Answer:
$38,227.86
Step-by-step explanation:
To calculate the present purchasing power equivalent of $1,000,000 in the future, taking into account inflation rates, we need to discount the future value by the cumulative inflation over the respective periods.
Given information:
Initial cash investment: $100,000
Number of years: 15
Inflation rate for the first seven years: 5% per year
Inflation rate for the last eight years: 8% per year
First, let's calculate the future value of the initial cash investment after 15 years:
Future value = Initial investment * (1 + average annual return)^number of years
Using this formula, the future value after 15 years would be:
Future value = $100,000 * (1 + average annual return) ^ 15
Next, we need to calculate the cumulative inflation over the respective periods. We can do this by multiplying the inflation rates for each period:
Cumulative inflation for the first seven years = (1 + 0.05) ^ 7
Cumulative inflation for the last eight years = (1 + 0.08) ^ 8
Now, we can calculate the present purchasing power equivalent by dividing the future value by the cumulative inflation:
Present purchasing power equivalent = Future value / (Cumulative inflation for the first seven years * Cumulative inflation for the last eight years)
Substituting the given values into the equation:
Present purchasing power equivalent = ($100,000 * (1 + average annual return) ^ 15) / ((1 + 0.05) ^ 7 * (1 + 0.08) ^ 8)
Since the average annual return is not specified, I'll assume it to be 0% (no additional return on investment).
Present purchasing power equivalent = ($100,000 * (1 + 0%) ^ 15) / ((1 + 0.05) ^ 7 * (1 + 0.08) ^ 8)
Simplifying the equation:
Present purchasing power equivalent = $100,000 / ((1.05) ^ 7 * (1.08) ^ 8)
Calculating the value:
Present purchasing power equivalent = $100,000 / (1.40255 * 1.71709)
Present purchasing power equivalent ≈ $38,227.86
Therefore, the present purchasing power equivalent of $1,000,000 in the future, considering the given inflation rates, would be approximately $38,227.86.