Calculating Single Period Interest

Welcome back to Interest, Savings, and Borrowing! You have completed the first lesson of this course, and you are now moving into Lesson 2 of 5. In the previous lesson, we learned how to read a financial statement by identifying its three key components: the principal, the rate, and the time period. Now it is time to put those pieces to work.

In this lesson, we will learn how to calculate the interest earned or owed over a single time period, and how to find the ending balance after that interest is applied. By the end, you will be able to take any principal and annual rate pair and confidently produce a dollar-and-cents result.

Think of the previous lesson as learning to read a recipe: we identified the ingredients (principal, rate, and time period) but did not actually cook anything. This lesson is where we turn on the stove.

The good news is that a one-period interest calculation uses skills we have already practiced. As you may recall from earlier courses, finding a percent of a number means converting the percent to a decimal and then multiplying. That same step is the heart of every simple interest calculation. If we can find 20% of a sale price, we can just as easily find 5% of a savings deposit.

When money sits in an account (or a loan goes unpaid) for exactly one period, the interest earned or owed equals the principal multiplied by the rate expressed as a decimal. Written as a formula:

Let's label these with shorter names so the math stays tidy:

Here, $P$ is the principal in dollars, $r$ is the annual rate written as a decimal (not a percent), and $I$ is the interest in dollars. For example, if the rate is 4%, we use $r = 0.04$. If it is 7.5%, we use $r = 0.075$.

That single multiplication is the entire calculation for one period. Let's see it in action.

Suppose you deposit $2,000 into a savings account that pays 3% annual interest. We want to know how much interest you earn after one year.

Step 1 — Convert the rate to a decimal. Move the decimal point two places to the left: $3\% = 0.03$.

Step 2 — Multiply the principal by the decimal rate.

After one year, the account earns $60 in interest. Notice how the process is identical to "finding a percent of a number," which we practiced in the very first course of this learning path.