Spacefem (spacefem) wrote,
Spacefem
spacefem

Financial Independence, the rule of 25, and the NPER function

If you like my spreadsheet rabbit hole finance posts, then you're weird and I'm surprised you exist but you're in for a treat.

According to Wikipedia The FIRE (Financial Independence, Retire Early) movement is a "lifestyle movement with the goal of gaining financial independence and retiring early." This article was started in 2018. Apparently the idea started decades ago, and most of the concepts started decades ago, but these past couple years it's taken off.

I got into it because I like to live below my means and they have the good ideas for it.

FIRE people (and maybe other people) assume that the stock market increases 4% a year. Or if it increases 7%, inflation might be 3%, net 4%. The picture has been better than that in recent years but 4% is apparently safe. It also means that if you save up 25x your annual expenses, you can live off stock market earnings. If you spend $40,000 a year, and save up $40K x 25, that's $1M. 4% of $1M is $40,000. Every year, forever, in theory, you can scrape off $40,000 off the top of your portfolio and you'll still have your $1M. (cue your favorite canadian band now if you'd like)

So there are two ways to achieve FIRE... get your required expenses down, or get your savings amounts up. If you spend $30K a year, you only need $750K. If you spend $75K a year, you need $1.8M.

I like my job and am not terribly interested in early retirement, but as a cheap engineer who loves math, I can't get enough of this, because it gave me a reason to use excel's NPER function... number of payments required to achieve a future value.

nper(rate, payment, present value, future value)

first you plug in numbers, like if you spend $40000 a year and can save $10000. You'll notice that "salary" isn't a thing that matters in the formula. I mean it makes life better, but it doesn't tell the whole story, one could earn $500K a year and give $400K to charity, save $20K and need to spend $80K. Then they'd only care about the 20K/80K in the formula. Likewise, I'm doing stuff like saving for a vacation and saving for my kids college that doesn't really "count" towards anything, they are not required expenses or contributing towards my retirement, so it all goes out the window. All that matters is expenses, and savings.

nper(4%, -$10000, 0, 25*$40000) = 41 years

SO BEAUTIFUL. I love spreadsheets so much. this works in microsoft excel or google sheets and who knows what all else.

Then as you play with the numbers, you realize that it's only the ratio that matters. If you save as much as you spend, you reach FI in 18 years. Doesn't matter if you save $10K/spend $10K or save $80K/spend $80K.

I translated it all to a "savings rate" because people like to think about that. Savings/total = savings rate. Save 10, spend 40 means you're dealing with 50 TOTAL and saving 10/50 = 20%. Not 25%... everybody with me? Savings/(savings + spending) = savings rate.

And here's where I fell out...

5% - 77 years
10% - 59 years
15% - 49 years
20% - 42 years
25% - 36 years
30% - 31 years
35% - 27 years
40% - 24 years
45% - 21 years
50% - 18 years
55% - 16 years
60% - 14 years
65% - 11 years
70% - 10 years
75% - 8 years
80% - 6 years
85% - 5 years
90% - 3 years

Yes that's right, if you have a 90% savings rate you only have to work for 3 years (I rounded up). That means if you earn $100K, save $90K and live happily on $10K, you'll have the $250K required to retire really soon! If your living expenses are $40K, you have to save $360K a year to do the same thing (actually you'll have $80K extra, just send it to me as a thanks for writing this entry).

Most of us strive to achieve 10%, then at some point realize the 17 year benefit of getting to 20%. And of course it doesn't tell the whole story. Will I get social security? Maybe. Will I have healthcare costs that aren't included in my "required expenses" now? Maybe. Will it even out in the end? Maybe.

But only goodness can come from saving more, and spending less, and I find this very motivating.

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Tags: finance
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