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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.
This is a 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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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.
$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.
Compound + Contribute 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?
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 Jared 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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