Mastering Continuous Compound Interest Calculation on the TI-84- A Step-by-Step Guide

How to Calculate Continuous Compound Interest on TI-84

Calculating continuous compound interest can be a complex task, especially if you’re not familiar with the mathematical formula involved. However, with the help of a graphing calculator like the TI-84, you can easily compute this type of interest. In this article, we will guide you through the steps to calculate continuous compound interest on a TI-84.

Understanding Continuous Compound Interest

Before we dive into the calculation process, let’s first understand what continuous compound interest is. Continuous compound interest is a type of interest that accumulates over time without being compounded at a specific interval. It is calculated using the formula:

A = P e^(rt)

Where:
A = the future value of the investment/loan
P = the principal amount (initial investment/loan amount)
e = the base of the natural logarithm (approximately 2.71828)
r = the annual interest rate (as a decimal)
t = the time the money is invested or borrowed for, in years

Steps to Calculate Continuous Compound Interest on TI-84

1. Turn on your TI-84 calculator and press the “MODE” button.
2. Scroll down to “2nd” and press the “MODE” button again to select “2nd” mode.
3. Press the “Math” button and scroll down to “e^x” (exponential function).
4. Enter the principal amount (P) by pressing the “Enter” key.
5. Press the “Math” button again and scroll down to “x” (multiply function).
6. Enter the annual interest rate (r) as a decimal and press the “Enter” key.
7. Press the “Math” button once more and scroll down to “x” (multiply function).
8. Enter the time period (t) in years and press the “Enter” key.
9. Press the “Math” button one last time and scroll down to “e^x” (exponential function).
10. The result displayed on the screen will be the future value (A) of the investment/loan with continuous compound interest.

Example

Suppose you want to calculate the future value of an investment with a principal amount of $10,000, an annual interest rate of 5% (0.05 as a decimal), and a time period of 10 years. Here’s how you would do it on your TI-84:

1. Turn on the calculator and press “MODE.”
2. Scroll down to “2nd” and press “MODE” again to select “2nd” mode.
3. Press “Math” and select “e^x.”
4. Enter “10000” as the principal amount (P).
5. Press “Math” again and select “x.”
6. Enter “0.05” as the annual interest rate (r).
7. Press “Math” again and select “x.”
8. Enter “10” as the time period (t).
9. Press “Math” one last time and select “e^x.”
10. The result displayed will be the future value (A) of the investment with continuous compound interest, which in this case is approximately $16,435.14.

By following these steps, you can easily calculate continuous compound interest on your TI-84 calculator. This knowledge can be particularly useful when making financial decisions or analyzing investment opportunities.