Suppose that an insurance agent offers you a policy that will provide you with a yearly income of $30,000 in 30 years. What is the comparable salary today, assuming an inflation rate of 3% compounded annually? (Round your answer to the nearest cent.)
PV = FV / (1 + r)^n
= 30000/(1.03)^30
= $12,359.60
Suppose that an insurance agent offers you a policy that will provide you with a yearly income of $50,000 in 30 years. What is the comparable salary today, assuming an inflation rate of 3% compounded annually?
To calculate the comparable salary today, we need to account for the effects of inflation. Here are the steps to follow:
Step 1: Calculate the future value of the annual income in 30 years using the inflation rate.
To calculate the future value, we will use the formula:
Future Value = Present Value * (1 + Inflation Rate)^Number of Years
In this case, the present value is $30,000, the inflation rate is 3% (or 0.03), and the number of years is 30.
Future Value = $30,000 * (1 + 0.03)^30
Step 2: Calculate the comparable salary today by finding the present value of the future value.
To calculate the present value, we will use the formula:
Present Value = Future Value / (1 + Inflation Rate)^Number of Years
Let's plug in the values and calculate the present value:
Present Value = $30,000 / (1 + 0.03)^30
Now, let's calculate the present value:
Present Value = $30,000 / (1.03^30)
Present Value ≈ $11,126.41
Therefore, the comparable salary today, assuming an inflation rate of 3% compounded annually, is approximately $11,126.41.
To calculate the comparable salary today, we need to adjust the future income of $30,000 by accounting for the inflation rate of 3% compounded annually.
The formula for calculating the future value of an investment with compound interest is given by:
FV = PV * (1 + r)^n
Where:
FV = future value
PV = present value (initial investment or income)
r = interest rate per period
n = number of periods
In this case, the future value (FV) is the income of $30,000, the interest rate (r) is the inflation rate of 3% or 0.03, and the number of periods (n) is 30 years.
To find the present value (PV), we rearrange the formula:
PV = FV / (1 + r)^n
Now let's plug in the values:
PV = 30,000 / (1 + 0.03)^30
Calculating this equation, we get:
PV ≈ 13,543.35
Therefore, the comparable salary today, adjusted for an inflation rate of 3% compounded annually, is approximately $13,543.35.