When you see a savings account with an interest rate of, say 1%, it looks small. And it is. But there’s a misconception about how small it really is: people underestimate the power of compound interest.
Let’s start with regular, simple interest. Imagine that you have $1,000 in a bank account that pays 1% interest annually. After a year, the bank gives you 1% of that principal sum, $10, as interest. You now have $1,010. The formula here is: Interest = principal x Rate x Time. That would be $1,000 for the principal, times 0.01 (which is 1%), times 1, for one year.
In addition to earning interest on the principal, compound interest actually allows your interest to earn its own interest, which can make a big difference in the long run. In other words, compound interest is the interest you earn on both your original money and on the interest you accumulate.
High-yield savings accounts offered by many online banks pay a 1% interest rate on your money, and pay it every month. But they actually compound interest every day—365 times a year. That means every little bit of interest gets put to work almost immediately.
The formula calculating the compound interest earnings for that is a little fancier:
P(1+(r/n))^(nt)-P = I
But once you plug in some numbers it gets a little better, say $1,000 invested at 1% compounded every day for a year.
$1,000(1+(.01/365))^(365*1)-$1,000 = $10.05
The interest accrued comes out to $10.05. OK, so not that much better than simple interest. It’s only a nickel more.
But when these numbers are bigger, it gets interesting. Make the timeframe 10 years and you get $105.17 in interest earned. Without compounding, you’d have $100.
Now, let’s say you have a 7% interest rate. In 10 years $1,000 brings you to $1,700 with simple interest (without compounding). If you were to have daily compounding—common in most bank savings accounts—you’d have $2,013. That’s almost 20% more thanks to daily compounding over the simple formula.
While you used to be able to invest in an online savings account at high interest rates, you can’t really do that today with the low rates set by the Fed. (However, investing in the stock market has historically yielded an annualized return of about 7%. Stocks don’t pay interest, but they do produce earnings and pay dividends; those earnings get reinvested and can earn even more. The more time your money stays invested, the more opportunity for compounding and growth.)
A handy thing to know when it comes to all of this is the “Rule of 72.” This rule gives you a pretty good estimate of how long it’ll take for you to double your money, given a certain interest rate. Just take 72 and divide it by whatever your interest rate is to see how many years it’ll take.
This is really helpful at illustrating the value and power of compound interest because it shows that the difference of just 1 percentage point—say between a 3% and 4% return is the difference of doubling your money in 24 years or 18 years.