# Doubling Time

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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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