36. Here are two useful rules of thumb. The “Rule of 72” says that with discrete compounding the time it takes for an investment to double in value is roughly 72/interest rate (in percent).

The “Rule of 69” says that with continuous compounding the time that it takes to double is exactly 69.3/interest rate (in percent).

a. If the annually compounded interest rate is 12%, use the Rule of 72 to calculate roughly how long it takes before your money doubles. Now work it out exactly.

b. Can you prove the Rule of 69?