Interest rates seem to be everywhere. Your bank charges interest on your credit card and your mortgage. Your savings accounts pay you interest. You can easily get lost in the blizzard of percentages, APRs and dollar amounts. Now, this might surprise you: All of those interest rates and figures are based on some very simple math used to calculate periodic interest over time.
What is Periodic Interest?
Periodic interest is based on simple interest. Simple interest is the percentage of interest savings accounts would earn or that lenders would charge if interest were calculated once per year. For example, a $100 savings account balance with a 3 percent simple interest rate figured only at the end of a year would earn exactly $3.
In practice, most interest is calculated more often. Periodic interest is the amount of interest earned over a stated time interval such as a day, month or quarter. Suppose interest on the 3 percent savings account is figured monthly. The periodic interest rate for one month is 3 percent divided by 12 one-month periods. The periodic interest rate is 0.25 percent and the amount of periodic interest earned on $100 equals 25 cents.
Compounding Interest over Time
Calculating periodic interest over time is important because it involves compounding. Let’s suppose that the 25 cents your $100 earns in one month at 3 percent simple interest is added to the account balance. You now have a balance of $100.25. Over the next one-month period, you have a little bit more in your account, so you will earn a bit more interest, which is again added to your balance.
Essentially, you earn interest on your interest. Each time this process -- called compounding -- is repeated, your balance grows, so the amount of interest you earn increases.
Using the example above, if you have $100 to start and then $100.25 at the end of month one, in month two, you'll earn 0.25 percent of $100.25, and at the end of month two, you'll have $100.50. In month three, you'll earn 0.25 percent on $100.50, and at the end of month three, you'll have $100.75, and so on. When you start with a larger balance, compounding can really add up.
Mathematical Formula for Calculating Periodic Interest
The process of figuring periodic interest over time, or compound interest, can be turned into a formula you can enter into a spreadsheet or programmable calculator. The formula is written as Y = P(1 + R/N)^NT. If you are calculating for a single year, leave off the T, which stands for the number of years. P is the amount of the loan or initial deposit. R is the simple interest rate and N is the number of times interest is figured each year. Y is the ending balance for the time for which you are calculating interest. The “^” symbol means the symbol that follows -- either N or NT -- is an exponent. This formula yields the ending balance, so to find the amount of interest earned, you must subtract the initial balance, or P, from the ending balance Y.
Interest Calculations and Balance Changes
Typically, your principal balance for most types of accounts changes as you deposit and withdraw money for a savings account or make payments on a loan. Banks and other financial institutions have slightly different methods of figuring interest in these situations, but they are all variations on the same thing. The bank starts with your previous balance, calculates interest and adds or subtracts amounts like payments, deposits and withdrawals each time interest is calculated to arrive at a new balance.