When is 12/12 Not Equal to 1? In Finance of Course. Learn effective rates!
Have You Ever?
Have you ever seen bank account interest rates and noticed that there are sometimes seemingly two different interest rates? What you're most likely seeing is the Interest Rate and Annual Percentage Yield (APY). An interest rate is the investment gain without taking compounding into consideration while the APY does. What you don't see is what's known as the Effective Rate. This Effective Rate is the rate on a per conppound basis period (in this case monthly). If that was confusing, no worries, it was. Allow us to explain.
Say you have an account that yields 12% a year and compounds monthly. If you wanted to find out how much the account made in a month what would you say is the monthly compounding rate? The answer: 0.948879...%
The Power of Compounding Interest
If you're like most people you probably assumed that the monthly rate is 1% (12% / 12 months = 1%). But because of compounding it's going to be less than 1%. The actual answer, 0.948879...%, can be calculated from a complicated formula found here.
Take this disclosure from the Capital One 360 Savings Account rate for instance. See where it says your interest rate and your Annual Percentage Yield?
If we take the 1.9% APY and use the formula we can get the effective rate. The effective rate is the rate in a per compound period basis (in our case monthly).
[(1+.019)^(1/12)-1]*100 = 0.156971...%
Banks take this effective rate to create the interest rate and the annual percent yield. The only difference being that the interest rate doesn't account for compounding while the APY does.
To demonstrate this take our effective rate, 0.156971...% and simply multiple by 12 to find our Capital One's magic 1.8337% number. If you compounded the effective rate it would equal the 1.9%:
[(1+0.156971)^12-1]*100 = 1.9%
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