You forget that the annuity loan also needs to be repaid.
Example with your assumed €250,000:
Annuity loan: €200,000
Interest rate: 2.41%
Repayment: 2%
Annual special repayment assumed: €5,000
Term: 20 years
Results in: monthly payment of €735.00.
Remaining debt after 20 years: €26,280.74.
The KFW loan could be repaid with €265.00 at a maximum monthly load of €1,000.
I calculated with 1.25% KFW interest rate and a repayment of 5% for a term of 10 years and a loan volume of €50,000:
Monthly installment: €260.42
Remaining debt after 10 years: €23,386.05.
KFW follow-up financing:
I assume the following here: interest rate of 4.5%, repayment 7.5%, although the bank will have a say in that.
Monthly repayment rate: €233.86. Remaining debt after 10 years: €1,286.51.
If the special repayments are not made each year on the annuity loan, it looks as follows after 20 years:
Annuity loan remaining debt: €97,339.87
The remaining KFW debt really no longer matters there, you are right.
If I now compare a pure annuity loan, it looks as follows:
Annuity: €250,000
Interest rate: 2.41%
Repayment: 3.55%
without special repayment!
Monthly installment: €993.33
Remaining debt after 20 years: €17,778.28.
If I now compare the loan costs after 20 years, I come to the following result:
Pure annuity: €56,178.28
Mixed calculation with KFW, annuity with special repayment:
1. KFW costs: €4,635.05 plus follow-up financing costs of €5,963.72.
2. Annuity: €52,680.74.
Total costs: €63,279.00 plus remaining debt of €26,280.
However, only if the special repayment is made annually. Without it, it looks bleak.