A pair of Air Jordan’s cost $61 when first released. Today, Air Jordan’s sell for about $185 a pair. What is the implied rate of price increase over the last 38 years?

We will use the formula for compound annual growth rate (CAGR):

r = \left( \frac{P_{\text{final}}}{P_{\text{initial}}} \right)^{\frac{1}{t}} - 1

where:

P_{\text{final}} = 185

P_{\text{initial}} = 61

t = 38

First, we calculate the ratio of the final price to the initial price:

\frac{P_{\text{final}}}{P_{\text{initial}}} = \frac{185}{61} \approx 3.03

Next, we apply the exponent and subtract 1:

r = \left( 3.03 \right)^{\frac{1}{38}} - 1

Using a calculator:

r\approx1.0296-1

r\approx0.0296

Converting to a percentage:

r\approx2.96\%

Thus, the implied rate of price increase over the last 38 years is approximately

2.96\%