The Rule of 72 and the Rule of 25: Two Shortcuts for Retirement Math
Two simple rules can answer most retirement questions with quick mental math. The Rule of 25 tells you how big a portfolio you need. The Rule of 72 tells you how fast that portfolio can grow. Together they give you a rough picture of where you stand and how long the road might be. Both are shortcuts. Both are useful. Both can mislead if you use them past their limits.
The Rule of 25: how much you need to hold
Take your yearly spending and multiply it by 25. That is roughly the size of the portfolio you need to support that spending for a long retirement.
The 25 comes from the 4 percent rule. If you can live on 4 percent of your savings each year, you need 25 times that amount saved. One divided by 0.04 equals 25. Bengen found in 1994 that about a 4.1 percent first year withdrawal lasted 30 years with 50 percent stocks and 50 percent intermediate term government bonds. The 1998 Trinity study tested withdrawal rates over 30 year periods. Both studies used past market data. They did not promise future returns, and they did not test retirements of 50 years.
Worked example: the Rule of 25
These are round hypothetical numbers. They are not a real household.
- Step 1. Yearly spending is $50,000.
- Step 2. Multiply by 25. $50,000 times 25 equals $1,250,000. That is the target.
- Step 3. Check the withdrawal. 4 percent of $1,250,000 equals $50,000 in the first year.
- Step 4. Change the spending to see the effect. At $40,000 of spending, the target is $40,000 times 25, which equals $1,000,000. At $60,000 of spending, the target is $60,000 times 25, which equals $1,500,000. Each extra $10,000 of yearly spending adds $250,000 to the target.
The Rule of 72: how fast money doubles
The Rule of 72 is simple. Divide 72 by your yearly rate of return. The answer is about how many years it takes your money to double. A higher rate means a shorter doubling time. A lower rate means a longer one.
The rule works in reverse too. Divide 72 by the number of years you have. The answer is about what return you need to double your money in that time. If you have 10 years, you need about 7.2 percent a year. If you have 20 years, you need about 3.6 percent a year.
Worked examples: doubling, checked by recomputation
Every example below was checked by recomputation. The exact doubling time uses the formula: years equals the natural log of 2 divided by the natural log of 1 plus the rate. The Rule of 72 is close to the exact answer at rates from 4 percent to 10 percent, but it is not exact.
| Yearly return | Rule of 72: 72 divided by the rate | Exact doubling time |
|---|---|---|
| 4 percent | 18.0 years | 17.7 years |
| 6 percent | 12.0 years | 11.9 years |
| 7 percent | 10.3 years | 10.2 years |
| 8 percent | 9.0 years | 9.0 years |
| 10 percent | 7.2 years | 7.3 years |
Worked example with $100,000 at a 7 percent annual return assumption. That return is an assumption, not a forecast. The Rule of 72 says the money doubles in 72 divided by 7, which equals 10.3 years. The exact time is 10.2 years. After 10 years, $100,000 times 1.07 to the power of 10 equals $196,715, or about $197,000, close to double. After 20 years, $100,000 times 1.07 to the power of 20 equals $386,968, or about $387,000, close to four times the start, because the money doubles twice.
Worked example with $250,000 at a 7 percent annual return assumption. After 10 years, $250,000 times 1.07 to the power of 10 equals $491,800, or about $492,000, close to $500,000. After 20 years, $250,000 times 1.07 to the power of 20 equals $967,000, close to $1,000,000. The rule gives a fast answer. The exact math gives the same answer, within a few percent.
Putting the two rules together
Use the Rule of 25 to find the target. Use the Rule of 72 to see how long growth might take to get you there. If your target is $1,000,000 and you have $250,000 now, you need the money to double twice. At a 7 percent return, each doubling takes about 10 years, so the trip takes about 20 years, with no new saving. With new saving each year, the trip is shorter. The rules do not replace a full plan. They help you check if a plan is in the right range.
Where the shortcuts mislead
Inflation is the first trap. The Rule of 72 doubles the dollar amount, not the buying power. If prices rise by 3 percent a year and your return is 7 percent, your real return is about 4 percent. The money doubles in dollars in about 10 years, but it takes about 18 years to double in buying power. Use 72 divided by 4, which equals 18.0 years. The exact time at 4 percent is 17.7 years. If you use the nominal return, you will think you are richer than you are.
Taxes are the second trap. The Rule of 72 uses the return before tax. If tax takes 1 point off a 7 percent return, the net return is 6 percent. The doubling time rises from 10.3 years to 12.0 years. That is almost two extra years for each doubling. A taxable account and a tax free account with the same gross return do not double at the same speed.
Fees are the third trap. A 1 percent yearly fee has the same effect as a 1 point tax. A 7 percent return minus a 1 percent fee is a 6 percent net return. The doubling time rises from 10.3 years to 12.0 years. A fee that looks small can add years to the plan.
The Rule of 25 has its own traps. It assumes the 4 percent rule holds for your time frame, and it assumes your spending stays flat after inflation. It does not count tax on withdrawals, health costs before Medicare at age 65, or a market fall early in retirement. It also assumes a steady return. Real returns jump up and down. A plan built only on these two rules is a sketch, not a finished plan. Use the rules to start, then test the plan with real spending, real tax, real fees, and a lower return than you hope for.
Education, not advice. This post explains two calculations. It is not personal financial advice. Your income, taxes, health, and family needs are your own. Check the rules that apply to you before you act.
Sources
- Bengen, William P. “Determining Withdrawal Rates Using Historical Data.” Journal of Financial Planning, October 1994. Financial Planning Association
- Cooley, Philip L., Carl M. Hubbard, and Daniel T. Walz. “Retirement Savings: Choosing a Withdrawal Rate That Is Sustainable.” American Association of Individual Investors, February 1998. AAII Journal
- Investopedia. “Rule of 72: Definition, Formula, and Example.” Investopedia
- Investopedia. “The 4% Rule: What It Is and How to Use It.” Investopedia
