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The historical society tells him that furniture similar to his has been appreciating in value at 10% per year for the last 20 years and that his furniture could be worth $10,000 now.
Is my expression 10,000(1+.1)^x?
If so, I have to find what it costed 20 years ago. Would I just raise the expression to the power of 20, or -20?
no
let the amount that it "costed" 20 years ago be x
then x(1.1)^20 = 10000
x = 10000/(1.1^20)
I get 1486.44
you might have seen the formula
Present Value = amount (1+i)^-n
then Present value = 10000(1.1)^-20
= 1486.44
If you know about negative exponents you will realize that the two equations are the same.
A new machine was purchased at the beginning of one year for $200. Each year the machine loses value. It is worth 90% as much as the previous year. What is the value of the machine at the end of the 4th year.
Yes, your expression, 10,000(1+.1)^x, is correct for calculating the current value of the furniture, where "x" represents the number of years.
To find the value of the furniture 20 years ago, you need to calculate the reverse of the current value equation. Instead of raising it to the power of 20, you need to raise it to the power of -20.
So the calculation for the value of the furniture 20 years ago would be:
Value_20_years_ago = 10,000(1+.1)^(-20)
This calculation will give you the estimated value of the furniture 20 years ago based on the historical appreciation rate provided.