In 2004, your family bought a new car for $15,000. Each year the value of the car is decreasing approximately 15% per year. Your father plans to keep the car 5 years before he buys another new car. What will be the value of the car when he's ready to trade?
What is the formula?
First Year = 15000 / 100 * 15 = 2250 (minus from 15000 = 12750)
Second year = 12750 / 100 * 15 = 1912.50 (minus from 12750 = 10837.50
Third Year = 10837.50 / 100 * 15 = 1625.63 (minus from 10837.50 = 9211.87)
Continue for year four and five :)
To calculate the value of the car after 5 years, we can use the formula for compound interest, which is:
A = P(1 - r/n)^(nt)
Where:
A = the final amount (value of the car after 5 years)
P = the initial principal (purchase price of the car, $15,000)
r = the interest rate per year (rate of depreciation, 15% or 0.15 in decimal form)
n = the number of times interest is compounded per year (assuming once per year, n = 1)
t = the number of years (in this case, t = 5)
Substituting the given values into the formula, we get:
A = $15,000(1 - 0.15/1)^(1*5)
Simplifying further:
A = $15,000(1 - 0.15)^5
To find the value of the car when your father is ready to trade, we need to calculate A.