Well, the first thing I'd note is that the "rule of 72" and "rule of 69.3" are both methods of estimating the time taken for a sum of money to double. It will very rarely return the exact value, so the rule should really only be used as part of checking an answer you got through other means. Secondly, the formula you've used for the rule is very very wrong. The rule tells you to divide 72 by the annual interest rate in percent. In this case, your estimate would be 72/2.25 = 32 years. What you've shown as the variable I is actually the amount of money after 1 year. Since the problem tells you to use annual compounding, a good next step would be to use the formulas you've been given to find an expression for the amount of money after n years. The problem asks you to find how many years it would take to double your money, so set that expression equal to 6000 and solve for n.
