Google is wrong about how to compound interest: Thoughts on NPV

[Gregory J.]

I noticed when googling "how to convert annual interest rate to monthly" it consistently gives the wrong answer. Dividing your annual interest rate by 12 ignores what Einstein described as the most powerful force in the universe: compound interest! your monthly interest compounds over the course of the year. The correct way to convert annual interest to monthly is:

1 + r_{annual} = (1 + r_{monthly})^12

The difference isn't staggering when looking at just one year, but of course many of us are in this for the long term and that's where it does matter.

To me, the biggest implication is in performing accurate Net Present Value (NPV) calculations. I know NPV isn't that popular of a tool on BP but I use it for all kinds of decisions that have different timing, different interest rates etc. things like cash on cash return, the 1% (or 2%) rule, 50% rule are ok ways to begin analyzing an individual deal, but NPV is the best tool for comparing deals and decisions that are very different. I'm not going to explain all the details of NPV here, but basically you convert any deal into a schedule of cash flows and NPV lets you understand what those deals are worth in today's dollars. It helps you compare very different questions. It is the time value of money; finance at its core. In my own personal life I have used it to answer questions like:

Do I pay down my principal mortgage by X amt to eliminate PMI XYZ months early or do I pay my student loans off early or do I save that money for a year in a savings account to invest in real estate assuming I could earn a certain rate? How does this change if I sell my house in 5, 10, or 20 years?

Should I invest extra in my 401(k) or get taxed on those dollars and invest it in real estate? (assume a certain return or fill in the details of a specific deal)

Should I sell my house now or rent it out?

The stock market is a scam for slaves who work until they are used up or dead, but my W-2 employer believes in it (and this is probably why). They match my contributions to my 401k 1 for 1 up to the first 3% of my salary. Should I keep that money after tax and invest it in RE, contribute to my 401k for the long term, or contribute enough to get the match and then withdraw it minus taxes and penalties to invest in REI? What if I don't withdraw it until I reach financial freedom and my income tax is much lower?

These questions are usually complex, seemingly different, and we have a tendency to answer them with feelings and mantras, but not real analytics. NPV gives you the tools to answer these with data. As long as you can project monthly cash flows in an excel spreadsheet and learn to use the NPV() function in excel then you can compare almost any decision or deal with NPV.