Confounded compounded interest!

We know that the earlier in life you can start saving the better. It's the power of compound interest.

If you begin saving for retirement at 25, putting away $2,000 a year for just 40 years, you'll have around $560,000, assuming earnings grow at 8% annually. Now, let's say you wait until you're 35 to start saving. You put away the same $2,000 a year, but for three decades instead, and earnings grow at 8% a year. When you're 65 you'll wind up with around $245,000 -- less than half the money.

However. Tara Siegel Bernard, a personal finance writer at The New York Times, throws some cold water on this rosy scenario.

The problem is that even if you do everything right and save at a respectable rate, you’re still relying on the market to push you to the finish line in the last decade before retirement. Why? Reaching your goal is highly dependent on the power of compounding — or the snowball effect, where your pile of money grows at a faster clip as more interest (or investment growth) grows on top of more interest. In fact, you’re actually counting on your savings, in real dollars and cents, to double during that home stretch.

Now my skill with mathematics, and hence my skill with money, is laced with magic, delusion, error and confusion, but I think I understand what she's getting at: the compounding kicks in in a big way at the end.

“The way the math really works out is unbelievably dependent on the final few years,” says Michael Kitces, director of research at the Pinnacle Advisory Group in Columbia, Md. “I just don’t think we’ve really acknowledged just what a leap the very last part really is.” 

Kitces explains the chart on the right:

While it is true that the client has accumulated $1,000,000 by the end of the 40-year time horizon, it's notable that after 30 years, the client still has less than $450,000! And of course, at that point the impact of a marginal $300/month of savings is fairly negligible; the client will succeed because of the investment returns. With an assumption of "just" 8% in growth, the classic rule of 72 means the client will double her wealth in 9 years.

Accordingly, by this savings approach, the best way to have $1,000,000 in 40 years, is to have $500,000 in 31 years, and then quickly double your money in the last decade and retire!

Let's roll out another scenario.

Consider the numbers for a 26-year-old who earns $40,000 annually, with a long-term savings target of $1 million. To get there, she’s told to save 8 percent of her salary each year over her 40-year career. Yet after 31 years of diligent savings, her portfolio is worth just slightly more than $483,000. To clear the $1 million mark, her portfolio essentially must double in the nine years before she retires, and the market must cooperate.

In my math brain, the market always cooperates, but I think I've read somewhere that it actually doesn't. Duh.

The problem, of course, is that twenty-somethings don't have money to save. I'm not sure I have an answer for that, except a radical change in how we view consumption in those years. Or lucking into a period later in life when some fool is paying you a huge salary and you can hide more under your mattress.

God bless us all.