For some of the higher savings rates, the reduction of the return rate from 5% to 2% adds only about a year to the FI path! For example, at a 60% savings rate going from a 5% return to a 2% average return, the path to FI goes from 12.2 to 14.4 years. The higher your savings rate and thus the shorter the horizon to FI, the less susceptible the length of the FI path becomes.Going from 5% to 2% could add a decade or more to the FI path! Regular retirees with a low savings rate will face a large impact when we change the rate of return. How responsive is the path to FI? Well, it depends on the savings rate: I also use savings rates from 20%-95% (the 5-15% bars would have been so high and messed up the scale). In the bar chart below I use 2%, 5% and 8% annual real returns. But of course, over any given decade, returns can be much higher or lower than that. Over the very long-haul, equities returned 6.7% even after inflation, see our post on the history of equity returns. Slightly more complicated math: What if we use different returns?ĥ% real returns isn’t necessarily a bad assumption. That’s exactly the sweet spot: it’s still a manageable savings rate for many FIRE planners and a surprisingly short time horizon to FI! Time to FI as a function of the savings rate. Qualitatively, I get pretty much the same results, even slightly shorter savings horizons than MMM (by a fraction of a year) because regular monthly savings get you to FI a little faster! For savings rates around 5-15%, it will take many decades to reach FI but at around 50-65% savings rates, we can cut down the accumulation phase to somewhere between 10 and 16 years. As I have written before, we should view the 4% number merely as a rule of thumb, rather than a scientific constant! And, of course, I am fully aware that a 4% withdrawal rate might not work for everybody and all the time. Just like MMM, I use 25 times annual consumption as the FI target. Like MMM, I use a 5% real (inflation-adjusted) annual return but I use monthly contributions, while MMM uses annual contributions. Just to warm up, let’s quickly replicate the results from the MMM blog post. Let’s get the computer warmed up and start calculating… the initial CAPE ratio when starting to save) matter? So, in typical Big ERN fashion, I take an ostensibly simple problem and make it more complicated! bond weights) on the path to early retirement? How much does the equity valuation regime (e.g. That got me thinking: Is the math really that simple? How sensitive is the savings horizon to different rates of returns? What happens if we use historical returns instead of one specific expected return assumption? How important is the asset allocation (stock vs. That’s because for every additional dollar we save we reduce the time to FI in two ways: 1) we grow the portfolio faster when we save more and 2) we reduce the savings target in retirement by consuming less. It details how frugality is able to slash the time it takes to reach Financial Independence (FI). Money Mustache articles is the “Shockingly Simple Math” post. The focus must be to think mathematically, rather than simply memorizing math facts.One of my favorite Mr. It is important that students figure out for themselves solutions to math problems rather than being told or shown what to do. Students must be given time to work freely with them. Endless drill and practice is not the solution.Įvery new math concept must first be introduced with manipulatives. They are being taught to simply parrot back math facts, memorize math formulas, and plug numbers into formulas. Too many children are “doing” math without understanding what they are doing. Making Math Meaningful is truly the best mathematical education you can offer your children! Students will be equipped to solve every kind of math problem or word problem, will have the understanding to apply their knowledge to everyday life, and will be prepared for algebra and other higher maths. Written specifically for the homeschool family, Making Math Meaningful guides the parent to introduce each concept using simple conversations (“ What I Am To Do” and “ What I Am To Say” are provided for you). MMM SIMPLE MATH HOW TOIt is the ideal program to elevate a child’s conceptual reasoning, because it uses math manipulatives to teach the child not only how to add, subtract, multiply, and divide, but more importantly, why and when. Making Math Meaningful is the original, award-winning, hands-on manipulatives math program.
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