# A Simple Guide to Compound Interest

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Compound interest is way easier to understand than you think!

In this article, we'll break down exactly how compound interest works with simple, step-by-step examples.

So take a deep breath, grab a snack to munch on, and let's figure out this compound interest thing together. You got this!

## What is Compound Interest Anyway?

Compound interest is when you earn interest on both your original principal (the amount you first invested or saved) and the interest that principal has earned over time.

For example, say you invest \$1,000 at a 5% annual interest rate. After the first year, you'll earn 5% interest on your \$1,000, which is \$50.

Now you have \$1,050 total in your account.

The next year, you'll earn 5% interest on the entire \$1,050 balance. That interest earned will be added back to your total balance, and then next year you'll earn interest on an even larger balance, and so on.

This is different from simple interest, where interest is only calculated on the original principal amount - so you'd keep earning \$50 each year on your original \$1,000 investment at a 5% interest rate with simple interest.

The cool thing about compound interest is that your money starts to snowball quickly, earning you more and more interest every year assuming you are saving rather than borrowing. But we'll see some examples of that in action soon enough!

First, let's recap:

• Compound interest = earning interest on your interest
• Simple interest = earning interest on only the original principal amount

Got it? Okay, we'll move on!

## How Does Compound Interest Work?

There are two main factors that impact how quickly your money grows with compound interest:

1. The compounding period
2. The frequency of compounding

Let's break down what each of these mean...

### Compounding Periods

The compounding period is how often the interest is calculated and added to your total balance.

For example:

• If interest is compounded annually, your interest gets calculated and added to your balance once per year.
• If it's compounded monthly, interest gets added every month.

Shorter compounding periods are better because interest gets added to your balance more frequently. More on that next!

### Frequency of Compounding

This is how many times per year interest gets compounded (added to your balance).

For example:

• If interest is compounded annually, the frequency is 1 time per year.
• If it's compounded quarterly, the frequency is 4 times per year.
• For monthly compounding, frequency is 12 times per year.

Higher frequency = more interest for you!

The takeaway is that more frequent compounding periods and a higher frequency of compounding means your interest will compound faster. Your money snowball will pick up speed more quickly!

Okay, let's see some real examples of how this works...

## Compound Interest In Action: Examples

Enough definitions - time for the fun part! Let's walk through some examples together to see compound interest in action.

### Example 1: Annual Compounding

Say you invest \$1,000 at a 5% annual interest rate, with interest compounded annually.

• Year 1:
• You earn 5% of \$1,000, which is \$50.
• Your total balance is now \$1,000 + \$50 = \$1,050
• Year 2:
• You earn 5% of \$1,050, which is \$52.50
• Your total balance is now \$1,050 + \$52.50 = \$1,102.50
• Year 3:
• You earn 5% of \$1,102.50, which is \$55.13
• Your total balance is now \$1,102.50 + \$55.13 = \$1,157.63

And so on...

See how your interest compounds each year?

### Example 2: Quarterly Compounding

Now let's look at quarterly compounding with the same 5% annual rate. That means compounded 4 times per year.

• Quarter 1:
• You earn 5%/4 = 1.25% of \$1,000 = \$12.50
• Your balance is now \$1,000 + \$12.50 = \$1,012.50
• Quarter 2:
• You earn 1.25% of \$1,012.50 = \$12.66
• Your balance is now \$1,012.50 + \$12.66 = \$1,025.16
• Quarter 3:
• You earn 1.25% of \$1,025.16 = \$12.82
• Your balance is now \$1,025.16 + \$12.82 = \$1,037.98
• Quarter 4:
• You earn 1.25% of \$1,037.98 = \$12.97
• Your balance is now \$1,037.98 + \$12.97 = \$1,050.95

And repeat! See how your balance is higher than with annual compounding?

### Example 3: Monthly Compounding

Finally, let's look at monthly compounding. This will compound 12 times per year.

We'll calculate the monthly rate as 5%/12 = 0.41667%

• Month 1:
• You earn 0.41667% of \$1,000 = \$4.17
• Your balance is now \$1,000 + \$4.17 = \$1,004.17
• Month 2:
• You earn 0.41667% of \$1,004.17 = \$4.18
• Your balance is now \$1,004.17 + \$4.18 = \$1,008.35
• Month 3:
• You earn 0.41667% of \$1,008.35 = \$4.20
• Your balance is now \$1,008.35 + \$4.20 = \$1,012.55

And keep compounding 12 times per year.

See how monthly compounding earns you even more?

Okay, let's recap what we've learned so far in this section:

• More frequent compounding = more interest for you
• Compounding monthly is ideal to grow your money faster
• Even small amounts compound into bigger balances over time

Powerful stuff! Now let's talk about how to calculate compound interest...

## Calculating Compound Interest

Figuring out exactly how much your money will grow with compound interest involves a bit of arithmetic but as you saw it is relatively straight forward! Next we will walk through some ways to calculate it.

### Multiplication Method

The simplest way is to use basic multiplication which provides a good approximation. Here's the formula:

``````A = P(1 + (r/n))^(nt)
``````

where:

• A = Total amount after t years
• P = Original principal
• r = Annual interest rate (decimal)
• n = Number of compounding periods per year
• t = Number of years

Let's plug in some numbers as an example:

• P = \$1,000
• r = 0.05 (5% as decimal)
• n = 12 (monthly compounding)
• t = 5 years
``````A = \$1,000(1 + 0.05/12)^(12*5) = \$1,000(1.00417)^60 = \$1,000(1.27) = \$1,270
``````

After 5 years at 5% interest compounded monthly, you'll have \$1,270.

### Fixed Formula Method

Alternatively, you can use this formula:

``````A = P(1 + i)^n
``````

Where:

• A = Total amount after n years
• P = Original principal
• i = Annual interest rate as decimal
• n = Number of years

Plugging in the same example:

• P = \$1,000
• i = 0.05
• n = 5 years
``````A = \$1,000(1 + 0.05)^5 = \$1,000(1.05)^5 = \$1,276.28
``````

Nearly the same result!

For the spreadsheet nerds, you can use built-in formulas in Excel, Google Sheets, etc.

The `FV` function calculates future value with compound interest.

``````=FV(rate, nper, pmt, pv, type)
``````

Where:

• rate = Annual interest rate (decimal)
• nper = Number of years
• pmt = Periodic payment (if any)
• pv = Present value (initial principal)
• type = Payment timing (0 for end of period, 1 for beginning)

Again using our example:

``````=FV(0.05, 5, 0, 1000, 0)
``````

Gives the same \$1,276.28 result.

Okay, let's keep this money train rolling...

## Start Saving Early for Compounding Power

One of the coolest things about compound interest is that time is your best friend.

The longer you save and invest, the more time your money has to compound and grow. This is why financial experts always recommend starting retirement saving as early as possible.

Let's look at an example to see why:

Say you're 25 years old. You invest \$5,000 and contribute another \$5,000 each year for 10 years (\$50,000 total) into an account earning 8% annually.

After 10 years you'll have contributed \$50,000 and earned \$21,232 in interest. Nice!

Now, say you waited until age 35 to start investing. You contribute \$5,000 each year for 30 years, until age 65. That's \$150,000 contributed.

But at 8% interest over 30 years, you'd have only \$772,750. Less than the \$893,170 you would have if you started at 25!

The 10 extra years early on helped your interest compound much more over time. So start early to maximize compounding!

Okay, let's talk pros and cons...

## Pros and Cons of Compound Interest

As with most things in life, compound interest has both good and bad points. Let's look at the key pros and cons:

### Pros

• Your money can grow exponentially over time
• Rewards those who start saving/investing early
• Frequency of compounding boosts your earnings
• Available on many savings and investment products

### Cons

• Works against you if you're paying interest (loans, credit cards, etc)
• Requires a long time horizon to realize full benefits
• More frequent compounding periods can be confusing
• May incentivize overly risky investments to chase returns

The key is focusing on the pros and using compound interest thoughtfully for your long-term financial goals.

## Compound Interest Investment Options

Many different savings and investment products utilize the power of compound interest. Common options include:

• High-yield savings accounts
• Money market accounts
• Certificates of deposit (CDs)
• Bonds
• Index funds
• Mutual funds
• Stocks (through dividend reinvestment aka DRIP)
• Real estate investments

The right option depends on your goals, timeline, and risk tolerance. Do your research to find the best fit for you!

Now you're probably wondering...

## How Can I Tell If My Interest Compounds?

Good question! Here are some tips for figuring it out:

• Read the Terms & Conditions - This should spell out how interest is calculated
• Bank Products - Interest on savings/CDs usually compounds daily or monthly
• Loan Products - Interest typically compounds daily or monthly
• Investments - Compounding frequency varies. Read the prospectus or call the provider.

Bottom line - compound interest is typically the norm these days. But when in doubt, ask.

## Compound Interest: Key Takeaways

We've covered a lot of ground here! Let's recap the key takeaways:

• Compound interest means earning interest on your interest over time
• More frequent compounding periods and higher frequency is better
• Use the multiplication formula, fixed formula, or spreadsheet functions to calculate
• Start saving early to maximize compounding over decades
• Utilize the power of compounding by investing in vehicles like stocks, bonds, mutual funds, etc.

Congrats, you now know more about compound interest than most people walking around out there so use this knowledge to improve your future self's financial well being.

Hopefully this gave you a solid foundation for understanding and harnessing the incredible power of compound interest. Your future rich self thanks you.

Now go forth and start letting your money work for you.

Happy compounding.

## References

Here are some external references for those that want to learn more or find alternative explanations:

• Texas State Mathworks [Source]
• Investopedia's article on 'Dividend Reinvestment Plans (DRIPs): Compound Your Earnings' [Source]
• Google Sheet's Future Value (FV) function [Source]