Question

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

Short answer

Purchasing power will be$\$7874$after$16$years when measured in today's dollars.

Step-by-step solution

Step 1. Meaning of inflation.

The inflation rate is a general and ongoing rise in the price levels in an economy.

Step 2. Finding the purchasing power after 16 years. 

Let the price level be $100$.

Inflation rate is $6\%$.

Price level after $16$years will be:

localid="1645902898978" $$\begin{gathered} ={(1+\frac{6}{100})}^{16}\times 100 \\ ={\left(\frac{106}{100}\right)}^{16}\times 100 \\ ={(1.06)}^{16}\times 100 \\ =2.54\times 100 \\ =254 \end{gathered}$$

The purchasing power of $\$20,000$after $16$years will be:

$$\begin{gathered} =\frac{\$20,000}{2.54} \\ =\$7874 \end{gathered}$$