Each year the value of a car decreases by 25% of its value the previous year. After 5 years, what is the value of a car originally worth $17,500? Express answer to the nearest dollar.
The residue value after each year is 100-25=75% of the previous year.
So after n years, the value is
P(0.75^n)
=$17,500 * 0.75^5
=...
I'll let you do the calculations.
To find the value of the car after 5 years, we need to calculate the value of the car after each year.
Year 1: The car is worth 100% - 25% = 75% of $17,500.
Value after Year 1 = $17,500 * 0.75 = $13,125.
Year 2: The car is worth 75% - 25% = 75% of $13,125.
Value after Year 2 = $13,125 * 0.75 = $9,843.75.
Year 3: The car is worth 75% - 25% = 75% of $9,843.75.
Value after Year 3 = $9,843.75 * 0.75 = $7,382.81.
Year 4: The car is worth 75% - 25% = 75% of $7,382.81.
Value after Year 4 = $7,382.81 * 0.75 = $5,537.11.
Year 5: The car is worth 75% - 25% = 75% of $5,537.11.
Value after Year 5 = $5,537.11 * 0.75 = $4,152.83.
Therefore, the value of the car after 5 years is approximately $4,152.83.
To find the value of the car after 5 years, we can use exponential decay formula.
Step 1: Convert the given decrease percentage to a decimal. Since the value decreases by 25%, we have 25/100 = 0.25.
Step 2: Calculate the value of the car after each year:
- After year 1, the value is 100% - 25% = 75% of the original value: 0.75 * $17,500 = $13,125.
- After year 2, the value is 75% - 25% = 75% of the previous year's value: 0.75 * $13,125 = $9,843.75.
- After year 3, the value is 75% - 25% = 75% of the previous year's value: 0.75 * $9,843.75 = $7,382.81.
- After year 4, the value is 75% - 25% = 75% of the previous year's value: 0.75 * $7,382.81 = $5,537.11.
- After year 5, the value is 75% - 25% = 75% of the previous year's value: 0.75 * $5,537.11 = $4,152.83.
Step 3: Round the final answer to the nearest dollar. The value of the car after 5 years is approximately $4,153.
Therefore, the value of the car after 5 years is $4,153.