Understanding Compound Interest: The Eighth Wonder of the World — Financial Guide

What is Compound Interest?

Compound interest is the interest you earn on interest. Unlike simple interest, which only pays interest on your original principal deposit, compounding adds earned interest back to your balance, meaning you earn interest on a larger amount in the next period.

The Compound Interest Formula

Discrete compounding growth is calculated as:

A = P \left(1 + \frac{r}{n}\right)^{nt}

Where:

**A** = the future value of the investment, including interest

**P** = the principal investment amount

**r** = the annual interest rate (as a decimal)

**n** = the number of times interest compounds per year (e.g. 12 for monthly)

**t** = the number of years the money is invested

The Power of Time: An Example

Consider two investors, Sarah and Michael, both earning an 8% annual return:

**Sarah** starts investing **$200/month** at age 25. By age 65 (40 years), she has contributed $96,000. Her portfolio value is **$610,000**.

**Michael** waits until age 35 to start. He invests **$400/month** (double Sarah's contribution) for 30 years. He contributes $144,000. By age 65, his portfolio is worth **$580,000**.

Even though Michael invested 50% more principal capital, Sarah ended up with more wealth because her money had an extra 10 years to compound. This highlights the most critical rule of investing: Start as early as possible.