Questions: Anders discovered an old pay statement from 12 years ago. His monthly salary at the time was 3,500 versus his current salary of 6,430 per month. At what (equivalent) compound annual rate has his salary grown during the period? (Do not round intermediate calculations and round your final percentage answer to 2 decimal places.) His salary grew at a rate of % compounded annually.

Solution Steps

To find the equivalent compound annual growth rate (CAGR) of Anders' salary over the 12-year period, we can use the formula for CAGR:

\[ \text{CAGR} = \left( \frac{\text{Ending Value}}{\text{Beginning Value}} \right)^{\frac{1}{\text{Number of Years}}} - 1 \]

In this case, the ending value is his current salary, the beginning value is his salary from 12 years ago, and the number of years is 12. We will then convert the result to a percentage.

Let the beginning salary \( S_0 = 3500 \) and the ending salary \( S_t = 6430 \). The number of years \( t = 12 \).

The formula for the compound annual growth rate (CAGR) is given by:

\[ \text{CAGR} = \left( \frac{S_t}{S_0} \right)^{\frac{1}{t}} - 1 \]

Substituting the values:

\[ \text{CAGR} = \left( \frac{6430}{3500} \right)^{\frac{1}{12}} - 1 \]

Calculating the ratio:

\[ \frac{6430}{3500} \approx 1.837142857142857 \]

Now, applying the exponent:

\[ \text{CAGR} \approx (1.837142857142857)^{\frac{1}{12}} - 1 \approx 0.05199072472941224 \]

To express CAGR as a percentage:

\[ \text{CAGR Percentage} = 0.05199072472941224 \times 100 \approx 5.199072472941224 \]

Rounding to two decimal places gives:

\[ \text{CAGR Percentage} \approx 5.20\% \]

Final Answer