Busting out a compounding interest formula

Compounding interest is actually pretty simple.

You just need to learn a bit of algebra and keep your brackets straight.

Simple compounding interest (monthly) just lets you do ONE single amount for the entire length of time.

Example: $5000 in 40 years at 5% interest

Complex compounding interest (monthly) lets you add a certain amount each time, periodically for the entire length of time.

Example: $5000 in 40 years at 5% interest, adding $5000 each year and compounding that as well.

Here’s a cute picture I whipped up with colours to help:
The only difference between Simple and Complex is highlighted in black bold type.

It’s the exact same as Simple, just with the additional brackets and additions to the formula at the end.

Here’s the legend:

$ = Amount Added

% = Rate converted into decimals

years = Total length of the compounding itself

12 = # of Compounding Periods in a year (12 stands for 12 months)*

*You can change it to 4 if you wanted to do compounding quarterly, because 3 months = 1 quarter

Or 1 if you wanted to compound yearly (1 = once a year = 1 period a year)

Let’s put it into action:

I want to see how much $5000 at a an interest rate of 5% compounding monthly would become in 40 years without any capital additions.

$ = $5000

% = 0.05
5% / 100 = 0.05, it needs to be a decimal

years = 40

So, that tells me that you’re going to get $36,792.09 at the end of 40 years at 5% with investing $5000.

Same example as above.

This time, I want to add $5000 each year at the end of each month (on January 31st for example).

So now, I want to see how much $5000 at a an interest rate of 5% compounding monthly would become in 40 years without an additional $5000/year addition , or an addition of $416.67 each month.

$ = $5000

% = 0.05
5% / 100 = 0.05, it needs to be a decimal

years = 40

You’re going to have $635,841.73 at the end of 40 years, adding $416.67 each month, compounding monthly for a total of $5000/year.

Geekify that! a.k.a. Additional Tweaking to the Complex Compounding Interest Formula

If you want to do additions at the START of each month to get a jump start (January 1st for example), you just multiply that total $635,841.73 by this formula at the end:

And you get:

[ $5000 * [ ( [ 1+(0.05/12) ] ^40*12 ) -1 ] * 12/0.05 ] % / 12 = $638,491.07

Or a slight difference of: $2649.34.

FB Notes:

Although if you think about it, you could count putting in money at the end of January, like Jan 31st to be the same as contributing at the start of the next month – Februrary 1st.

So there you go. Compounding interest, explained in a pretty picture.

RESOURCES:

Don’t want to deal with math formulas or figuring out best practices for compounding interest to be used for retirement?

I have the pre-made retirement sheet here that already has all the formulas worked in, and you just enter in the numbers and let the sheet calculate.

Related Posts:

• Compounding Interest, de-mystified
• 5 Finance Basics
• Re-Commit and Start on your money goals: Build a budget & analyze it
• Answer to Gail’s Polly Riddle
• Money Hacks

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