How to Use Desmos for Compound Interest Calculations

Using Desmos, a powerful online graphing calculator, can simplify how you visualize and calculate compound interest. Let’s break down the steps using an example where Emmett deposits $90 at a 5% annual interest rate, compounded yearly, and we want to find out how much he will have after 2 years.

**Step 1: Understand the Compound Interest Formula**
The formula for compound interest is:
A = P(1 + r)^t
Where:
- A is the amount of money accumulated after n years, including interest.
- P is the principal amount (the initial deposit or investment).
- r is the annual interest rate (decimal).
- t is the time the money is invested or borrowed for, in years.

In our case:
- P = $90
- r = 0.05 (which is 5% as a decimal)
- t = 2
So we can rewrite the formula specifically for this scenario:
A = 90(1 + 0.05)^t
This simplifies to:
A = 90(1.05)^t

**Step 2: Input the Formula into Desmos**
To use Desmos effectively, follow these steps:
1. Open the Desmos graphing calculator in your web browser.
2. In the first line of the input area, type:
`A(t) = 90(1.05)^t`
- Remember to use parentheses around `1.05` and the `^` key for the exponent.
3. By entering this, you have defined a function A(t) that calculates the amount of money Emmett will have after t years.

**Step 3: Calculate the Amount After 2 Years**
There are a couple of ways to find the value after 2 years in Desmos:

**Option A – Using a Table**
1. Click the gear icon next to your expression.
2. Select **Add Table**.
3. In the first column of the table, input `t` values (0, 1, 2).
4. In the second column, type `A(t)` to see the corresponding amounts.
- This table will automatically calculate the values for you.

**Option B – Direct Evaluation**
1. In the next line of Desmos, type:
`A(2)`
2. Press Enter, and Desmos will provide you with the amount Emmett will have after 2 years.

This method shows how technology can aid in understanding financial concepts like compound interest. Visualizing the growth of money over time helps students grasp these important principles, potentially applying them to real-life financial decisions such as savings and investments. By using Desmos, students can easily experiment with different principal amounts, rates, and time periods to see how they affect overall savings. This hands-on approach encourages deeper learning and engagement in math topics related to finance and beyond.