I sometimes wonder what people from the Dark Ages think about our flashy culture and unrestrained society today. Not to mention our smartphones, computers and auto flushing indoor toilets. That would likely blow their brains out from shock to see us now.
We’ve come a very long way. The awe that they would experience is something sort of like when I found out about the power of saving and investing – in combination with the miracle that is compounding. This shizzle is witchcraft!
The real headline is “How to Calculate Compound Interest with Regular Contributions” but yeah…it sounded boring.
Table of Contents
Mathethical Witchcraft
This is perhaps an example that might sound familiar but answer the scenario below honestly…
Would you rather have a million dollars right now or a penny that will double itself for a month?
If you asked me this when I was a teenager, I would have taken the cold million bucks, called you crazy, and ran off with the million. But I guess that’s why people think teenagers are stupid…
That would have been a gigantic mistake on my part because that penny doubled for an entire month comes out to be over 5 million dollars on the 30th day. It would be over $10 million if you landed on the 31st of the month!
Seriously, it’s money witchcraft!
And perhaps I’m slow but I’ve never looked into the magic formula used to compute compounding interest until I was already blogging. There are calculators online to do it but, I don’t know, from the raw, manipulate form, it feels more real.
Disclaimer, I am horrible at math. Well, not horrible-horrible, but more like average-horrible for an Asian, that was actually born in Asia.
This math-y post will be super easy. Sometimes a personal finance blogger writes a math post and my eyes glaze over 60% way through. This will not be such a post. I’ll make it so easy, an idiot can understand it. As proven by this idiot already.
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Compound Interest Formula
Principle * (1 + Rate) ^ Time = Amount
The math is actually easy enough. It is your starting principal multiplied by the rate of your market return and power the duration (years you will remain invested).
From there it’s just as simple as plugging in numbers and letting your calculator do the work for you. Better yet plug the numbers in this formula into Google Search and it will automatically spit out the answer without even having to press enter.
Our Example:
$1,000,000 * (1 + 0.07)^10 = $1,967,151.36
Let’s say our starting balance is a cool million dollar. And the market returned at 7% average for the next 10 years as if you have everything thrown into the comprehensive Total US Stock Fund. By the end of the decade, you would have gotten double your money by doing literally nothing!
Rule of 72
But that’s not the only delightful magical thing to compounding. The rule of 72 is a quick mental shortcut. Whatever the interest rate is, divide it by 72 and that number will be how long it will take for the original number to double. To double money in 10 years, get an interest rate of 72/10 = 7.2%.
The rule of 72 can also be used in reverse to count inflation. If inflation rates pace at 2%, your money will lose half its value in 24 years.
Flatlinesober voice now: please math responsibly and remember US inflation paces at around 2%-3% per year.
Compounding Interest + Contribution Formula
From a more practical point of view, make room for continuing contributions. Do you imagine really not adding to that original principle for 10 years? What is the formula for compound interest with regular contributions?
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The only thing you would need to know is how much your annual savings is. Most often it is a number that’s more or less constant if you keep a nice budget. Take all of your estimated annual savings (including retirement) and plug it into this formula:
This formula is ugly, trust me, as a non-math person I was like…ew. But if you break it down it really is just plugging in the numbers and letting the formula do your stuff. I don’t know who came up with it but it checks out.
(*Math corrected :))
Principle * (1 + Rate) ^ Time
+
Annual Savings * ((1 + Rate) ^ Time – 1) ÷ Rate
= Amount Total
You know what’s funny? I had to get Hubby to double-check the math for me and he said that it was easy and that it wouldn’t make a very good post. But see he’s a total nerd. He may have known this but I sure didn’t! I’m going to bet the general public haven’t either. Because once again, that formula is UGLY. That’s formula is so ugly, it doesn’t even have a mama.
Could that be why the US personal savings rate in December of 2017 was a disgustingly low…2.7%?!? Argh.
Back to Our Example:
The 150 smacks came from our family’s annual savings because that’s our projected mad-dash saving estimate for the next 10 years. Saving and investing is the main way to wealth.
$1,000,000 * (1 + 0.07)^10
+
$150,000 * ((1 + 0.07) ^ 10 -1) ÷ 0.07
Amount Total = $4,039,618.55
Shiny! At the end of the 10th year, it looks like we will have $4 million dollars invested!
So far, our plan stops at 10 years. Beyond that really depends on what life might launch at us. The contributions formula is what makes the compounding and extreme savings really bring it home. We quadrupled the original principle in the time for a child to go from crib to finishing 5th grade! So neat!
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I wasn’t familiar with the Rule of 72, always excited to learn something new!
So what will you do when you reach that shiny $4 million?
Get myself some math lessons HAHA 😉
I didn’t know about the 72 rule either. This is super helpful. And I feel the same way about mathy posts hehe. 😉
This is a very important concept for investing. The average market return including dividends is actually around 10% annually. Invest as soon as you have some disposable income and your returns will grow very quickly.
Ok, question from a total math dummy here. What is the roof symbol? Is it “to the tenth power?” I love these formulas because I have some complicated way I have been figuring out our future returns that is not this simple!!!
Yes it’s to the x power. I’ve called it “carrot” for like…8 years and then writing this out…I couldn’t remember the official name of it. I’m dumbbbbb.
2.7% savings rate is pitiful. But I don’t blame the math or the ugly formulas.
It’s just people feeling good. The economy has been on an absolute TEAR the past few years. Jobs are strong, stocks are going up, people feel on top of the world. And when they do, they loosen the purse strings a bit and spend, because they don’t see that eventually this too shall pass. It may not be this year or next, but eventually something will likely happen that knocks folks down a few pegs and they’ll wish they’d saved more. We saw it in the early 2000’s with the dotcom bubble, we saw it in 08-09, we’ll likely see it again.
Keep on socking away that money and you’ll be golden 🙂
Dave you are so no nonsense. I thought it was pitifully low too but I chalked it up to December/Xmas. Which doesn’t even make sense, it’s overall around 3% which is just as ridiculously low!
Let’s help Make Savings Rates Great Again!
I like the Rule of 72 , makes it so much easier.
4 Million in 10 years! And you will still be so young:) That’s awesome. Take the money and travel the world.
I will be…37? I think that’s…old..lololol. That’s middle aged ?? *hides*
Lol, this is how I feel when I post something that involves math/derivatives/etc. I created such an awesome post (at least I thought so) then wondered why no one read it. FireBear: A ton of people do not know what a put is, the statistics of the stock market, sequence of returns risk, how to do math in their head, etc. You need to explain it better and also write more posts on the basics so that one day people will read those other posts. Think of your audience. ”
This is super well explained and cute :D.
I hope this made sense… Which post of yours are you talking about?!
Hi! I think there might be a typo. The equations you posted for calculating the interest with annual contributions are all different:
-Pinterest graphic: Annual Savings * (1 + Rate) ^ Time – 1 ÷ Rate
-Explanation in text: Annual Savings * (1 + Rate) ^ Time ÷ Rate
-Google screenshot: $150,000 * ((1 + 0.07) ^ 10 – 1) ÷ 0.07 <– this is the correct one
-Explanation in text of Google screenshot: $150,000 * (1 + 0.07) ^ 10 ÷ 0.07
Thanks!
Humbug!!! Oh I missed the parentheses. Thanks for the correction!! ? I warned everyone about the math!!
Yep, and the “-1”. But all looks good now 🙂
Well done, Lily. Math isn’t that hard!! ?
In all seriousness, the simplicity sometimes scares people away I think.
“Oh that’s too easy. It can’t be right.”
Way to help get the message out there – save, save, save!! ?
I had a typo…yes it is super hard! ?
Lily, why do you have to make my head hurt with so many maths??? I’m an English major! JK. 4 mill after ten years is no joke! I’ve begun enjoying the benefits of compounding lately, and I can confirm it’s magical.
If you hit the first $100k then it’s smooth sailings from there! That’s what I found hehe.
Great post! I love the Rule of 72. I do not see myself hitting 4 million, but I really do not feel I will need that much. We live in a low cost of living area. Anyway, I loved the post and feel people could benefit from it.
Thankies 🙂
Hey Lily! One correction for your post, it should be “to the power of the duration” in your first equation instead of “square rooting the duration”. Trust me, I’m an engineer!
Omg and I knew that too. Darn midnight math; Thank you!! :3
Nice job Lily – you will have some healthy investments in 10 years . Makes me want to hurry up and have DINC 😀
Wait….C as in cat? or Children?!
Oooh now this is interesting and new for me! Who would’ve thought that there would be some kind of formula for this?! I’m terrible at math, English was my strongest subject because I was such a book room, but I’ll try this out lol.
I know right haha!
That’s called the Future Value formula. Compounding rocks!
Savers FTW! Can’t wait for your Jan expense report! Mine is up tonight!
There’s an actual name for it?!!?! Haha we do have a good report coming up for Jan 🙂
Lol I can’t believe you used Google to do the calculation, I didn’t realize you can do that.
Yea, once you understand the math, you gotta take advantage of the power of compound interest!
Mathematical Witchcraft aka Mathamagic, performed by Mathematical Witches and Mathemagicians.
The compound interest formula is so simple, yet compound interest is so powerful.
I remember learning about the Rule of 72 when I worked at a financial literacy org!!! So crazy.
I love the penny example Lily. Had to double check your math just to make sure you weren’t pulling my leg. I for one am a firm believe in investing early. Too many young kids are to focused on buying a new fancy car or traveling the world after they graduate from college, and put off saving until some time later down the road. I’d like to consider myself somewhat smart, as I starting investing in my companies 401K in my first job as a result of some mentoring from my first manager. That decision has paid dividends (pun intended) for me, as I have a nice nest egg built up for retirement.
BTW – first time reader of your blog, and I like all the various tips and articles you provide. I’ll be back.
Thanks for drilling it down to a level that I can understand. I get the whole penny thing, but the rest is a new (and manageable) way to view my finances.