A boat costs $92,000 and depreciates in value by 15% per year. How much will the boat be worth after 10 years?
18,112.45
78,200
18,941.98
69,000
Is the answer the first one? Could somebody write down the steps for me please? Pleas help asap! Thanks
Use depreciation formula:
Future value = Present value (1-rate)^(number of years)
rate is in % per annum = 0.15
number of years = 10
Present value = 92000
To find out how much the boat will be worth after 10 years with a yearly depreciation rate of 15%, you can follow these steps:
Step 1: Calculate the depreciation amount for each year.
Depreciation amount = Initial value * Depreciation rate
Depreciation amount = $92,000 * 0.15 = $13,800
Step 2: Calculate the remaining value after each year of depreciation.
Remaining value = Initial value - Depreciation amount
In year 1: Remaining value = $92,000 - $13,800 = $78,200
In year 2: Remaining value = $78,200 - $13,800 = $64,400
In year 3: Remaining value = $64,400 - $13,800 = $50,600
... and so on until year 10.
Step 3: Calculate the value after 10 years.
After 10 years: Remaining value = $18,112.45
Therefore, the boat will be worth $18,112.45 after 10 years.
To find out how much the boat will be worth after 10 years, you can use the formula for calculating compound interest. In this case, since the value of the boat is decreasing by 15% each year, you can think of it as compound depreciation.
Here are the steps to calculate the final value of the boat after 10 years:
1. Start with the initial value of the boat: $92,000.
2. Calculate the depreciation rate: 15% can be expressed as 0.15.
3. Calculate the annual depreciation amount: Multiply the initial value by the depreciation rate: $92,000 * 0.15 = $13,800.
4. Subtract the depreciation amount from the initial value to get the value after the first year: $92,000 - $13,800 = $78,200. This is the value of the boat after one year.
5. Repeat steps 3 and 4 for each subsequent year, using the value from the previous step as the new initial value.
- After the second year: $78,200 - ($78,200 * 0.15) = $66,470.
- After the third year: $66,470 - ($66,470 * 0.15) = $56,499.50.
- And so on, until you reach the 10th year.
6. After 10 years, the boat will be worth approximately $18,941.98.
Therefore, the correct answer is the third option: $18,941.98.