While browsing a local Sunday paper, I found a question in a Q&A column about APR and APY. (I haven’t been able to find a link to the original article yet, but it appeared in the 9/17/06 edition of the San Mateo County Times). Here’s the reader’s question and Mr. Cliff Pletschet’s (the columnist’s) response:
Q: World Savings advertised an annual percentage yield (APY) of 5.76% on a 10-month certificate of deposit, but a rate of 5.60% was typed into my passbook after I opened the account. The teller and her supervisor explained that I was getting the lower rate because the CD was for 10 months only and that if I wanted to get the higher rate I would have to roll over the CD after 10 months. I demanded my money back and opened a one-year CD at another bank for an APY of 5.70 percent. Can you explain what happened here? -A.B, Fremont
A: The math gets a little confusing, and the people at World Savings actually gave you the wrong information or you misunderstood their explanation. You would have received the 5.76 APY had you opened the account at World. The 5.60% is the actual rate on an APY of 5.76. The difference is the result of compounding, and, under federal law, banks must disclose the APY as the true return on a bank account, according to Julie Holbert, World Savings customer service manager.
Unfortunately, the mistunderstanding or misinformation sent you off to another bank where you actually ended up with a lower rate. In all araeas of investing, no matter how simple the process may seem, there’s an ongoing learning process.
The answer is spot-on (and as an aside, here’s the FDIC law that requires banks to disclose APY figures), but I’d like to delve into a little deeper an explanation by going through the difference between APR and APY and how they relate. This way, we won’t make the same mistake if we find ourselves in this person’s situation.
First, don’t get bogged down by the three-lettered finance acronyms. Unfortunately, APY and APR look so similar as to be interchangable, and their spelled-out definitions (annual percentage rate and annual percentage yield) don’t give us much of an additional clue about what they really are. In fact, neither the reader or (it seems) the professionals at World Savings understood the difference well enough to understand what was going on!
The difference between APR and APY essentially boils down to compounding.
Annual Percentage Rate, or APR, is the rate most people normally think of when you consider the interest you’re earning in an account and ignores the effect of compounding (e.g. being paid interest on not only the money you’ve put in, but the interest that you earned on that money in the previous period).
Annual Percentage Yield, or APY, is the more common calculation used by banks (and savvy investors) to make an apples-to-apples comparison of different CDs, savings accounts, and other investment vehicles of different lengths and terms by standardizing the term to one year (annual) and assuming compounding.
The general equation that converts APR into APY is the following:
APY = (1 + APR/n)n – 1
where n = the number of times in a year that you’re paid. For example, if you’re getting interest paid out each 6 months, then n = 2. If you’re getting interest paid each quarter, then n = 4. If you’re getting paid each month, then n = 12. And so on.
So what happened to our reader? He misunderstood that the rate being typed into his passbook was in fact the APR, not the APY. The reader doesn’t specify it, but if we assume World Savings compounds this CD daily in the same manner it does all the others, then:
APY = (1 + 5.6%/365)(365) – 1 = 0.05759314 or 5.76%
However, keep in mind that this doesn’t mean that if you bought a $100 10-month CD that you’d get $5.76 by the end of the term. You’d only get the full APY if you had bought a CD that lasted the full 12 months. On a 10-month CD, you’d actually only get around $4.78, or 83.3% of the full $5.76 because you invested your CD for 83.3% of a full year. Another example: I bought a 3-month CD from Schwab that earns 5.41% APY, but that doesn’t mean I’m going to get 5.41% of my investment at the end of 3 months, but only 1/4th of it, or 1.3525%.
So, in summary, here are the key things you need to know to make a good investment in a CD, savings, or other interest-bearing account:
- Understand the difference between APR and APY
- Use the APY provided by financial institutions to make an apples-to-apples comparison across all the various opportunities out there
- Make sure you know the term of the investment (e.g. 3-months, 6-months, 13-months, etc.)
- Make sure you know how often the interest is compounded
- And most important, educate yourself so that “professionals” won’t lead you to make a bad decision when they make a mistake!