Comparing Interest Outcomes
Introduction
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.
Two Paths From the Same Starting Point
Building a Side-by-Side Comparison
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:
| Year | Simple Balance | Compound Balance |
|---|---|---|
| Start | $1,000.00 | $1,000.00 |
| 1 | $1,100.00 | $1,100.00 |
| 2 | $1,200.00 | $1,210.00 |
| 3 | $1,300.00 | $1,331.00 |
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.
Where the Extra Dollars Come From
