Monday, September 01, 2014

Eternal Prosperity for Your Posterity

Assumptions and Definitions:

Individual X and spouse will raise two children each of whom will have spouses and raise two children (four grandchildren for individual X and spouse).

Individual X and spouse and all descendants successfully attend college around age 20, complete grad school and begin productive work or start and run a business from 20-30, marry for life someone of similar means and have two healthy children at age 30, raise their families successfully and are able to save modestly till retirement age, retire at age 60, live and retire comfortably (not lavishly) the entire time, and die at age 90.

Undergrad education costs $200,000, and grad school or starting a business costs $100,000.

All such individuals live with spouse and minor children in a $600,000 home that required a 20% downpayment to purchase at age 30 with a 30 year fixed mortgage at an affordable interest rate and can invest money till age 60 at 7% real growth and 3% thereafter (i.e. nominal rates of 10% and 6%, respectively, above 3% inflation) taxed at reasonably low average rates.

Prosperity: Having such a life.

Protoparents: The original two spouses who begin the process of eternal prosperity for their posterity.

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Given the miraculous effect of exponential growth (compounding interest), there exists a minimum "critical mass" number N for which Protoparents could fund an endowment for each grandchild at birth that would allow each of these grandchildren to live prosperously and do the same for each grandchild, and so on, ad infinitum … effectively guaranteeing eternal prosperity for their posterity.

What is the value of N?

Turns out, N is about $80,000 in 2018.

Following are some key milestones along the way (attainment of any one of these by each prospective protoparent should enable them to achieve critical mass for themselves and all their posterity):

Age 0:

Grandchild G is born, whose grandparents establish a trust fund in the amount of $80,000.

Age 10:

G’s trust fund balance is $160,000.

Age 20:

G’s trust fund balance is $320,000, and G is in college. $200,000 is paid out to cover undergraduate tuition, leaving a balance of $120,000.

Age 30:

G’s trust fund balance is $240,000. G has completed graduate school and begun work or started a business, has married and has two children, and owns a home with spouse that required G and spouse each to contribute $60,000 toward the down payment. $100,000 is paid out to repay grad school or business loans and $60,000 to cover G’s contribution toward the down payment on the home, leaving a balance in G’s trust fund of $80,000.

Protoparent Goal: $80,000 + $80,000 + $60,000 = $220,000
Protoparent Spouse’s Goal: $80,000 + $80,000 + $60,000 = $220,000

Age 40:

G’s trust fund balance is $160,000.

Protoparent Goal: $440,000
Protoparent Spouse’s Goal: $440,000

Age 50:

G’s trust fund balance is $320,000.

Protoparent Goal: $880,000
Protoparent Spouse’s Goal: $880,000

Age 60:

G’s trust fund balance is $640,000. Parents of G and spouse all die at age 90, leaving G and spouse each $640,000. G now has liquid assets equal to $1,280,000. Since G and spouse were of similar means, G’s spouse now also has liquid assets totaling $1,280,000. Together, G and spouse have $2,560,000 in liquid assets. G and spouse establish $80,000 trust funds for each of their four grandchildren, at a total cost of 320,000. This leaves $2,240,000 total liquid assets for G and spouse, together, which provides them with a safe 4% real return of $89,600, with no mortgage payment. Assuming their home has doubled in value, subtracting 1% annual property tax leaves them with a comfortable $77,600 real annual income, with no housing expense, for the rest of their lives.

Protoparent Goal: $1,760,000
Protoparent Spouse’s Goal: $1,760,000

Age 90:

Total liquid assets for G and spouse have remained at $2,240,000 during their entire 30 year retirement, since they’ve only withdrawn real annual returns equal to 3% over inflation. G and spouse die with $2,240,000 in liquid assets, leave, and leave $960,000 to charity and $640,000 to each of their two children … and the cycle recurs.

Notes:

The above assumes that neither G nor spouse saves any of their own money from work. If together this couple can save an extra $10,000 per year on average for 35 years (age 25-60), this would add $1,400,000 to their total liquid assets at retirement, raising their annual retirement income to $145,600, enabling them to establish a nearly $2.5 million family charitable foundation at their deaths, which after 90 years (3 generations), assuming all descendants followed suit, would grow to almost $25 million in charitable endowments while doing almost $50 million in philanthropic work (in real 2018 dollars) by that time.

Starting at age 25, average annual savings of $20,000 would grow to approximately $440,000 by age 40 at 7% real interest, achieving the indicated protoparent savings goal for age 40. This is an achievable initial goal for many aspiring protoparents (double this average annual savings figure would be required for single-earner households).

Naturally, life rarely conforms to such rigid schedules and round numbers as these. Nevertheless, I think it's useful to have rough long-term financial and legacy goals. Makes working and saving more fun!

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Copyright © 2006-present: Christopher R. Borland. All rights reserved.

Friday, August 01, 2014

College Rankings Conundrum

Love them or hate them,
college and university rankings are an important feature of the American higher education landscape. In articles addressing the trouble with college rankings, John Tierney and Malcom Gladwell opine on various factors driving the college admissions race.

USNews College Rankings are focused on big name prestige and are usually the most quoted; but they're not necessarily the most valid or useful.

Washington Monthly College Rankings focus on the other side of the coin: social mobility, research prowess, and serving the public good.

Forbes publishes a well-known annual list of America's Top Colleges.

Rankings by stateuniversity.com are widely cited and well regarded.

The London Times provides yearly World University Rankings. See The Times Higher Education rankings here: U.S. Liberal Arts College Rankings.

In this day of quarter million dollar undergrad degrees, the USNews lists of Best Value Universities get lots of well-deserved attention.

Other lesser-known lists warrant consideration, also (see here and here).

In the hyper-competitive early 21st century higher-ed arena, getting in to college – and then getting out, successfully – is arguably more important than where one matriculates.

Ultimately, success for graduating high schoolers will depend mostly on the factors that have always mattered most: relationships, talent, and tons of hard work and persistence.

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Copyright © 2006-present: Christopher R. Borland. All rights reserved.

Tuesday, July 01, 2014

The MacTutor History of Mathematics Archive

Mathematics teachers, students, and other math fans and enthusiasts will absolutely love the MacTutor History of Mathematics Archive (MHMA) maintained by the School of Mathematics and Statistics of the University of St. Andrews, Scotland (the third oldest university in the English speaking world, behind Oxford and Cambridge, founded in 1413).

This comprehensive site allows users easy access to thousands of biographies of important mathematicians throughout the ages, informative articles on hundreds of math history topics, treatises on dozens of famous mathematical curves, fascinating time lines of mathematicians' lifetimes and key events in math history, a helpful glossary of mathematical terminology, indices of female mathematicians and math educational history, and links to other noteworthy math history sites.

Math fans can spend many enjoyable and informative hours on the MHMA. The articles and other resources it contains combine rigor with accessibility as scholarly works that nevertheless remain perfectly intelligible, interesting, and useful to the lay reader lacking a mathematics degree. It's no wonder the site gets two million hits per week and almost one million unique visitors per month.

One of my favorite sections is the quotations index, which lists pithy quotations by famous mathematical figures.

Here are a few gems I lifted from this area of the site:

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George Pólya

The first rule of discovery is to have brains and good luck. The second rule of discovery is to sit tight and wait till you get a bright idea.

To teach effectively a teacher must develop a feeling for his subject; he cannot make his students sense its vitality if he does not sense it himself. He cannot share his enthusiasm when he has no enthusiasm to share. How he makes his point may be as important as the point he makes; he must personally feel it to be important.

A mathematics teacher is a midwife to ideas.

Look around when you have got your first mushroom or made your first discovery: they grow in clusters.

A GREAT discovery solves a great problem, but there is a grain of discovery in the solution of any problem. Your problem may be modest, but if it challenges your curiosity and brings into play your inventive faculties, and if you solve it by your own means, you may experience the tension and enjoy the triumph of discovery.

Bertrand Russell

The method of "postulating" what we want has many advantages; they are the same as the advantages of theft over honest toil.

The desire to understand the world and the desire to reform it are the two great engines of progress.

Although this may seem a paradox, all exact science is dominated by the idea of approximation.

The whole problem with the world is that fools and fanatics are always so certain of themselves, but wiser people so full of doubts.

Boredom is a vital problem for the moralist, since at least half the sins of mankind are caused by the fear of it.

Men who are unhappy, like men who sleep badly, are always proud of the fact.

A habit of basing convictions upon evidence, and of giving to them only that degree or certainty which the evidence warrants, would, if it became general, cure most of the ills from which the world suffers.

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Check here for the MHMA biography of Zeno of Elea, here for a discussion of the epicycloid curve (here for the Java-enabled version), here for a index of chronologies of important discoveries in mathematics, here for an index of time lines of mathematicians, here for the quotations index, and here for topics in the history of mathematics education.

If you like numbers, and you enjoy history, you'll love MacTutor History of Mathematics Archive.

See you there!

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Copyright © 2006-present: Christopher R. Borland. All rights reserved.

Sunday, June 01, 2014

Get The Solutions Manual

While textbooks required for demanding math and physical science courses generally provide explanations and examples designed to help students review covered material or make better sense of teachers' lectures, the sample exercises included are often too limited or few in number to paint a complete picture of the topics presented. Answers are usually given for odd-numbered homework problems, but oftentimes this just isn't enough.

The issue for many students in these tough classes is how to get those particular answers.

Wouldn't it be nice if there was a companion book that would actually list the step-by-step solutions for each odd-numbered problem in a given math or physical science textbook ... not just the answers?

In most cases, there is such a book. It's called the "solutions manual," and possession of one of these miracle volumes can sometimes make all the difference between ease and stress, progress and frustration, success and failure.

The solutions manual is the perfect compliment to the required text for any important math or science course. When stuck in the mud on a particular homework exercise, students can simple appeal to the solution shown in the manual, allowing them to answer their own questions and continue their forward progress with the assignment. Instead of pulling out their hair over a particularly vexing problem, students can use the solutions manual to quickly figure out what they've been doing wrong, and then apply the techniques illustrated in the manual's solution to other similar exercises, saving valuable time and energy (e.g. solutions to even-numbered exercises can typically be inferred from those given in the manual for corresponding odd-numbered problems). In this way, the solutions manual acts as a virtual tutor, enabling students to make much more efficient and effective use of time spent doing homework or studying for exams.

I always recommend that students about to take a difficult math or science class invest in a copy of the solutions manual for the textbook required for that class. The best way to find a copy is to visit the publisher's web site or do a Google search using the full name of the text followed by the author's name and preceded by the phrase "solution manual" or "solutions manual" (without quotes). Once you have an ISBN number for the appropriate solutions manual, you may be able to find a less expensive copy by searching for it on amazon or eBay

(Note: the term "solutions manual" usually refers to the "student solutions manual" containing solutions to odd-numbered problems; the "instructors solutions manual" shows solutions to all problems in the text, but is available only to course instructors).

Don't pound the table, become discouraged, or fall behind ... just get the solutions manual!

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Copyright © 2006-present: Christopher R. Borland. All rights reserved.

Thursday, May 01, 2014

What NOT To Bring To Show And Tell

Most of us have fond memories of grade school "Show and Tell" times, when we as youngsters could bring "cool stuff" to share in front of the class.

"Show and Tell" fosters confidence, introduces little ones to the art of public speaking and presentation, and injects welcome variety (and uncertainty ...) into the daily classroom routine. Thankfully, this old-fashioned pedagogic technique has not gone the way of the Dodo, and is still practiced in many early elementary school classrooms throughout the country.

Nevertheless, some "cool stuff" really ought to stay at home.

An elementary school near Dallas was evacuated recently when a second-grade student innocently brought a deactivated hand grenade to present during his class's "Show and Tell" period.

The principal took the prudent step of emptying out the entire school until police could determine that the neutered explosive device posed no threat. Though it contained a pin, the grenade was empty and harmless, and ultimately no one was hurt.

Can you imagine the lecture this kid got? My ears burn just thinking about it.

An article in Yahoo! News documents the incident.

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Copyright © 2006-present: Christopher R. Borland. All rights reserved.