I am looking at the lectures about advanced investments and in the first lecture of the series, the professor mentions,

To increase the return without bearing more risk one has to invest with pre-tax dollars via pension fund, 401k or individual retirement account.

• These accounts either let you to invest with salary before it is taxed or let you deduct your investment from your taxable income.
• You will be taxed eventually but always in the future. This is better than getting taxed now because you will have more of your money making money.

Then he shows example including,

If your tax rate is 25% and the annual return is 15% and you invest for 30 years before you retire then you will have \$62 for every dollar invested pre-tax rather than \$50 if you invest post-tax.

How do you calculate to get \$50 and \$62?

Here is a screenshot from the video with two other cases as well. The tax rate is 25% fixed.