Upon initial observation, a 7% return on one’s investment may not appear very noteworthy. However, what if you were informed that your capital may potentially increase twofold during a span of approximately 10 years?
The aforementioned visual representation employs the rule of 72 shortcut, but also incorporates the logarithmic formula to provide a more accurate depiction of the time required for monetary growth at various annualized rates.
Reasons Why Math Skills Are Valuable
An investor can get a rough estimate of how long it will take to double their money by applying the traditional rule of 72. By taking the number 72 and dividing it by 7%, which is the rate of return, an investor might watch their initial investment of $10,000 grow to $20,000 in around ten years’ time.
The rule of 72 can be used as an approximate estimate for determining when your money will double, but a logarithmic equation is a more exact way to arrive at this number. Logarithmic equations can be used to determine when your money will double.
In a nutshell, it takes the natural log of two and divides it by the natural log of one, then adds that number to the rate of return.
Take into consideration the case of an investor who invested in the S&P 500. Throughout its history, returns have typically averaged 11.5% between 1928 and 2022. Assuming these typical rates, their money would be doubled in just over six and a half years.
If they were to save this money in an account with an average savings rate of 0.6%, it would take their money an additional 120 years to achieve this potential. If they were to invest this money in the stock market, it would take their money an additional 100 years.
If an investor kept their money in a savings account, the value of their money would decrease over time as measured in real terms, taking into account the effects of inflation. Historically speaking, the average rate of inflation over the past century has been 3.3%.
