Some Ways To Think About Work, Savings, And Expenses

Scope And Purpose Of This Post

This post covers some new formulas that I came up with on my own that deal with a quantity (like the monetary value of your retirement portfolio) that experiences both exponential growth and regular contributions.  It is very unlikely I am the first to come up with these formulas, but it has been hard for me to find these formulas on the internet.  This post also covers some implications of these formulas, and some ways to think about the opportunity costs of savings and expenses, especially in terms of work until retirement.

Most notably, Example 5 tries to answer whether using a toll road increases or decreases the amount of time spent working/commuting until retirement.  The math/logic in the example can be used more generally to think about whether any expense is worth the extra work you must do to pay the expense.

You do not have to do any of the math yourself; you can make a copy of my Money Formula Demo Google Sheet and change some of the inputs.  To make a copy, go to the "File" menu at the top of the spreadsheet and select "Make a copy".

Misc Math

Scope And Purpose Of This Post

This post is a grab-bag of various math things that have been useful more than once in my life, and thus publishing them on my blog might help me and others in the future.

Pretty math pictures generated by Roger's Online Equation Editor.

Sections:

• Value Over Time With Growth And Contributions
• ESPP Returns
• Simple Regression Stuff
• Mental Squaring
• Chi Squared Distribution Test
• Distribution Approximations
• J-Family of Means