Compound interest takes into account the interest on the accrued interest. 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. 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% |
