Calculation of total costs mixed financing + loan + building society savings?

Hello,

to calculate the total costs of a mixed financing consisting of a bullet loan and simultaneously a building savings contract, which repays the loan after 10 years, I see two ways:

I add the interest costs from the bullet loan and the loan phase of the building savings contract and subtract the credit interest from the savings phase of the building savings contract: - (interest bullet loan) - (debit interest loan phase building savings contract) + (credit interest savings phase building savings contract)

A second way is to add the monthly costs over the entire term and subtract the loan amount from this, basically a black-box calculation where you compare the payments against the income (i.e. the loan).

With the latter calculation, I get a significantly lower cost amount than with the first. What is my thinking error in the second calculation?

PS: For simplicity, I have omitted other costs such as closing fees, tariff change fees, agio, etc.

because the loan balance differs

But it is about exactly the same contracts. The loan from the [Bausparvertrag] is fully repaid in the end.

and the regular loan?

One question would be whether subsidies (aka Wohnriester) are involved... That could explain the difference if contributions were omitted/forgotten.

What is my thinking error in the second calculation?

In my humble opinion, neither approach is conclusive. Shouldn't one determine the effective blended interest rate or effective overall interest rate (also total effective interest rate ... now you have all the search terms together)? You can "simply" do this yourself by representing all cash flows (or the total cash flow) in a spreadsheet of your choice and then calculating the internal rate of return. In doing so, fees can also be easily taken into account (and they should be!).