So im having trouble with this QUESTION :::
Its suppose you buy a car with a value of $9,250. Each year the value of your car will depreciate by 5.1%. How much will your car be worth in 8 years?
So I did the problem 9250 / 100= 92.50 which is 1% 92.50 x 5.1 = 471.75 which is 5.1% 471.75 x 8 = 3774 9250 - 3774 = 5476 The answer is >$5476<
But the answers for the questions are
A(12,446.89
B(7,195.37
C(7,933.91
D(6,085.15
Im really confused do I have to round up ? To 6,085.15 ?
if it depreciates by 5.1%, that means that each year its value is 94.9% what it was the year before. So, after 8 years, the value is
9250 * 0.949^8 = 6085.15
oobleck is correct
To calculate the value of the car after 8 years, we need to calculate the depreciation for each year and subtract it from the original value.
Step 1: Convert the percentage to decimal form.
5.1% = 0.051
Step 2: Calculate the annual depreciation.
Depreciation = Original value * Depreciation rate
Depreciation = $9,250 * 0.051 = $472.75 (rounded to the nearest cent)
Step 3: Calculate the remaining value after each year.
Year 1: $9,250 - $472.75 = $8,777.25
Year 2: $8,777.25 - $472.75 = $8,304.50
Year 3: $8,304.50 - $472.75 = $7,831.75
Year 4: $7,831.75 - $472.75 = $7,359.00
Year 5: $7,359.00 - $472.75 = $6,886.25
Year 6: $6,886.25 - $472.75 = $6,413.50
Year 7: $6,413.50 - $472.75 = $5,940.75
Year 8: $5,940.75 - $472.75 = $5,468.00
After 8 years, the car will be worth $5,468.00.
Therefore, none of the given answer choices (A, B, C, D) match the correct answer of $5,468.00.
To answer this question, let's break it down step by step:
1. Start with the initial value of the car, which is $9,250.
2. Each year, the value of the car depreciates by 5.1%. To calculate the depreciation, first find 5.1% of the initial value. One way to do this is by multiplying $9,250 by 0.051 (convert 5.1% to decimal form). You'll get $472.75 as the amount that the car depreciates each year.
3. Next, determine how much the car will be worth after 8 years. To do this, multiply the annual depreciation amount ($472.75) by the number of years (8). This gives you a total depreciation of $3,782.
4. Finally, subtract the total depreciation from the initial value of the car: $9,250 - $3,782 = $5,468.
Based on these calculations, the car will be worth $5,468 after 8 years, not $6,085.15. It seems like there might be an error in the given answer choices, or perhaps you made a mistake in the calculation.