The rule of 72's states that the number of years for an investment to double is approximately 72 divided by the interest rate percentage. For example, about 12 years are required for an investment to double at 6% interest (12 years = 72/6). Find the exact rate required to double an investment in 6, 8, 9, 12, 18, and 24 years, and compare this with the approximate rule of 72's rate.