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.
From Identifying to Computing
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.
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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:
Interest=Principal×Rate
Let's label these with shorter names so the math stays tidy:
I=P×r
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.
I=P×r=2,000×0.03=60
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.
Knowing the interest amount is useful, but we usually also want to know the total amount sitting in the account (or owed on a loan) once that interest is included. This total is called the ending balance, and it is simply the original principal plus the interest:
Ending Balance=P+I
Continuing our savings example, the deposit was $2,000 and the interest was $60, so:
Ending Balance=2,000+60=2,060
After one year, the account holds $2,060. We can also express this in a single combined formula:
Ending Balance=P+(P×r)=P×(1+r)
Both versions give the same answer. The combined form, P×(1+r), is a handy shortcut because it wraps everything into one multiplication: 2,000×1.03=2,060.
The same formula works when money is borrowed instead of saved. Imagine you take out a short-term personal loan of $5,000 at an annual simple interest rate of 8%. After one year, how much interest do you owe, and what is the total amount due?
Step 1 — Convert the rate:8%=0.08.
Step 2 — Calculate the interest:
I=5,000×0.08=400
Step 3 — Find the ending balance:
Ending Balance=5,000+400=5,400
You would owe $400 in interest and a total of $5,400. Whether the context is a savings deposit or a loan, the math is the same. The only difference is perspective: interest is money earned when you save and money owed when you borrow.
Here are a few tips to keep your calculations accurate as you practice:
Always convert the percent to a decimal before multiplying. Writing 5,000×8 instead of 5,000×0.08 gives a result that is 100 times too large.
Match the time unit to the rate. If the rate is annual, one period means one year. We are focusing on single-period calculations in this lesson, so this match is straightforward for now.
Round money to two decimal places when a result has more than two. For instance, if I=1,250×0.037=46.25, the answer is $46.25. If the result were 46.257, we would round to $46.26.
The table below summarizes every step in one place so you can use it as a quick reference:
Step
What to Do
Example (P = $1,250, r = 3.7%)
Convert rate
Percent → Decimal
3.7% → 0.037
Find interest
I = P × r
1,250 × 0.037 = 46.25
Find balance
P + I
1,250 + 46.25 = 1,296.25
In this lesson, we learned that calculating simple interest for one period comes down to one multiplication: I=P×r. We then find the ending balance by adding that interest back to the principal: Ending Balance=P+I. These two small steps turn the financial components we identified in the previous lesson into real dollar amounts.
Up next, you will work through a series of hands-on tasks that walk you through each step, from converting rates to computing ending balances. This is your chance to build confidence and make the one-period calculation second nature before we extend the idea to multiple periods in the next lesson.
