Computing Simple and Compound Interest – Discovering the Math of Finance and Investments

Interest is basically a percentage of some amount of money. It’s either the amount of money that you pay someone for the use of their money (such as for a loan or credit card) or the amount that you’re paid for the use of your money (such as with a savings account at a bank). The concept and practice of determining interest have been around since ancient Babylonian mathematicians created tables of numbers to determine how long it takes to double one’s money at a particular interest rate.

Understanding the Basics of Interest

Interest is money. And if you’re the borrower, you pay for the privilege of using the money. If you’re the lender, you’re paid the interest for your service of providing the money. The amount of money being borrowed or loaned is the principal or the initial amount. The rate of interest is the percentage of the principal that it costs to borrow the money (or that you’re paid for using the money). And the time is the period — in years, months, or days — that the transaction is taking place. Yes, I know, that’s a lot of terms to keep straight, but they’re all important when it comes to understanding how to compute interest.

Simply Delightful: Working with Simple Interest

Interest on money is the cost of buying things on credit. The fee you pay for the privilege of using someone else’s money is the interest, and the amount you get for lending someone money also interests. The simplest computation of interest is simple interest (now, isn’t that handy).

In this section, you see how simple interest works and how the different components, such as principal, rate, and time, interact with one another.

Stepping it up a notch: Computing it all with one formula

The formula for simple interest, I = Prt, gives you the amount of interest earned (or to be paid) given an amount of money, an interest rate, and a period of time. You want the amount of interest as a separate number when you’re figuring your expenses or taxes as a part of doing business. But, as I shown in the previous section, you frequently want the total amount of money available (or to be repaid) at the end of the time period.

Taking time into account with simple interest

Loans don’t have to be for whole years. You can borrow money for part of a year or for multiple years plus a fraction of a year. If the time period is half of a year or a quarter of a year or a certain number of months, the computation is pretty clear. You make a fraction of the time and use it in place of the t in I = Prt.

When you get into a number of days, however, the math can get pretty interesting. For instance, when dealing with a number of days, the discussion then involves ordinary or exact simple interests. I explain each of the scenarios in the following sections.

Surveying some special rules for simple interest

Simple interest is relatively easy to compute, but leave it to some folks to come up with shortcuts or rules to make the computation — or estimations of the computation — even easier. The rules I’m referring to are the Banker’s Rule, the 60-day 6% method, and the 90-day 4% method. I explain each in the following sections.

The Banker’s Rule

The Banker’s Rule is a common method of computing interest that combines ordinary interest and exact time. This definition seems a bit of a contradiction, but here’s how it works: The ordinary interest rule of using 360 days is applied, and the exact number of days is used. So instead of computing interest on three months and calling it 1 ⁄4 of a year, you determine exactly how many days are in those three months and divide by 360.

Last word

Computing the total amount of money that results from applying compound interest takes a jazzy formula. Besides involving multiplication, addition, and division, this formula also requires you to work with exponents. The hardest parts of working with the formula are entering the values correctly into the formula and performing the operations in the right order.

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