The Psychology of APR and APY
Up until a little while ago I was like many people that didn’t know the difference between APY and APR. In fact, I didn’t even know there was a difference. I kind of always assumed it was the same thing, just two different names for it, or even if it was different it simply wouldn’t affect me. I have learned that many times it is the things we know little of that have the greatest impact in our lives. So, I would like to share what I’ve learned regarding APY, APR, and our minds.
APR
APR stands for annual percentage rate. It is also commonly referred to as interest rate. As the name suggests it is the percent of interest that you will pay or be paid for a period of time. For example, say you open a credit card that has an APR of 24%.
Usually credit cards have a monthly periodic rate which means the interest compounds each month. So you will take 24% and divide it by 12 — a year has 12 months — this will give you your monthly interest rate (periodic interest rate) which in this example is 2%.
Every month your balance will be multiplied by 0.02 (2%) and the product will be added to your balance. The process will rinse and repeat for the remainder of your balance.
Month 1:
Balance — $2,000
$2,000 x 0.02 = $40
$2,000 + $40 = $2,040Month 2:
Balance — $2,040
$2,040 x 0.02 = $40.80
$2,040 + $40.80 = $2,080.80
Obviously payments would reduce your balance and subsequently reduce your interest payment but you can see how your interest compounds each month and a part of your payment would actually only go towards paying the interest. By the end of the year you would be paying more than 24% because interest has been added to whatever you owe.
APY
APY on the other hand stands for annual percentage yield. This is the actual percent of interest you would pay on a balance if you ignore payments made. A credit card with an interest rate of 24% actually yields almost 27% to the lender.
The Elephant in the Room
Would you have gotten this credit card if it said 27% instead of 24%? Would the bank have approved you for a $2,000 line of credit if they were getting 24% annual percentage yield? These are valid questions to ask, and in fact you should be asking them (at least to yourself).
Training your mind to notice these differences first requires becoming aware that they exist. If you know the difference between APR and APY your brain will assess the real cost of the loan or the real return on your investment and you can make better informed financial decisions in your home, education, and business.
If you look around at credit cards, loans, investments, etc. a pattern will emerge. A pattern we are all susceptible to unless we actively search for and do our best to recognize.
Generally when talking about loans, credit cards, and other debt — banks, private institutions, and lenders will show you the APR. When talking about investments, savings accounts, certificate of deposits, and other investment vehicles — they will show you the APY.
The reason for this is simple psychology. People want to pay less and earn more. APR appears to be less, and APY appears to be more. This is simple business, wouldn’t you do the same if you are trying to sell something?
Only $3.99!
A similar psychological methodology can be seen somewhere else, at the center point of American culture — the retail and service business. Go to almost any store and you are guaranteed to see a price tag that ends in 99 cents or even dollars in more expensive items.
This trick is known as “the left digit effect” or “odd-pricing” and it has been around for a while.
They show that lowering a price by one cent to a 99 ending affects magnitude perceptions when the left digit changes (e.g., $3.00 to $2.99) …These studies, contrary to some of the earlier views (e.g., Gabor 1977; Knauth 1949), provide experimental evidence that nine-ending prices are perceived to be smaller than a price one cent higher. These experimental results also corroborate Stiving and Winer’s (1997) finding, using scanner data, that the left digit exerts a stronger influence than the right digits in price evaluation. (Penny Wise and Pound Foolish: The Left-Digit Effect in Price Cognition; Manoj Thomas, Vicki Morwitz)
Basically, because we read from left to right, we attribute more importance to the left-most digit. In the case of $3.99, the 3 dollars resonate more with us but the cost is actually 4 dollars.
This effect is not directly embedded in APR and APY but it shows us how vulnerable our minds can be. The similarity here is the object of manipulation — our perceptions. When the price is $3.99 we perceive the cost to be about 3 dollars, when in reality the price is 4 dollars. When we see an APR of 24% we perceive that we are paying 24% interest on our balance, when we are in fact paying closer to 27% interest.
Likewise, if we open a savings account we may incorrectly believe that we are getting more money than we are. I made that mistake when I first opened an account with SoFi (Social Finance), I was excited that I would be earning 2.25% APY on my money (now it’s about 1.60% APY due to fed cuts) and right away I began calculating something like this:
0.0225 annual percentage yield as a decimal
12 months in a year
0.0225 / 12 = .001875 monthly interest rate as a decimalMonth 1:
$1000 x 0.001875 = $1.87
$1,000 + $1.87 = $1,001.87Month 2:
$1,001.87 x 0.001875 = $1.88
$1,001.87 + $1.88 = $1,003.75
I had the incorrect notion that the annual percentage yield was an annual percentage rate. The calculations had already been done for me. If I put $1,000 in my account, I would have $1,022.50 at the end of the year, that was the yield (duh!). The APR was would actually be about 2.23% which means that the above calculations should have been something like this:
0.0223 annual percentage rate as a decimal
12 months in a year
0.0223 / 12 = .00185 monthly interest rate as a decimalMonth 1:
$1000 x 0.00185 = $1.85
$1,000 + $1.85 = $1,001.85Month 2:
$1,001.85 x 0.00185 = $1.85
$1,001.85+ $1.85 = $1,003.70
You’ll notice that the actual results can be considered negligible by most standards.
$1,000 at 2.25% APY: $1,022.50
$1,000 at 2.25% APR: $1,022.73$10,000 at 2.25% APY: $10,225
$10,000 at 2.25% APR: $10,227.33$100,000 at 2.25% APY: $102,250
$100,000 at 2.25% APR: $102,273.35
The results become more important the more zeros you add to the end of whatever your investment is. However, most of us are not in the position where confusing APY for APR in an investment is a serious problem.
In reality the reverse of that is most damaging to people, confusing APR for APY (not APY for APR as in the previous example), and it is there that these numbers make a bigger and more profound difference in people’s lives over the long term. For example:
A credit card debt of $2,000
$2,000 at 24% APR: $2,536
$2,000 at 24% APY: $2,480
In conclusion, the next time you, a friend, or a family member are looking at taking out a loan or opening a line of credit and they flash the APR at you, ask the lender— “so what is the annual percentage yield?” If you don’t want to ask then pull out your phone, crunch some numbers or type “apr to apy calculator” in google, and you will get your answer faster than they can say “your application has been submitted”.
