## compound interest

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.

### 29 Responses to “compound interest”

1. Holly@ClubThrifty Says:

HA! Yeah, he does have some fuzzy math from time to time. I really do wish that 12% was the norm. It would make things so much easier. =/

2. Bardiac Says:

Except if 12% were the norm, inflation seems likely to be way high, and that hurts regular folks who can’t just put in 100K for 30 years WAY worse.

• nicoleandmaggie Says:

Yeah, it depends on if it’s real or nominal growth. I’m all for productivity growth, assuming we do it responsibly and don’t kill the planet or increase the already widening income gap.

3. Leah Says:

I both love and hate compound interest. I did a retirement calculator on maxing out my Roth IRA each year from now on, starting with last year. Imagine my shock when I realized that, had I started two years earlier, I would have way more. I can’t remember exactly, but at least over \$200k more. Good incentive to max out each year and to put a little more each paycheck in my 403(b). Wish I had the money to max that out too.

4. Debbie M Says:

It’s even worse when you add the anti-magic of inflation. (Fortunately, ours has been low for a long time and has never gone crazy.)

Still, it’s awesome that you can have more money than you’ve actually saved. And it’s even possible to have more money than you’ve actually earned and been given.

5. OMDG Says:

Ah math. Gets you every time.

• OMDG Says:

I agree, math rules. Question — Have you ever done a post on how much a family should plan on saving for retirement (i.e. what kind of target #s should they be shooting for)? Obviously it depends on lifestyle, health issues, etc. but I wanted to try to do some financial planning these next several months.

• nicoleandmaggie Says:

I think there’s an ask the grumpies on that somewhere in our archives with links to calculators. In general the answer is to put away 15-20%/year if you’re planning a “regular” retirement age. More if you start later, less if you start earlier.

6. Emily @ evolvingPF Says:

Great, concise explanation! It is maddening that DR implies that being 50% wrong in his return assumption results in only a 50% reduced portfolio. I’m going to link to this from my post about DR’s investment advice.

7. […] it is certainly exciting to see how compound interest can magnify a portfolio over a long timeline, using a 12% annualized rate of return to predict retirement account balances is irresponsible.  Thankfully, Dave Ramsey’s advice is to […]

8. frugalscholar Says:

Ah, the annoying Dave Ramsay’s 12%. Another annoying thing: all the personal finance blogs that talk about “high interest savings accounts.” These are currently paying around .85%!

Thanks for doing the math.

9. SP Says:

I hate Dave Ramsey. Yes, you should save and save early, but you should also use realistic assumptions.

Also… i was going to argue that it really isn’t magic, it is math, because the phrase “magic of compound interest’ has always irked me. But in some ways, math = magic (logical magic!) – I guess it doesn’t hurt to look at it that way

10. Rosa Says:

The other thing about that 1% is that it doesn’t matter if you lose it to lack of performance or management fees – except that you can predict the management fees and it would be *really* magic to predict performance to within 1% year after year.

Which, I’ll assume, makes any account Ramsey’s shilling an even worse bet than just “the market” would account for.

(Also amen on the “high interest” savings accounts. I just had to do the math – with GRAPHS – for my husband on why we should move money into stock accounts instead of his “high interest” savings account. He sneers at savings bonds but I-bonds have been outperforming his “high interest” savings account.)

11. Thanks for this post. Yes, saving and investing is great. But promising crazy numbers seems to be based on the premise that people need lottery like numbers to be motivated. I also wrote in All the Money in the World about the David Bach-esque promise — if you’d been putting like \$3000 away for 40 years that would net you a large amount now. This is true, sort of, but putting \$3000 away in the stock market in 1970 as a 22-year-old would have been quite a feat, since the average wage at that time in nominal \$ was \$9000. So yes, saving a third of the average income when you’re just starting out, and presumably earning a lot less, will in fact get you great results, but I don’t think anyone doubted that a 20-something saving half of his income will come out great.

• nicoleandmaggie Says:

At least with interest rates you can use real instead of nominal in your predictions so as not to ignore that pesky but if so important inflation. Of course, that makes 12% even more ludicrous.

12. […] nicoleandmaggie referenced my post on Dave Ramsey’s flawed teaching on wealth building in her explanation of why slightly overestimating your rate of return slightly has a huge impact on your ultimate balance. […]