Retirement, the American dream. Even more so than home ownership. Because in the end, all we want to do is have fun and not have to work, right?
There are so many opinions out there about how much you need to retire that I honestly have no idea exactly how much it is I’m supposed to have saved up before I can quit working. So now here’s yet another opinion you can consider.
Let’s make the very simplistic assumption that, after you retire, if you continue to have an income equal to what you earned before you retired, that that will be enough for you to live on. So if your salary is $100,000 before you retire, we’re assuming that you can live on $100,000 a year. Obviously, this is incredibly simplistic and inaccurate, but it makes doing the math easier. Now let’s also say that you have some way of earning a fixed interest rate on your money every year, and call that r. If your salary is s dollars, then you’ll need to save up s/r dollars before you retire, since that s/r dollars will give you s dollars of interest a year, which presumably you can live off of.
Now the question is, if you save a proportion p of your income, how many years will it take until you save up enough to retire? Just for the sake of simplicity, let’s say the interest compounds annually. So at the end of the first year, you’ll have saved sp dollars from your income, and then with interest, you’ll have sp(1+r) dollars. At the end of the second year, you’ll have sp(1+r)2 + sp(1+r) dollars. Continuing this pattern, we see that after n years, you’ll have sp((1+r)n + (1+r)n-1 + … + (1+r)) = sp((1+r)n+1 – 1) / r dollars. Since the goal is s/r dollars, we just set these two equal to each other and solve for n, and we get n = log(1 + 1/p) / log(1 + r) – 1.
That means that the number of years until you retire only depends on the proportion p of your income that you save and the annual return r you can get on your money. It doesn’t depend on your salary s. Which makes sense, since you’re living off of your annual salary in retirement, whether it was $30,000 or $250,000.
Let’s say that you can get an 8% return on your money every year and you save 25% of your income. If you plug in r = 0.08 and p = 0.25 into the formula above, you get n = 19.91. You can retire in 20 years! OK, so saving 25% of your income might be optimistic. Given that you only get to take home maybe 60% of it, that means you have to save over 40% of your take-home pay. So now if we try p = 0.15, meaning you save about a quarter of your take-home pay, we get n = 25.47. Still not that bad; if you start working at 23, that means you can retire by age 50.
Another interesting question is how much of your income you need to save to retire in a certain number of years. If we solve for p instead of n in the equation above, we get p = 1 / ((1+r)n+1 – 1). So if you want to retire in 30 years and you can get the same 8% return on your money, we can plug in n = 30 and r = 0.08 into that expression, and we get p = 0.101. So you only need to save about 10% of your income to retire in 30 years. That doesn’t seem that bad! Then again, 30 years is a long time…
Of course, the simplifying assumptions above are probably optimistic. Your health care costs probably rise during retirement, and without a job, a lot of your insurance will have to be paid out of pocket. On the other hand, if you have a mortgage, it’ll probably be paid off. It’s hard to say how optimistic or pessimistic the assumptions are, but this math kind of makes you hopeful about retiring at a reasonable age, doesn’t it?