To determine how many years it will take for [tex]$80 to be worth $[/tex]40 at an inflation rate of 5.4%, we can use the rule of 72. The rule of 72 is a simplified way to estimate the number of years required to double the value of an investment (or halve the value of money) given a fixed annual rate of inflation or interest.
The formula according to the rule of 72 is:
[tex]\[ \text{Years} = \frac{72}{\text{Inflation Rate}} \][/tex]
Here, the inflation rate is 5.4%. By substituting this value into our formula, we get:
[tex]\[ \text{Years} = \frac{72}{5.4} \][/tex]
Calculating this, we find:
[tex]\[ \text{Years} \approx 13.33 \][/tex]
Therefore, the time it will take for [tex]$80 to be worth $[/tex]40 at an inflation rate of 5.4% is approximately 13.3 years.
Thus, the correct answer is:
A. 13.3 years
