How long will it take money to double itself if invested at 6.5% compounded annually

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The Doubling Time formula is used in Finance to calculate the length of time required to double an investment or money in an interest bearing account.

It is important to note that r in the doubling time formula is the rate per period. If one wishes to calculate the amount of time to double their money in a money market account that is compounded monthly, then r needs to express the monthly rate and not the annual rate. The monthly rate can be found by dividing the annual rate by 12. With this situation, the doubling time formula will give the number of months that it takes to double money and not years.

In addition to expressing r as the monthly rate if the account is compounded monthly, one could also use the effective annual rate, or annual percentage yield, as r in the doubling time formula.

Example of Doubling Time Formula

Jacques would like to determine how long it would take to double the money in his money market account. He is earning 6% per year, which is compounded monthly. Looking at the doubling time formula, we need to consider that the 6% would need to be divided by 12 in order to come to a monthly rate since the account is compounded monthly. Given this, r in the doubling time formula would be .005 (.06/12). After putting this into the doubling time formula, we have:

After solving, the doubling time formula shows that Jacques would double his money within 138.98 months, or 11.58 years.

As stated earlier, another approach to the doubling time formula that could be used with this example would be to calculate the annual percentage yield, or effective annual rate, and use it as r. The annual percentage yield on 6% compounded monthly would be 6.168%. Using 6.168% in the doubling time formula would return the same result of 11.58 years.

Alternative to Doubling Time

For quick estimations of how long it takes to double the money on an investment, some may choose to use the rule of 72. The rule of 72 is found by dividing 72 by the rate of interest expressed as a whole number. For example, a rate of 6% would be estimated by dividing 72 by 6 which would result in 12 years. As stated, this is only an estimation as a 6% rate would take 11.90 years using the actual doubling time formula.

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• Formulas related to Doubling Time
• Rule of 72
• Doubling Time - Continuous Compounding
• Doubling Time - Simple Interest
• Solve for Number of Periods - PV&FV

The Rule of 72 is a math rule that lets you estimate how long it will take to double your nest egg for any given rate of return. It makes a good teaching tool to illustrate the impact of different rates of return, but it makes a poor tool to project the future value of your savings, particularly as you near retirement and need to be more careful how your money is invested.

Learn more about how this rule works, and the best way to use it.

How the Rule of 72 Works

To use the rule, divide 72 by the investment return (the interest rate your money will earn). The answer will tell you the number of years it will take to double your money.

For example:

• If your money is in a savings account earning 3% a year, it will take 24 years to double your money (72 / 3 = 24).
• If your money is in a stock mutual fund that you expect will average 8% a year, it will take you nine years to double your money (72 / 8 = 9).

As a Teaching Tool

The Rule of 72 can be useful as a teaching tool to illustrate the risks and outcomes associated with short-term investing versus long-term investing.

When it comes to investing, if your money is used to reach a short-term financial destination, it doesn’t much matter if you earn a 3% rate of return or an 8% rate of return. Since your destination is not that far off, the extra return won’t make much of a difference in how quickly you accumulate money.

It helps to look at this picture in real dollars. Using the Rule of 72, you saw that an investment earning 3% doubles your money in 24 years; one earning 8% takes nine years. That's a big difference, but how big is the difference after just one year?

Suppose you have $10,000. After one year, in a savings account at a 3% interest rate, you have $10,300. In the mutual fund earning 8%, you have $10,800. Not a big difference.

Stretch that out to year nine. In the savings account, you have about $13,050. In the stock index mutual fund, according to the Rule of 72 your money has doubled to $20,000.

This is a much bigger difference that only grows with time. In another nine years, you have about $17,000 in savings but about $40,000 in your stock index fund.

Over shorter time frames, earning a higher rate of return does not have much of an impact. Over longer time frames, it does.

Is the Rule Useful As You Near Retirement?

The Rule of 72 can be misleading as you near retirement.

Suppose you are 55 with $500,000 and expect your savings to earn about 7% and double over the next 10 years. You plan on having $1 million at age 65. Will you?

Maybe, maybe not. Over the next 10 years, the markets could deliver a higher or a lower return than what averages lead you to expect.

Because your window of time is shorter, you have less ability to account for and correct any fluctuations in the market. By counting on something that may or may not happen, you may save less or neglect other important planning steps like annual tax planning.

Note

The Rule of 72 is a fun math rule and a good teaching tool, but you shouldn't rely on it to calculate your future savings.

Instead, make a list of all the things you can control and the things you can't. Can you control the rate of return you will earn? No. But you can control:

• The level of investment risk you take
• How much you save
• How often you review your plan

Even Less Useful Once in Retirement

Once retired, your main concerns are to take income from your investments and figure out how long your money will last, depending on how much you take. The Rule of 72 doesn't help with this task.

Instead, you need to look at strategies like:

• Time segmentation, which involves matching up your investments with the point in time when you will need to use them
• Withdrawal rate rules, which help you figure out how much you can safely take out each year during retirement

The best thing you can do is to make your own retirement income plan timeline to help you visualize how the pieces are going to fit together.

If financial planning were as easy as the Rule of 72, you might not need a professional to help. In reality, there are far too many variables to consider.

Using a simple math equation is no way to manage money.

Frequently Asked Questions (FAQs)

What interest rate would double your money in five years?

You can reverse the Rule of 72 to work backward from your timing target. If you want to double your money in five years, divide 72 by five. According to the Rule of 72, it would take about 14.4 years to double your money at 5% per year.

Does a stock split double your money?

No, a stock split does not double your money. Your brokerage will automatically adjust the value of each share after the split. In a 2:1 stock split, each share will be worth half as much. In a 3:1 stock split, each share will be worth a third as much.