Hi Guys,
Wondering if someone can shed some light on this topic.
Post in question: http://www.mrmoneymustache.com/2012/01/13/the-shockingly-simple-math-behind-early-retirement (http://www.mrmoneymustache.com/2012/01/13/the-shockingly-simple-math-behind-early-retirement)
In the spreadsheet the formula for "Investment Gains This Year (% of one year's take-home Income)" is given as:
http://i.imgur.com/56VbHJw (http://i.imgur.com/56VbHJw)
(http://i.imgur.com/56VbHJw)
I am not sure why the savings rate is divided by 2 in the equation. It's probably something simple that I'm overlooking, but why is that factor there?
Thanks!
Since presumably you are saving the money evenly throughout the year, you divide it by 2, because at the beginning of the year you will have none of that money, at the end of that year you will have all that money - on average you will have half that money. The money can't grow until you save it. It's an approximation, but not a terrible one.
Here's the second part of the equation written out:
(Total Savings for Year / 2) * Annual Investment Return
Since everything is reckoned in "years of take-home pay", savings rate is equal to savings for the year; cutting this in half gets you your average balance for the year.
| Annual return (Front load) | Annual return (Even contributions) |
| 1% | 0.4991708% |
| 2% | 0.9966996% |
| 3% | 1.4926104% |
| 4% | 1.9869268% |
| 5% | 2.4796716% |
| 6% | 2.9708672% |
| 7% | 3.4605355% |
| 8% | 3.9486977% |
| 9% | 4.4353747% |
| 10% | 4.9205869% |
| 11% | 5.4043540% |
| 12% | 5.8866956% |
| 15% | 7.3253544% |
| 20% | 9.6962990% |
| 25% | 12.0355029% |
| 30% | 14.3448406% |
| 40% | 18.8805365% |
| 50% | 23.3151731% |
| 75% | 34.0205220% |
| 100% | 44.2695041% |