Economics Investments Personal Finance

Q&A: What is compound interest?

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 MonthInterest Rate
January2%
February4.04%
March6.12%
April8.24%
May10.4%
June12.62%
July14.87%
August17.17%
September19.51%
October21.90%
November24.34%
December26.82%

You can see the difference between how often the rate is compounded here:

Compound FrequencyAPRAPY
Annually24%24%
Monthly24%26.82%
Daily24%27.12%

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