate the value inside the parentheses:
1 - 0.1075 = 0.8925
So, the formula becomes:
V = 20800 * (0.8925)^13
Now, calculate the exponent:
(0.8925)^13 ≈ 0.2635
So, the formula becomes:
V = 20800 * 0.2635
Finally, calculate the multiplication:
V ≈ 20800 * 0.2635 = $5482.80
So, the value of the car after 13 years, to the nearest cent, will be approximately $5482.80.
Similar Questions
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?
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?
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 $15,500. After each year, the resale value decreases by 20%. What will the resale value be after 3 years?Use the calculator provided and round your answer to the nearest dollar.
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.