44. Future values and continuous compounding (S2.4) 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?