## Saturday, November 28, 2020

### Back-of-the-Envelope Retirement Savings Calculator

This is my really simple "back-of-the-envelope" retirement calculator. It reduces retirement planning calculations to the bare minimum.

Accounting for all of the variables in retirement planning requires a complicated model. In this post, I've made some simplifying assumptions. I've tried to develop a "bare bones" model so that we can focus better on the big picture, and still get results that are useful.

### The Observations Back-of-the-Envelope Retirement Savings Calculator

Notes: Enter data only in the peach cells. You can use the arrows and sliders on the side and bottom of the calculator to scroll. On some phones you may need to double click to enter data; it may also be helpful to switch to landscape mode. On some computers, you may have to enter some fields more than once for it to "take."

### How Much Money Will You Need to Retire?

The key simplifying assumption was to estimate the savings you will need at retirement using
a simple multiple of your expected expenses in your first year of retirement. This eliminates many of the calculations in traditional retirement models. This approach is consistent with the so-called 4% withdrawal rate approach.

### What is a 4% Withdrawal Rate?

That simply means that in your first year of retirement you withdraw 4% (+/-) of your retirement savings. The assumption is that in subsequent years you will increase your withdrawals to keep pace with inflation.

If a large portion of your retirement income will be guaranteed, a higher than 4% withdrawal rate may be sustainable. For example, at a 5% withdrawal rate, a \$1,000,000 portfolio would support a first-year withdrawal of (\$1,000,000 x 5%=) \$50,000. Conversely, at a 5% withdrawal rate you would need retirement savings of (100% / 5%=) 20 times the initial withdrawal amount. So, in order to support a first-year withdrawal of \$50,000, you would need retirement savings of (\$50,000 x 20=) \$1,000,000.

On the other hand, in an unfavorable investment environment a lower than 4% withdrawal rate may be more judicious. For example, given the extraordinarily low current interest rates in the last half of 2020, and a stock market at above average valuations, some experts are suggesting that a 3% withdrawal rate may be more appropriate.

For more on the 3-5% withdrawal approach, see the links at the end of  the post.

### How the Model Works

In the graphic above, the example is for a 25 year old, Pat, making \$100,000/year who plans to retire on his 65th birthday. Pat estimates that, in today's dollars, he will spend \$70,000 in his first year of retirement (including income taxes). Using this site and given his current \$100,000 salary, Pat estimates that he will receive about \$30,000 in Social Security and pension income his first year of retirement. That leaves (\$70,000 - \$30,000=) \$40,000/year that his investments need to cover.

Assuming a 4% withdrawal rate, Pat will need a (25 times \$40,000=) \$1,000,000 investment portfolio when he retires. Here, we assume Pat has no current retirement savings, so he'll need to accumulate all of it between now and retirement. Note that if Pat already had \$20,000 in savings, he'd only need about \$904,000, not \$980,000, from his new savings since the \$20,000 would be expected to grow to about \$96,000 by the time he retires.

### What Percent of His Salary Does Pat Need To Save Each Year?

The next step is to calculate how much Pat needs to save each year, in today's dollars. To do so, we need an estimate of what his pre-retirement annual return on investment will be. It's easier if we remove inflation from the equation. Pat expects to earn 7%/year on his total portfolio, and expects inflation to average 3%/year. Thus, he entered (7% - 3%=) 4% as his "real," after-inflation return. Given that, Pat needs to invest \$10,500/year in today's dollars.

The final step is just to calculate how much Pat needs to save and invest as a percentage of his salary. Since the dollar value will change every year, but the percentage does not, it is best to focus on the percentage. \$10,500 / \$100,000= 10.5%.  So, if Pat invests 10.5% of his salary each year, and his investments earn 4%/year after inflationexpenses and taxes, we would expect him to accumulate the needed \$1,000,000.

### Summary

This very simple sequence of calculations shows that if Pat invests 10.5% of his salary each year and earns 4%/year, after inflation, expenses and taxes, by age 65 we expect him to have accumulated about \$1,000,000 in today's dollar. According to the 4% withdrawal rate theory, this amount, invested in a diversified portfolio, has a good chance of supporting \$40,000/year in withdrawals during a typical 30-year retirement. Combined with his \$30,000/year from Social Security and his pension, this will yield the desired \$70,000/year in pre-tax income in today's dollars.

This is a "back-of-the-envelope" approach. It's probably better suited for young investors just getting started. When you're under, say, 45 there are so many unknowns that the critical thing is just to get in the ballpark - to just get started! If you're over 55 or so, consider supplementing it with additional, more detailed, analysis.

Notes:
Retirement savings are assumed to be invested in a "diversified portfolio" (say, 20-80% equities), and to grow tax-free in retirement accounts (e.g., in an IRA or 401k).
All dollar amounts are in today's dollars.
The 4% rule assumes all of your retirement income is coming from investments. The larger the percentage of your expenses that will be covered by guaranteed income such as Social Security, the better the chances that a higher initial withdrawal rate will be successful.
The 4% rule is designed to support about 30 years in retirement. If you are planning a shorter retirement (or, have already retired), you may be able to increase your withdrawal rate.  If you're planning a longer retirement you'll need to reduce your withdrawal rate.
The model assumes you begin collecting your pension and social security as soon as you retire.

### Related Articles & Posts

How Much Money Will You Need to Retire?  A look at the "big picture," using some typical/strawman assumptions.
Start Retirement with a 4% Withdrawal Rate: an intro to the 4% withdrawal concept, from Time magazine. For a more detailed discussion, see Wikipedia and, for even more, see
Beyond the 4% Rule: How Much Can You Spend in Retirement?
Inflation Calculator if you want to translate the required savings from today's dollars to the equivalent amount on your planned retirement date
Social Security Income Estimator: the official site.  For an approximation, see this site, or my graph.
Many versions of Quicken include a basic retirement calculator (see Planning - Financial Calculators in the Quicken menus).
Start Investing for Retirement When You're Young: Graphs showing the surprising impact of starting at age 25 vs 35 or 45.
What Will \$100,000 be Worth Invested in the Stock Market for 20 Years?: a look at the variability of market returns (a key reason withdrawal rates must be kept low).
Build Your Own Pension Using Immediate Annuities: A way to mute the impact of market variability.
Do You Need a Personal Strategic Plan? a process for setting goals and establish priorities.

Additional easy-to-use graphs based on these concepts:
The graphs are helpful for giving a "big picture" perspective and understanding trends. Note that graphs below may be slightly out-of-date if Social Security benefits have changed significantly since the graphs were created)
Assumptions for the "4% Withdrawal Rate" Retirement Savings Graphs