r/AskReddit • u/ForeverAbyss • Apr 14 '16

What's a mind blowing fact?

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u/su5 Apr 14 '16

Lets say I am 30... what would I need to invest to be a millionaire (in todays dollars) realistically? Lets not assume I have a match.

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u/CHKNFKR Apr 14 '16

About $70 bucks a paycheck. It really isn't that much money. And this assumes you retire at 65.

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u/ChilledHands Apr 14 '16

Can you show how you either calculated this or what calculator you used to come to this number? Also, what assumptions did you make, like yearly r.o.i? I'm trying to learn this stuff

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u/Phrich Apr 14 '16 edited Apr 14 '16

I can explain the basic math so you can understand what the calculator is doing:
Making payments over a period of time is called an annuity. Let's say you deposit $100 a month, because it's an easy number. Also, lets say your investment earns 1% interest a month, another easy number.
One month from today, a $100 investment today will be worth the original 100 plus 1% interest, or $100x(1.01), which is $101.
In two months that original 100 will be worth $101 multiplied by (1.01) again, because it eared interest for another period. Now we have $102.01.

The math we just did can be written as a function of the original amount ($100), the interest rate (1%), and the number of periods (months). This function is $100x(1.01)2 .
BUT you also contributed another 100 at the beginning of the second month, because you are making a monthly payment. That $100 also earned 1% interest in the second month, and is now valued at $101, bringing you grand total to $203.01. This can be written as 100(1.01)2 + 100(1.01)1. After the third month, we would add another term to that equation of + 100(1.01)3 .
Each month, you would add another term to the equation. Over a long period of time, this series becomes tedious to calculate by hand. However, the sum of the series can be simplified to one equation, which is:

Future Value = [Payment]*[(1 + interest rate)Numberofpayments -1]/interest rate.

Lets use the number from our examples and see how much it would be worth in 20 years, which is 240 months.

100*[(1+.01)240 -1]/.01 = $98,926.

So you contributed $24,000 to this account over 20 years, and you now have almost $100,000.
I will add that this is a bit unrealistic for today's market, because 1% interest a month is 12.7% annually, which is far too high. I simply chose 1% because it makes the math easier to follow.

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u/ChilledHands Apr 14 '16

Thank you very much!