Final answer:
The rule of 70 is a mathematical shortcut used to estimate the time it takes for an investment to double at a given annual growth rate by dividing 70 by the percentage rate of return.
Step-by-step explanation:
The rule of 70 is a way to estimate the doubling time of an investment, based on its annual percentage growth rate. By dividing the number 70 by the annual rate of return, you can approximate how many years it will take for the initial amount of money to double. For example, using this rule with a 7% return suggests that money will double in about 10 years, which aligns with the scenario provided.
An in-depth explanation of the rule of 70 shows that this calculation is most accurate with rates under 10%. If pandemic cases are growing at a rate of 3.5% per day, the rule would indicate a doubling time of 20 days. Similarly, a bank deposit with a 2% annual interest rate would double in about 35 years, which the rule predicts accurately. Sometimes, the rule of 72 is used as a substitute approximation formula, particularly for higher rates. It simply states that dividing 72 by the annual growth rate gives a rough estimate of doubling time.