A new car is purchased for the price of $35,000. If the value of the car depreciates at a rate of 12% per year, when will the car be worth half of the original rate?
I put down (this was wrong): 35000 (0.12/12) = 75000
350 (0.12/12) 175 = 612.5
= about 6 years
V = Vo(1-r)^t = 35,000/2
35,000(1-0.12)^t = 17,500
Divide both sides by 35,000:
(0.88)^t = 0.5
Take Log of both sides:
t*Log(0.88) = Log 0.5
t = Log 0.5/Log(0.88) = 5.42 Years.
Well, I'm sorry to say that your calculations have gone a bit off track. But don't worry, I'm here to help you straighten things out, with a touch of humor, of course!
To find out when the car will be worth half of its original price, we can set up an equation. Let's call the number of years it takes for the car to depreciate in value by half as "x".
Now, we know that the car depreciates at a rate of 12% per year. So after x years, the car will be worth (100% - 12% = 88%) of its original value.
Setting up the equation, we have:
$35,000 * (0.88)^x = $17,500
Now let the funny math begin! We need to solve for x, so let's bring in the circus:
Step 1: Divide both sides of the equation by $35,000:
(0.88)^x = 0.5
Step 2: Take the logarithm of both sides (I promise not to logarithm any clowns during this process):
log((0.88)^x) = log(0.5)
Step 3: Use the logarithmic property to bring x down from the exponent:
x * log(0.88) = log(0.5)
Step 4: Divide both sides by log(0.88) to isolate x:
x = log(0.5) / log(0.88)
Step 5: Grab your calculator, calculate those values, and you'll find...
x ≈ 6.37
So, after about 6.37 years, the car will be worth half of its original price. And remember, even though math can be confusing at times, laughter is always the best solution!
To find out when the car will be worth half of its original value, let's calculate step by step:
Step 1: Calculate the depreciation amount per year.
Depreciation rate = 12%
Depreciation amount per year = 12% of $35,000 = 0.12 x 35,000 = $4,200
Step 2: Calculate the new value of the car after each year.
Year 1: $35,000 - $4,200 = $30,800
Year 2: $30,800 - $4,200 = $26,600
Year 3: $26,600 - $4,200 = $22,400
Year 4: $22,400 - $4,200 = $18,200
Year 5: $18,200 - $4,200 = $14,000
Year 6: $14,000 - $4,200 = $9,800
Based on the calculations, the car will be worth half of its original value ($17,500) in approximately 6 years.
To find out when the car will be worth half of the original rate, you need to determine how much the car's value will decrease each year.
The rate of depreciation is given as 12% per year. To calculate the amount the car's value will decrease each year, you need to find 12% of the original price ($35,000).
12% of $35,000 can be calculated as follows:
12/100 × $35,000 = $4,200
So, each year, the car's value will decrease by $4,200.
To find out when the car will be worth half of the original rate, you can divide the original price ($35,000) by 2, since half of the original rate means the car is worth half the original price.
$35,000 ÷ 2 = $17,500
Now, you can calculate how many years it will take for the car's value to reach $17,500, with depreciations of $4,200 per year.
$35,000 - $4,200 = $30,800 (value after the first year)
$30,800 - $4,200 = $26,600 (value after the second year)
$26,600 - $4,200 = $22,400 (value after the third year)
$22,400 - $4,200 = $18,200 (value after the fourth year)
$18,200 - $4,200 = $14,000 (value after the fifth year)
After five years, the car's value has reached $14,000, which is less than $17,500. Therefore, it will take more than five years for the car to be worth half of the original rate.
Let's continue the calculation:
$14,000 - $4,200 = $9,800 (value after the sixth year)
After six years, the car's value has reached $9,800. This is less than $17,500. Therefore, it will take more than six years for the car to be worth half of the original rate.
Let's continue:
$9,800 - $4,200 = $5,600 (value after the seventh year)
After seven years, the car's value has reached $5,600. This is less than $17,500. Therefore, it will take more than seven years for the car to be worth half of the original rate.
Let's continue:
$5,600 - $4,200 = $1,400 (value after the eighth year)
After eight years, the car's value has reached $1,400. This is less than $17,500. Therefore, it will take more than eight years for the car to be worth half of the original rate.
Based on this calculation, it will take more than eight years for the car's value to reach $17,500 and be worth half of the original rate.