Suppose that an insurance agent offers you a policy that will provide you with a yearly income of $40,000 in 30 years. What is the comparable salary today, assuming an inflation rate of 5% compounded annually?
To calculate the comparable salary today, we need to account for the effect of inflation over the 30-year period. Inflation erodes the purchasing power of money over time, meaning that the same amount of money will buy less in the future.
To calculate the comparable salary, we can use the concept of future value and discounting. We will first calculate the future value of $40,000 after 30 years, taking into account the 5% annual inflation rate. Then, we will discount this future value back to today's dollars.
Here's how you can calculate the comparable salary today:
Step 1: Calculate the future value after 30 years with 5% annual inflation:
We can use the formula for future value (FV) of a present value (PV) compounded annually for n periods at a given interest rate (r):
FV = PV * (1 + r)^n
In this case, the present value (PV) is $40,000, the interest rate (r) is the inflation rate of 5% or 0.05, and the number of periods (n) is 30 years.
FV = $40,000 * (1 + 0.05)^30
FV = $40,000 * (1.05)^30
Calculating this using a calculator, we get:
FV ≈ $128,339.70
Step 2: Discount the future value back to today's dollars:
To discount the future value back to today's dollars, we need to reverse the formula for future value. Instead of calculating the future value, we can calculate the present value (PV) by dividing the future value by (1 + r)^n.
PV = FV / (1 + r)^n
PV = $128,339.70 / (1 + 0.05)^30
PV = $128,339.70 / (1.05)^30
Calculating this using a calculator, we get:
PV ≈ $40,000
So, the comparable salary today, accounting for an inflation rate of 5% compounded annually, would be approximately $40,000.