One of the things Dave Ramsey is infamous for is making the claim that the stock market returns 12%/year. Lately he’s been saying well, his money market funds return that. (Uh huh.) Then he goes through an exercise showing how much money you’ll make if you put away X, assuming an interest rate of 12%/year. It’s a lot. Because of the magic of compounding.
And obviously that 12% number is garbage. (Reality is probably closer to 7%.) However, after he makes this claim, he’ll often say, “Even if I’m half wrong…that’s still a lot of money.”
The implication being, if the interest rate is closer to 6% you’ll end up with half of that huge number he just calculated, which is still a huge number.
Of course you don’t.
Because compound interest doesn’t work that way. As time goes on tiny differences are magnified with each compound, so that 6% difference starts out as half as big, but ends up compounding over time to something much larger than half as big.
Here’s a calculator because that’s more fun than doing the math by hand. (Or at least it’s more fun than either typing out the formula or typing out the derivation of the formula.)
Take a Principal of 100,000. Don’t add anything to it. Assume a 12% interest rate that compounds once per year for 30 years. You get $2,995,992.21 . Or almost 3 million dollars.
Now let’s assume it’s actually half of 12%, or 6%. If you’re thinking, I could totally live on 1.5 million dollars… you probably could. But a 6% interest rate over 30 years only gives you $574,349.12, or half a million dollars. Not chump change, but not enough to live through retirement on, even assuming these are real interest rates (putting things in today’s dollars instead of tomorrow’s inflationed dollars) and not nominal (if you assume 2% inflation, the real interest rate is 2 points lower than the nominal rate).
Half the interest rate compounded doesn’t result in half the earnings, but instead far less than that.
Losing just 1%, for a rate of 11% gives $2,289,229.66, which is a loss of about 700K!
The truth is that compound interest is magical, and the longer your time horizon, the less you need to put in to get big numbers out the other end. However, it’s not quite as magical as a 12% interest rate would have you believe. If Dave Ramsey is 50% wrong, you’re much worse than 50% worse off.