An antique dresser was purchased for $7500 in 2005. The dresser increases in value by 9% per year. Find the value of the dresser in 2025.
So i thought it would be :
A = 7500(1+0.09)^(20)
A = 42033...
However I have been told it could be:
Value = 7500 + 7500*0.09*20 = $21,000
Which is the correct method?
the first method uses compound interest which would be the normal way of doing it.
The second uses simple interest, a method used for very short periods of time and certainly does not fit into a 25 year period
I would be my money on
A = 7500(1+0.09)^(20)
Thank you very much.
The correct method to calculate the value of the antique dresser in 2025 depends on the question's specifics.
If you want to calculate the compounded appreciation over time, the correct formula to use is the one you mentioned:
A = P(1 + r)^n
Where:
A = final value of the dresser
P = initial value of the dresser
r = annual rate of increase (as a decimal)
n = number of years
In this case, the initial value (P) is $7500, the annual rate of increase (r) is 9% (which is equivalent to 0.09 as a decimal), and the number of years (n) is 2025 - 2005 = 20.
Using this formula, the calculation would be:
A = 7500(1 + 0.09)^20
A ≈ $41,331.84
So your initial calculation is correct. The value of the dresser in 2025, based on a 9% annual increase, would be approximately $41,331.84.
On the other hand, if you want to calculate the total value increase over time without compounding, you can use a different method. The second approach you mentioned assumes a simple annual increase, without compounding:
Value = Initial Value + (Initial Value * rate of increase * number of years)
In this case, the calculation would be:
Value = $7500 + ($7500 * 0.09 * 20)
Value = $7500 + $13,500
Value = $21,000
So if you are looking for the total value increase without compounding, the second method is applicable. However, if you want to account for compounded appreciation, the first method is more accurate.