The effect of depreciation can be computed using a formula similar to the formula for compound interest.
a. Assume depreciation is the same each month. Write a problem involving depreciation and solve it.
b. Develop a general formula for depreciation defining what each variable in the formula stands for.
This is not straight line depreciation but a constant percentage depreciation per month.
let value after a month be d times value the month before. (like 0.97 or something)
Then value after n months = original value * d^n
for example if I buy a $500 appliance
and d = .97 per month
then after 2 years
value = 500(.97)^24
= 500(.481)
= $ 241
a. Let's say you bought a car for $30,000 and it depreciates at a rate of $500 per month. We can use the formula for compound interest to calculate the effect of depreciation.
The formula for compound interest is:
A = P(1 + r/n)^(nt)
In this case, the initial value of the car (P) is $30,000, the rate of depreciation (r) is $500, the number of times the interest is compounded per year (n) is 12 (since it's monthly), and the number of years (t) is 1 (since we're calculating for one year).
To find the final value of the car (A) after one year, we can substitute the values into the formula:
A = 30000(1 + 500/30000)^(12*1)
A = 30000(1 + 1/60)^(12)
A ≈ 30000(1.01667)^(12)
A ≈ 30000(1.2071)
A ≈ 36212.97
Therefore, after one year, the value of the car would depreciate to approximately $36,212.97.
b. The general formula for depreciation can be expressed as follows:
A = P(1 - r/n)^(nt)
- A represents the final value or amount after depreciation.
- P represents the initial value or amount before depreciation.
- r represents the rate of depreciation.
- n represents the number of times the depreciation is compounded per year.
- t represents the number of years the depreciation occurs for.
By plugging in the appropriate values for each variable, you can calculate the effect of depreciation on any given amount or object.