Prepayment Penalty for Loans vs. Current Interest Earnings

Always interesting what complicated calculations are made when a simple comparison is enough.
So once again: saving instead of repaying is worthwhile if:

Sparzinsen * 0.75 > Kreditzinsen

Unfortunately, this is simply wrong because repayment reduces the remaining debt and thus the total amount of interest paid. Conversely, with investment in fixed-term deposits, there are compounding interest effects.
A serious way to represent this is in Excel or by using one of the many repayment/interest calculators available online. Then, do not compare the percentages but the total values of interest costs or income over the period X.

That is why he wrote interest and not interest rate. One could at most say that the Soli is not taken into account. so *0.73xyz

If he meant it that way, the comparison is no longer quite so trivial, as mentioned. I bet that 90% of people fail at a combined compound interest / repayment calculation.

Well, I would say 50% of homeowners (or hope so). For the others, there are calculators. Incidentally, this also applies when comparing two financings. The comparison often swings the other way, especially with different terms or components involving building society savers, if you compare absolute financing costs instead of interest rates.

He meant that repayment and investment can be evaluated mathematically equally, but with the investment, taxes still have to be deducted.

Unfortunately, it is wrong because the outstanding debt decreases through repayment, and thus the total amount of interest paid. On the other hand, investing in fixed deposits has compound interest effects.

Compound interest on the credit side is initially just as good as on the debt side. They are equivalent. However, a small difference arises because repayments are made 12 times a year with the corresponding positive compound interest effects. Deposit interest is only credited once a year. Example with 2% interest: (1+2%/12)^12 > 1+2%. Anyway, if the interest rates are this close together, it is better to repay. There can also be very secondary effects because deposit interest counts as income. For example, with more income, daycare fees increase, children lose eligibility for BAföG, and there are who knows how many other places where income is calculated and compared as soon as you want to claim any government benefits or subsidies.

Whereas some offers do pay out monthly. But most really do pay out, so you have to reinvest the interest straight away each time.