Hey there, fellow finance enthusiasts! Today, we’re diving into the magical world of compound interest. It’s often said that Albert Einstein called compound interest the “eighth wonder of the world”. Well, once you see how it works, you’ll know why! Figuring compound interest is key for understanding the power of long-term growth in their portfolios.

## Table of Contents

- What is Compound Interest?
- The Basics: How It Works
- Simple Interest vs. Compound Interest
- Figuring Compound Interest with More Examples
- Final Thoughts

## What is Compound Interest?

First things first – what exactly is compound interest? In simple terms, compound interest is the interest that accrues on both the principal amount of money invested and the accumulated interest itself. **It’s like a snowball rolling down a hill, picking up more snow (or money) as it goes. **The longer it rolls, the bigger it gets!

## The Basics: How It Works

The true power of compound interest reveals itself over time. The longer you let your money grow, the more exponential the growth becomes.

Let’s break it down with a simple example.

Imagine you invest $1,000 in a savings account that earns an annual interest rate of 5%. At the end of the first year, you’ll earn **$50** in interest, giving you a total of $1,050. Now, here’s where the magic happens: in the second year, you’ll earn interest on $1,050, not just your original $1,000. So, you’ll earn **$52.50** in interest the next year, giving you a total of $1,102.50. And so on… That is the snow ball!

## Simple Interest vs. Compound Interest

Simple interest is calculated only on the principal amount of a loan or deposit. Compound interest, on the other hand, is calculated on the principal and also on the accumulated interest over previous periods.

Before we dive into the calculations, here are some important things to know:

**“P” = Principal,**the original amount you put in.**“r” = interest rate**, the percentage at which your money grows,**expressed on a periodic basis**, e.g. 5%**per year**(it can be annually, semi-annually, quarterly, monthly, daily, etc.)**“t” = time**, using the same periodic basis of the interest rate.

### Calculating Simple Interest

- Calculated on the principal only.
**Formula**: P x r x t**Example**: $1,000 at 5% for 3 years = $1,000 x 0.05 x 3 = $150. You earn $150 in interest after 3 years.

### Calculating Compound Interest

- Calculated on the principal and also on accumulated interest.
**Formula**:

**Example**: $1,000 at 5% compounded annually for 3 years = $1,000 x (1 + 0.05)^3 – $1,000 ≈ $1,157.63 – $1,000. You earn $157.63 in interest after 3 years.

### Compound Interest in Excel

In Excel, we are going to use the Future Value formula (FV function). For more information about the FV function, you can check this link.

FV function has this syntax: *FV(rate,nper,pmt,[pv],[type])*

In order to know how much we earned, we calculate FV(5%,3,0,-1000,0) less “P”. For “pmt” we used 0 because we are not doing any payment each period. Oh, and for “[pv]” (present value), we need to use negative 1000!

## Figuring Compound Interest with More Examples

### Example 1: The Early Bird vs. The Late Bloomer

Meet Sarah and Mike. Sarah starts investing $100 a month at age 25 and stops contributing at age 35. Mike, on the other hand, starts investing $100 a month at age 35 and continues until he’s 65. Both earn an average annual return of 7%.

**Sarah**: Invests for 10 years ($12,000 total contribution), starting at age 25**Mike**: Invests for 30 years ($36,000 total contribution), starting at age 35

Who ends up with more money???

In the chart above, you’ll see that, even though Sarah invested for a much shorter period, she ends up with more money than Bob at age 65. This is the magic of figuring compound interest!

### Example 2: The Rule of 72

The Rule of 72 is a simple way to estimate how long it will take for your investment to double. Just divide 72 by your annual interest rate (this is an approximation!).

For example, if you have an interest rate of 8%, your money will double in about 9 years (72 ÷ 8 = 9).

Let’s visualize this with another chart.

As you can see from the chart, the higher the interest rate, the faster your money will double. This simple rule can be a handy tool for making quick estimates about your investments.

## Final Thoughts

Well, compound interest is the closest thing we have to a real-life money tree. In figuring the magic of compound interest, you discovered that even small contributions could make a big difference over time. It won’t make you rich overnight, but with patience and consistent investing, it can help you grow your wealth significantly over time.

If you found the topic of interest rates intriguing, you might want to read about how the Federal Reserve defines interest rates in this article: Understanding FED Interest Rate Decisions and How to Control Inflation: the Absolute Guide

So, next time you hear someone say they’re planting a money tree, you’ll know they’re probably talking about the magic of compound interest. Be consistent and let the eighth wonder of the world work its magic for you!

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