A friend of mine recently asked my thoughts about what percentage of earned income should go towards savings, which I presumed to mean for retirement savings. I gave him an instantaneous answer (10%) without putting too much thought behind it beyond a consideration that he was young and anything more was unlikely to be achieved. However, I think this question deserves a bit deeper of an answer.

I think the right way to answer this is to do a numerical analysis which starts by figuring out what a dollar saved might be worth at various points in the future. By which I mean figuring out not only what it might grow to if invested, but what that amount might buy at that time. A simple analysis includes two numbers, the average stock market return (say 10% per year) and an average inflation rate (say 4.5% per year). (These numbers are my recollection of values I remember reading in a number of different articles as supported by historical data.) Subtracting the inflation rate from the market return gives a real growth rate of 5.5% per year. For someone in their early 20’s thinking about retiring in their late 60’s, which means 45 years of compounding, each dollar saved would turn into $11.13 of buying power [$11.13 = $1.00 x (1.0 + 0.055)^45]

But there are three immediate issues with this result. First, it falsely implies that market returns and inflation come around like clock-work and never vary year after year. We know that simply isn’t true, and we can analyze historical values to get a better picture through statistics — but I’m going to put off addressing that in this post as I need more time to find data sources and/or do some spreadsheet or script programming. Second, it only considers the return on money invested in a single year rather than yearly contributions over many working years. And third, no consideration is made for the size of a nest egg actually needed for retirement. I can address the second and third issues in this post.

We’ll start that out by thinking about the pattern made by year after year savings. Which is that each successive year of savings has one less year to compound and grow. Spelled out, that looks like this:

- Year 1 savings: $X invested and compounding for 45 years
- Year 2 savings: $X invested and compounding for 44 years
- Year 3 savings: $X invested and compounding for 43 years
- ….
- Year 45 savings: $X invested and compounding for 1 years

If we let G be the annual growth rate after inflation, and we plug in the simple 5.5% growth rate from the simplistic analysis above for G, this could be described by the series of equations:

Retirement Balance = X*(1+G)^45 + X*(1+G)^44 + X*(1+G)^43 + .... + X*(1+G)^1 = X * [(1+G)^45 + (1+G)^44 + (1+G)^43 + .... + (1+G)^1] = X * 194.246

If you contributed $1.00 to your retirement savings each year for 45 years, and you managed to earn a 5.5% growth rate on it after inflation, you’d have $194.25 of buying power when you retired. (In absolute terms, you’d have an account balance of $790.80 due to the 10% market growth rate, but it would only buy goods worth $194.25 in today’s dollars.) It should be easy to see how this scales. If X is $1,000.00 instead of $1.00, then your retirement nest egg ends up being $194,246. Not a bad number by any means, but if you’re like me, that still doesn’t give you an idea of what percentage of income to contribute to retirement savings each year. So how do we relate the nest egg size to the retirement savings rate needed? Well, we can make a few more assumptions to start to tie things together:

- For a typical life expectancy, many articles on retirement say that you should not spend more than 4% of your nest egg in any single year if you don’t want to run out of money. For a $194,246 nest egg, that means you’d have to be living on $7,769.84 each year.
- Let’s also assume you don’t want to change your standard of living when you enter retirement. A simplification of this is that your income in retirement must equal your income prior to retirement. Combining this with the above withdrawal rate assumption means you’re spendable income prior to retirement would also be $7,769.84.

So the question left is what savings rate allows you to invest $1,000 into retirement savings yet leaves you with $7,769.84 in spendable income? A simple calculation shows you’d need to save 11.40% of an annual gross income of $8,769.84 to meet these requirements.

It is very important to keep in mind the number of assumptions we made to get that value! For example, I don’t particularly believe most people need the same income in retirement that they needed prior to retirement. Will you be making mortgage payments after you retire? What about college expenses for kids? etc. Likewise, the 4% withdrawal rate is an assumption that is based on a simplification of growth in your nest egg even as you withdraw part of it, as well as how long you’ll live. What if you’re in retirement and you run into an economic situation like today where stocks are down, some bonds are actually defaulting, and interest rate cuts are lowering savings, CD, and other yields. What if you live to be 120 instead of dieing at 89.7 years old? etc. While changes in these two assumptions could cancel each other out, let’s run a scenario where only one changes and see the effect it has on the savings rate needed. Let’s assume you want to be more conservative and only withdraw 3% of your nest egg each year. You’d now need to be saving 14.65% of a pre-tax income of $6,827.38 in order to not change your standard of living when you retire. A small assumption change had a significant savings rate effect!

Just to summarize, here are the key assumptions in the above analysis. Make sure you understand these before you assume a 11.40% savings rate is appropriate for you!

- Constant investment growth rate (10.0%) and inflation rate (4.5%).
- Number of years over which to save and compound growth (45 years).
- Retirement withdrawal rate (4.0%).
- Income change at retirement (0.0%).

Keep in mind that the important numbers in the above paragraphs are the retirement savings rates of 11.40%, and/or 14.65%, and not the specific dollar amounts. The math will work out, assuming the other assumptions don’t change, no matter what you’re actual annual income is. For example, if you were making $50,000 a year, you’d need to save $5,700/year (11.40% of your income) in order to build a nest egg of $1,107,202.20 by retirement, and thus have an income of $44,288.09 (4% of your nest egg) per year during retirement.

Also keep in mind that the above analysis assumed your income doesn’t change at all over the 45 working years until retirement. That (hopefully) doesn’t accurately model reality for you or me. I didn’t include any sort of income changes because the number of assumptions you have to make just makes things that much more complicated. What rate of change do we put on the income? Which year’s income do we want to match in our retirement years? Hopefully given my explanation above you can see how to put in factors for these and derive your new income savings rate.

One last comment before I close out this post relates to another, completely different, approach to determining your retirement savings rate. I’ve often heard people use the phrase “until it hurts” when describing how much to save. The idea is that you keep increasing the amount you save until doing so causes real financial pain in your life. My fear with this plan is mainly that people will stop way too early and end up missing out on the huge power of compounding by not doing any retirement savings early on in their life. IMO, there’s never a better time to train yourself to save a decent proportion of your earned income than when you’re young and have fewer ‘needs’ imposed by a larger family size. I also think it’s better to do some math-backed planning early on, the numbers aren’t that hard, and you can always adjust the plan and redo the numbers if you decide assumptions need to be changed.

1 RedG3 // 2008.12.30 at 11:28 am

This has been very helpful, I have another question though. How would one take into account the rate of change of their income when wanting to calculate your savings? How much more complicated does this make the calculation, because I am interested in this value. Are there any other assumptions I would need to make when taking income change into account besides which year’s income I would want to match in retirement?

2 davmp // 2009.01.02 at 6:00 am

@ RedG3: Thanks for the question! I ended up responding by writing up a new post. See http://geographic-independence.com/how-do-changes-in-income-effect-a-retirement-savings-rate/