Chapter 3.2, Problem 81E

In a conversation with a friend, you note that you have two real estate investments, one that has doubled in value in the past $9$ years and another that has doubled in value in the past $12$ years. Your friend says that the first investment has been growing at approximately $8\%$ compounded annually and the second at $6\%$ compounded annually. How did your friend make these estimates? The rule of $72$ states that the annual compound rate of growth r of an investment that doubles in n years can be approximated by $r=72\text{/}n$. Construct a table comparing the exact rate of growth and the approximate rate provided by the rule of $72$ for doubling times of $n=6,7,\dots ,12$ years. Round both rates to one decimal place.