**Rule of 69**

Use N = 69 when dealing with any continuous growth process, or when you have a periodic growth process and the rate is between 0% and 0.5%.

**Example:**A culture of cells grows at a continuous rate of 6.9% per day. In how many days will the number of cells double? Solution: Simply calculate 69/6.9 = 10, so the answer is about 10 days.**Example:**A credit card has an annual rate of 4.8%, with interest compounded monthly. How many months does it take for the credit card balance to double if you never make any payments? Solution: Since the annual periodic rate is 4.8%, the monthly periodic rate is 4.8/12 = 0.4%. Therefore, it will take around 69/0.4 = 172.5 months for the balance to double. (Approximately 14 and a half years).

**Rule of 72**

Use N = 72 when the growth rate is between 4.9% and 11%.

**Example:**Since 2007, a business has grown annually by 8%. At this rate, when will the business double? Solution: We compute 72/8 = 9, so the business will double in size in about 9 years. This means in 2016 it will be roughly twice as large as it was in 2007.