Comparing Interest Outcomes

Welcome to the fifth and final lesson in Interest, Savings, and Borrowing! Over the course of this unit, we have built a solid toolkit: reading interest terms, computing single-period interest, calculating simple interest across multiple periods, and most recently, working through compound interest year by year. Each lesson added a new layer, and now it is time to bring both methods together for a head-to-head comparison.

In this lesson, we will place simple and compound interest side by side using the same principal, rate, and time. We will calculate the ending balance for each method, measure the dollar difference between them, and explore why compounding produces larger growth the longer we wait.

Simple and compound interest share the same three inputs — principal ($P$), rate ($r$), and time ($t$ periods) — yet they handle the base differently. Simple interest sticks with the original principal every period, while compound interest folds each period's earned interest into the balance so the base grows.

When there is only one period, both methods give the exact same result. The real question is: how much more does compounding earn when we stretch the time to several years or beyond? The rest of this lesson answers that question with concrete numbers.

Let's line up both methods with a familiar set of numbers: $1,000 at 10% annual interest for 3 years.

With simple interest, each year adds the same flat amount: $1,000 × 0.10 = $100. With compound interest, each year's interest is calculated on the updated balance, as we practiced in the previous lesson. Here is how the two paths compare:

At the end of Year 1, both methods produce exactly $1,100. By Year 3, compound interest has reached $1,331 while simple interest sits at $1,300. The compound method earned $31 more, entirely from interest accumulating on previously earned interest.