Multi Period Simple Interest

Welcome back to Interest, Savings, and Borrowing! You are now on Lesson 3 of 5, which means you are more than halfway through this course. In the first two lessons, we learned how to read the key components of a financial statement and then how to calculate interest for a single period. Those skills gave us the building blocks; now we are ready to stack them up.

In this lesson, we will extend the one-period calculation to multiple periods. We will see how simple interest accumulates over two, three, or more years, and we will learn how to find both the total interest and the ending balance. The central idea is surprisingly straightforward: every single period uses the original principal as its base.

Before we jump into the math, let's build some intuition. Imagine you lend a friend $1,000 and agree on 10% simple interest per year. After one year, your friend owes $100 in interest. What about year two?

With simple interest, the answer is another $100 — not $110. The interest charge is always calculated on the original $1,000, regardless of how much interest has already piled up. The $100 earned in year one does not become part of the base for year two.

This "same base every time" rule is the defining feature of simple interest, and it is what makes the multi-period calculation so predictable. Each year adds the exact same dollar amount of interest because the base never grows.

The one-period interest formula from the previous lesson is $I = P \times r$. For simple interest over multiple periods, we repeat that same calculation for each period, always plugging in the original principal $P$.

Let's trace through a concrete example. Suppose we deposit $4,000 into an account that pays 5% annual simple interest and we leave it there for 3 years.

Notice how the "Base Used" column never changes. Each year produces the same $200 because the base is always the original $4,000. After 3 years, the total interest is $600, and the ending balance is $4,000 + $600 = $4,600.