Simply put, compound interest is interest earned on the interest that has already been earned. This can be a great thing for investors, but a bad thing for borrowers.
Real-life application:
Investors
The S&P 500 has had an average annual return of 8.9% over the last 30 years (1980-2019). If someone invests $1,000 into a S&P 500 mutual fund at the beginning of 1980 and holds it until the end of 2019, they would have $12,907.33. However, if there was no compounding and the 8.9% was just simple interest, the $1,000 would only turn into $3,670 after those 30 years.
Borrowers
A credit card with an APR of 24% may have a higher APY based on how often it is compounded. How this happens is by dividing the APR by how often it is compounded, then making that frequency the exponent:
APY = (1 + APR/n)^n – 1
where n = number of times compounded
For this example, we will say the frequency is monthly. So the 24% APR is divided by 12 to come to a monthly interest rate of 2%. When this is compounded month to month, this is what happens to a card that starts on January 1st:
| End of Month | Interest Rate |
| January | 2% |
| February | 4.04% |
| March | 6.12% |
| April | 8.24% |
| May | 10.4% |
| June | 12.62% |
| July | 14.87% |
| August | 17.17% |
| September | 19.51% |
| October | 21.90% |
| November | 24.34% |
| December | 26.82% |
You can see the difference between how often the rate is compounded here:
| Compound Frequency | APR | APY |
| Annually | 24% | 24% |
| Monthly | 24% | 26.82% |
| Daily | 24% | 27.12% |
