Question

Rosalie the Retiree knows that when she retires in 16 years, her company will give her a one-time payment of \(20,000. However, if the inflation rate is 6% per year, how much buying power will that \)20,000 have when measured in today’s dollars? Hint: Start by calculating the rise in the price level over the 16 years.

Short answer

we will start by calculating the price level and understanding the definition.

Step-by-step solution

Step 1. Definition

Inflation is a situation in an economy when the average prices of all the goods and services increased because of some market pressures.

Step 2. Explanation

Let the original price level is 100 if the inflation rate is 6% per year, then the price level after 16 years will be:

=$$\begin{gathered} {\left[{}^{\frac{1+6}{100}}\right]}^{16}\times 100 \\ {\left\{\frac{100+6}{100}\right\}}^{16}\times 100 \\ {\left\{\frac{106}{100}\right\}}^{16}\times 100 \\ {\left\{1.06\right\}}^{16}\times 100 \\ 2.54\times 100 \\ 254 \end{gathered}$$

the purchasing power of $20000 after 16 years will be:

$$\begin{gathered} =\frac{\$20000}{2.54} \\ =\$7874 \end{gathered}$$