# Explaining Simple Interest, Compound Interest, APR, and APY

Recently, my niece was trying to calculate how much money would be in her savings account in six months. She was using the APY as a simple interest rate and thus was coming up with a number larger than what would actually be in her account. It was a small difference, but she seemed to believe the bank was “ripping her off” and was quite upset over the matter.

Although people who astutely follow their own personal finances are quite aware of the differences between these three things, many people believe that all interest rates are basically the same. The fact is that they’re quite different, and knowing and understanding these differences can make a huge difference in the amount of money you can expect to pay on your bills and make on your investments.

Most people believe all interest functions like simple interest. Simple interest basically is the amount you borrowed times the interest rate. In other words, 5% interest on \$1,000 is \$50. This is the rule most of us are taught in primary school and the one that is most ingrained in our minds, but it’s not the method that most businesses use when calculating interest.

The simple fact of the matter is that if you really believe that all interest rates work like simple interest, you’re going to lose a lot of money.

So how else is interest calculated? Many organizations (such as banks and credit card companies) use compound interest to calculate how large your finance charges are and how much interest you get. Compound interest is interest which is added back to the original amount. Organizations do this on a regular basis and use a method that is most effective for their business, allowing them to report an interest rate to consumers that doesn’t actually describe the full situation of the payments.

For example, most organizations use compounded interest, compounded monthly. This is in line with how most credit cards and many banks calculate interest. Let’s look again at that \$1,000 over a year at 5% interest. If we use simple interest, the total is just \$1,050, as we saw above. But if we compound the interest each month, our calculation is a bit trickier, as we have to figure the balance at the end of each month.

Let’s work this out. If we start with \$1000 at the start of the first month, at the end of the first month, it will have earned 1/12th of the interest it should earn over the year. With simple interest, we don’t care about how much it’s earned during that first month, but with compound interest compounded monthly, at the end of the first month, we add that 1/12th of interest to the original amount and start over again. 1/12th of 5% of \$1,000 is \$4.17 (rounded to the nearest penny), so we add this amount to the \$1,000 to get a starting balance of \$1,004.17 at the start of the second month. We repeat this for each month (during the second month, it earns 1/12th of 5% of \$1,004.17, and then so on…). At the end of the year, we have \$1,051.16, which is \$1.16 more than if we just used simple interest.

If you increase the amount or the interest rate, the difference between simple interest and compound interest is even greater, and that is an amount of money that companies would really like to have in their pocket. So here’s what they do:

If you’re borrowing money (using a credit card, for example), they quote you an APR, which is the simple rate. So, even though it’s compounded monthly and thus the growth of the balance in a year will be more than that rate, they advertise the lower simple rate. Let’s look at an example: let’s say you borrow \$3,000 on a credit card at a 24.99% APR. At first glance, the interest rate seems to indicate that you would have to pay \$749.70 extra after a year, but that’s just not the case. If the credit card compounds monthly, you’ll actually owe a total of \$3,841.82 – an extra \$92.12. It’s even worse if they compound more often than monthly.

On the other hand, if you’re saving money, they quote you an APY. An APY is the percentage you’ll earn as a difference between the starting balance and the ending balance in a year. If it is compounded more often than each year, your real interest rate is lower. Let’s say that the bank quotes you a 4% APY on your investment of \$5,000. At the end of the year, you will have \$5,200 in your account, but if you withdraw after six months, you won’t have \$5,100 in your account. Why? You’re not really earning 4% interest. If the account is compounded monthly, you’re actually only earning about 3.929% interest, compounded monthly. Thus, at the six month mark, you only have \$5,099.03 in your account! Given enough accounts, that difference is quite a bit of money, an amount that the bank can use for other investments.

##### Trent Hamm
###### Founder of The Simple Dollar

Trent Hamm founded The Simple Dollar in 2006 after developing innovative financial strategies to get out of debt. Since then, he’s written three books (published by Simon & Schuster and Financial Times Press), contributed to Business Insider, US News & World Report, Yahoo Finance, and Lifehacker, and been featured in The New York Times, TIME, Forbes, The Guardian, and elsewhere.