When you borrow money by taking out a loan for college, a car, or any other loan, you’ll be charged interest. Additionally, if you don’t pay off a credit card balance in full by the statement due date, you’ll also be charged interest on the balance owed. Lenders make money by charging interest to a borrower as a percentage of the amount of the loan, or the credit card balance due.
When you deposit money in a bank account that pays interest—
Interest is typically expressed as an annual percentage rate, or APR. To keep more of your money, it’s wise to shop around and borrow at the lowest interest rates. Likewise, lend your money and deposit it in the bank that offers the highest possible interest rates, so you earn more.
But how does your money actually earn interest? There are two basic types of interest: simple interest and compound interest.
Simple Interest Simple interest is, well, pretty simple! That’s because it’s calculated on the original principal amount.
Say you borrow $100 from your friend John at a 5% annual rate of simple interest for a term of 3 years. Here’s how the interest would be calculated for the loan:
| Loan year | Principal amount (dollars) | APR (percent) | Annual interest earned (dollars) | Balance due (dollars) |
| 1 | $100 | 5% | $5 | $105 |
| 2 | 100 | 5 | 5 | 110 |
| 3 | 100 | 5 | 5 | 115 |
Notice that the 5% APR is always calculated on the original principal amount of $100. At the end of the third year you have to pay $100 plus $15 in interest. In other words, your $100 loan cost a total of $115.
Compound Interest Compound interest is more complex because it’s calculated on the original principal amount and also on the accumulated interest of a deposit or loan. Compound interest allows you to earn interest on a growing principal balance, which allows you to accumulate interest at a much faster rate. Interest can be compounded on any period of time, such as daily, monthly, semiannually, or annually.
Say you get the same loan of $100 for 3 years from your friend John, but this time he charges you 5% interest that compounds annually. Here’s how the interest would be calculated:
| Loan year | Principal amount (dollars) | APR (percent) | Annual interest earned (dollars) | Balance due (dollars) |
| 1 | $100 | 5% | $5 | $105 |
| 2 | 105 | 5 | 5.25 | 110.25 |
| 3 | 110.25 | 5 | 5.51 | 115.76 |
Notice that the 5% APR is calculated on an increasing principal balance. At the end of the third year you’d owe the original amount of $100 plus interest of $15.76. Your $100 loan cost $115.76 with annual compounding interest. This table also shows you how much you’d earn if you deposited $100 in the bank and earned a 5% annual return that compounds annually.
FLH-
| Loan year | Principal amount (dollars) | Semiannual percentage rate (percent) | Annual interest earned (dollars) | Balance due (dollars) |
| 1 (January) | $100 | 2.5% | $2.50 | $102.50 |
| 1 (July) | 102.50 | 2.5 | 2.56 | 105.06 |
| 2 (January) | 105.06 | 2.5 | 2.63 | 107.69 |
| 2 (July) | 107.69 | 2.5 | 2.69 | 110.38 |
| 3 (January) | 110.38 | 2.5 | 2.76 | 113.14 |
| 3 (July) | 113.14 | 2.5 | 2.83 | 115.97 |
Let’s see how much you’d pay if John charged you 5% compounded semiannually, or every 6 months, shown in Table 1, above.
At the end of the third year you’d owe the original loan amount of $100 plus $15.97 of interest. With semiannual compounding your $100 loan would cost $115.97. Likewise, this table shows how much you could earn from $100 in savings if compounded semi-
Remember that the more frequent the compounding, the faster the interest grows.
Annual percentage yield (APY) is the amount of interest you’ll earn on an annual basis that includes the effect of compounding. APY is expressed as a percentage and will be higher the more often your money compounds.