If inflation has been running at 3.74% per year and a new car costs $33700 today, what would it have cost 5 years ago?
To find out the cost of the new car 5 years ago, we need to take into account the cumulative effect of inflation over those 5 years.
First, we need to find the cumulative inflation rate over 5 years. We can use the formula:
Cumulative inflation rate = (1 + annual inflation rate)^number of years - 1
Plugging in the values, we get:
Cumulative inflation rate = (1 + 0.0374)^5 - 1
= 0.2101
This means that prices have increased by 21.01% over the past 5 years due to inflation.
To find the cost of the new car 5 years ago, we need to "reverse" this inflation by reducing the current price by 21.01%. We can use the formula:
Cost 5 years ago = current cost / (1 + cumulative inflation rate)
Plugging in the values, we get:
Cost 5 years ago = 33700 / (1 + 0.2101)
= $27,986.42
Therefore, the new car would have cost approximately $27,986.42 5 years ago, accounting for inflation.