Compound Interest Explained

0. Prerequisites

• Simple Compound

1. Preface

If you understand how compound interest works and how to use it properly, it can be a powerful tool for growing your money over time.

Let's explore compound interest in more detail and see how we can apply it to our personal finances!

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2. What Is Compound Interest?

The term compound interest is used to describe the way in which interest gets added to your original investment over time, so you earn interest not only on the principal but also on all of the accrued interest.

This can be represented by the following formula:

Variable	Definition	Example
$\large {\textcolor{#61A0AF}{A}}$	final amount	$1643.62
$\large {\textcolor{#F5D491}{P}}$	initial principal value	$1000
$\large {\textcolor{#96C9DC}{r}}$	interest rate	0.05
$\large {\textcolor{#F9B9B7}{n}}$	number of times interest applied per time period	4
$\large {\textcolor{#F06C9B}{t}}$	number of time periods elapsed	10

If we replace the variables with the example numbers...

For example...

• if $\large {\textcolor{#F9B9B7}{n}}$ = 1 and $\large {\textcolor{#F06C9B}{t}}$ = 5, compounding would happen 1 time (annually) a year for 10 years.
• if $\large {\textcolor{#F9B9B7}{n}}$ = 4 and $\large {\textcolor{#F06C9B}{t}}$ = 10, compounding would happen 4 times (quarterly) a year for 10 years.
• if $\large {\textcolor{#F9B9B7}{n}}$ = 12 and $\large {\textcolor{#F06C9B}{t}}$ = 8, compounding would happen 12 times (monthly) a year for 8 years.

You'll get to play around with these numbers later in the article!

In other words, the interest you earn each year gets added to your original investment. And the following year's interest is then calculated on that new amount. You can see how quickly, over time, compound interest will grow your money into something much larger than it was initially!

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3. What's an Example?

Here's an example to help illustrate how compound interest works. Let's say you invest $1,000 at a 5% fixed interest rate. In the second year, you will earn $50 in interest, and in the third year, you will earn $51.25 in interest because 5% of the original investment plus the previous two years' interest:

	Principal	Interest	Final
Year 1	$1,000.00	$50.00	$1,050.00
Year 2	$1,050.00	$52.50	$1,102.50
Year 3	$1,102.50	$55.13	$1,157.63
...	...	...	...
Year 28	$3,733.46	$186.67	$3,920.13
Year 29	$3,920.13	$196.01	$4,116.14
Year 30	$4,116.14	$205.81	$4,321.94

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4. Why Should You Care About It?

The main reason to care about compound interest is that it's a powerful way to grow your money over time, especially in long-term investments like retirement savings accounts or investment funds.

Basically, it can make you really rich! 🤑

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5.    📊   Compound Interest vs. Simple Interest

Both simple interest and compound interest are used to calculate the amount of money that you will be paid for an investment.

However, the main difference between simple and compound interest is how they factor in previous years' earnings.

Simple ー earns a fixed percentage of the principal each year; no accumulated interest is added to the principle.

Compound ー earns a fixed percentage of the principal and previously earned interest each year; any interest earned is added to the principle.

Using the table above and comparing it to simple interest, here's an example!

5.1. Compound Interest Example

	Principal	Interest	Final
Year 1	$1,000.00	$50.00	$1,050.00
Year 2	$1,050.00	$52.50	$1,102.50
Year 3	$1,102.50	$55.13	$1,157.63
...	...	...	...
Year 28	$3,733.46	$186.67	$3,920.13
Year 29	$3,920.13	$196.01	$4,116.14
Year 30	$4,116.14	$205.81	$4,321.94

5.2. Simple Interest Example

	Principal	Interest	Final
Year 1	$1,000	$50	$1,050
Year 2	$1,050	$50	$1,100
Year 3	$1,100	$50	$1,150
...	...	...	...
Year 28	$2,350	$50	$2,400
Year 29	$2,400	$50	$2,450
Year 30	$2,450	$50	$2,500

You can see in the graph below that after 30 years of accruing interest, and with no additional money, your final compound interest value will be roughly double the final simple interest value and more than quadruple your principal!

You can visualize the differences below using the interactive chart. Feel free to explore different values to see the effects!

The main takeaway is that compound interest means you will earn more money in less time than you would with simple interest because it factors in all of the previously earned interest.

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6.   📊   The Effects of Compound Interest Payout Frequency

Most interest payments for your savings account are paid monthly, while dividends can vary from monthly to quarterly.

This time, try tweaking the frequency parameter to see the effects of payout frequency on your final value.

In short, the more frequently the payments are, the more your money will compound.

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7. Compounding Interest Working For or Against You

As we previously discussed, compound interest can work against you if you are the one borrowing money. And you want to avoid that.

But, on the flip side, when you invest or lend money, you will be the beneficiary of compounding.

Compound interest is a powerful tool, but don't let it work against you!

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🥳   Final Thoughts

Compound interest is a powerful personal finance tool that can work for or against you, depending on how it's utilized. It can grow your money much more quickly over time, so it's definitely worth taking the time to understand how it works.