Final answer:
The item that costs $5000 now would have cost approximately $4603.38 four years ago, after adjusting for an annual inflation rate of 2.07%.
Step-by-step explanation:
Calculating the Original Cost Before Inflation
To find out how much an item that costs $5000 now cost 4 years prior, taking into account an annual inflation rate of 2.07%, we can use the formula for compound interest in reverse. This is because inflation is essentially compounding yearly in this context. The formula to find the present value (PV) is:
PV = FV / (1 + r)^n
where:
- FV is the future value or the current price of the item ($5000)
- r is the annual inflation rate (0.0207)
- n is the number of years (4)
Using these values, we calculate the original cost as follows:
PV = $5000 / (1 + 0.0207)^4
PV = $5000 / (1.0207)^4
PV = $5000 / 1.08564849
PV ≈ $4603.38
Thus, the item would have cost approximately $4603.38 four years ago.