### Time to retirement

There is a vast amount of misleading information out there about how to save for retirement. Unfortunately, there are no secret tricks that allow you to retire early (unless you are lucky enough to inherit a large fortune). In reality, early retirement requires saving a large chunk of your after tax income. But just how much of your income do you need to save? Many people have already published excellent articles on how to calculate the amount of savings needed to retire after working for a given length of time (see this article, and this article.) I took their method, simplified it a bit, and plotted the results. I'll explain a bit more about how I generated this plot, but for now, here it is:

The essential idea behind this figure is that the fraction of your income that you save indicates two things -- 1. how much you are putting away each month, and 2. how little money you can live on. This number, which I'll call savings rate, is the one that is easiest for a worker to control. As a concrete example, let's say that Joe makes $100,000 after taxes each year. If he saves $10,000 each year, then his savings rate is 10%. OK, pretty simple so far. Now we need just one more number: the rate of return on investments. This is where my simplifying assumption comes in. Many people suggest that you withdraw no more than 4% of your savings each year in retirement, but they also maintain that you can expect to earn more than that in the stock market. To be conservative, I assume that you only earn 4% return on your investments annually. (If you're interested, we'll see the impact of changing this number below.) I also assume that we're starting at the very begninning of our subject's career, so Joe has no money already saved, and that his income doesn't change over time. (Hopefully this is not the case, but it's safer not to count on big raises in the future.) Finally, our most stringent criterion: we want Joe to be able to live *indefinitely* in retirement, so he doesn't out-live his savings, and he'll have something for his kids to inherit. OK, those are the assumptions. By looking at the figure, we can see that at Joe's savings rate of 10%, he can retire after working for about 60 years. That doesn't sound very appealing, but I hope it is empowering to notice that if Joe manages to save 30%, or $30,000 per year, he could retire safely in just 30 years!

Now, I promised that we could look into the effect of our assumption that the annual rate of return on investments is 4%. In the following figure I have plotted the results of this calculation for different rates of return. Note that these also assume the subject withdraws that amount every year in retirement, which might not be a good idea because it doesn't allow for bad years early in retirement.

So there it is, thanks for reading!

**Disclosure:** Nothing in this article should be construed as tax advice, a solicitation or offer, or recommendation, to buy or sell any security. This article is not intended as investment advice, and I do not represent in any manner that the circumstances described herein will result in any particular outcome. Past performance is no guarantee of future results.

### Authors and Contributors

Written by Peter Weir (@ptweir) in 2017.