Question

The impact of inflation on a $50,000 pension can be measured by the purchasing power P of $50,000 after t years. For an innation annually, Per year compounded anually given by the following.

P 50,000e⁰.⁰⁴
At what rate (in dollars per year) is purchasing powr changing when t 137 (Round your answer to the nearest cent.)

Answer 1

The rate at which purchasing power is changing for a $50,000 pension after 137 years at a 4% annual inflation rate is found by taking the derivative of the purchasing power function and evaluating it at t = 137, rounding the result to the nearest cent.

Step-by-step explanation:

The impact of inflation on purchasing power can be calculated using given formulas. In this case, we have P = $50,000e0.04t as the function that represents the purchasing power of a $50,000 pension after t years at a 4% annual inflation rate. To find the rate at which purchasing power is changing at t = 137 years, we first need to take the derivative of P with respect to t, which gives us P' = $50,000 × 0.04e0.04t. Substituting t = 137 into P' yields the rate of change of purchasing power at that particular time, and we can round this value to the nearest cent for precision.

It is important to note the relationship between inflation and purchasing power. As inflation increases, the value of money in terms of what it can buy (its purchase power) decreases. This concept is crucial for understanding the long-term impacts of inflation on fixed incomes such as pensions.