Interest Rate: APY and APR

When the bank pays you interest on a savings account, it quotes the interest rate in APY — Annual Percentage Yield. When the bank charges you interest on a loan (car loan, credit card, mortgage, etc.), it quotes the interest in APR — Annual Percentage Rate. So, if you have a savings account that the bank pays you 5% APY and a car loan that you pay the bank 5% APR, are you even with the bank, ignoring the effect of taxes? You guessed it, NO, the bank wins. This is because for the same interest rate, APY is always larger than APR. So the bank wants you to think the interest it pays you is higher than it actually is and it wants you to think the interest you are paying them is smaller than it actually is. Sneaky, huh?

JLP at AllFinancialMatters gave the formula:

APY = (1 + APR ÷ n)n – 1

where n = the number of compounding periods.

Don’t want to use a calculator but let Excel calculate for you? Here’s the formula for Excel:

APY = EFFECT(APR, n)

Put =EFFECT(5%, 365) in a cell and you will get 5.127%, which means the APY on a 5% APR loan is actually 5.127%.

The equivalent formula is

APR = n * (1 + APY)1/n – n

The formula for Excel is:

APR = NOMINAL(APY, n)

Put =NOMINAL(5%, 365) in a cell and you get 4.879%, which means the APR on a 5% APY savings account is actually only 4.879%.

When you compare the interest rate on a savings account with the interest rate you pay on a loan, be sure to convert to either APY or APR for an apple-to-apple comparison.

Paying off a loan is often the best guaranteed return you can earn. Because of the effect of taxes on interest income, the equivalent return for paying off the loan is a lot higher than the interest rate on the loan. Suppose you have a car loan at 7% APR monthly compounding, and you are in the 28% combined federal and state marginal tax bracket, in order to break even, you would have to earn an APY of

((1 + 0.07 / 12)12 – 1) / (1 – 0.28) = 10.04%

or in Excel:

EFFECT(7%, 12) / (1 – 0.28) = 10.04%

In other words, the return on paying off a car loan at 7% APR is 10.04%!

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Comments

  1. Anonymous says

    I really like this post, but I did find an error. In the last Excel example, the NOMINAL function was used when it should have been the EFFECT funtion. Using Nominal would give you 9.42% rather than the 10.04%.

  2. mac says

    Can anyone help me figure this out?
    I lent a friend 10,000.00 and agreed that he pay me interest at 8% APR. We would like to know what he owes me if he doesn’t pay me after exactly 1 year. Is there a simple formula? as he paid some back early and will pay some back late
    Thanks
    mac

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