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 6% compounded annually? (Round your answer to the nearest cent.)
Hint:Use the compound interest formula
Future=present*(1+i)^n
Here
Future=40000
n=30
i=0.06 (6%)
Solve for Present.
6964.4
To calculate the comparable salary today, we need to adjust the future income for inflation.
Step 1: Calculate the inflation factor.
The inflation factor is calculated using the formula: (1 + inflation rate)^number of years.
In this case, the inflation rate is 6% and the number of years is 30.
Inflation factor = (1 + 0.06)^30
Step 2: Calculate the comparable salary today.
The comparable salary today is calculated by dividing the future income by the inflation factor.
Comparable salary today = $40,000 / inflation factor
Let's calculate this:
1. Calculate the inflation factor:
Inflation factor = (1 + 0.06)^30
Inflation factor = 5.743
2. Calculate the comparable salary today:
Comparable salary today = $40,000 / 5.743
Comparable salary today ≈ $6,960.71
Therefore, the comparable salary today, assuming an inflation rate of 6% compounded annually, is approximately $6,960.71.
To calculate the comparable salary today, considering the inflation rate, we need to account for the effect of inflation over the 30-year period.
The formula we can use to calculate the comparable salary is:
Comparable Salary = Future Value / (1 + Inflation Rate)^Number of Years
In this case, the Future Value is $40,000, the Inflation Rate is 6% (or 0.06), and the Number of Years is 30.
Plugging in these values into the formula:
Comparable Salary = $40,000 / (1 + 0.06)^30
Now, let's calculate this using a calculator (or a spreadsheet):
(1 + 0.06)^30 = 5.74
Comparable Salary = $40,000 / 5.74
Comparable Salary = $6,964.79 (rounded to the nearest cent)
Therefore, the comparable salary today, considering an inflation rate of 6% compounded annually, would be approximately $6,964.79.