What is the math behind Early Retirement Calculator?

[jh123]

I just finished reading The Shockingly Simple Math Behind Early Retirement and playing around with the Early Retirement Calculator as well as the spreadsheet linked in the article, but I still don't completely understand the formulas used for the calculations.

For example, with annual savings of $30,000 and annual return on investment of 5%, I would expect an ROI of 30000 * 0.05 = $1,500, but the first row of the table shows $750.

What am I missing here? Is there somewhere that displays all of the formulas used for the Early Retirement Calculator?

Thanks!

[dandarc]

Assumes you're putting funds in evenly throughout the year, so you only get 1/2 (6 months worth) of return on that year's contribution.

Bit of a nod towards conservatism I suppose to assume the even spread of the money going in vs. all at beginning of the year. Bit more aggressive assumption than "all goes in at the end of the year".