There is a special type of mortgage in the Netherlands (Bank Savings Mortgage or bankspaarhypotheek in Dutch), which I presume, does not exist anywhere else in the world. The construct is that you have a mortgage on your house for a certain amount, say 200000 €, and split it up into two parts:

- one part with a loan (in this case 200000), where you pay only interest
- a second part which is a savings account.

Usually both of these accounts have the same interest rates and you pay a fixed amount per year so that in the end the savings account can be used to pay off the loan. For the bank, this construct is exactly identical to having just one account with a loan that is paid off like an annuitary mortgage with a fixed amount per month.

The difference is in the way this type of mortgage is taxed. On the loan part, the interest is tax deductable, and the savings account is not taxed at all. Therefore in comparison with an annuitary mortgage, where the loan gets less over time (it is equivalent before taxes), there is more tax deduction. And this is what makes it an attractive type of mortgage.

With this type of mortage it is possible to pay off parts of the loan part or to add extra money to the savings account. When given a choice, adding a given amount to the savings account is a lot more attractive than using it to pay off the mortgage. Even though it is equivalent to the bank, putting it into the savings account leads to a higher tax deduction.

But of course, the government has put forward some rules to prevent people from profiting too much, and these make it challenging to determine an optimal scheme to pay of the mortgage to minimize total payments made. For this purpose, this post examines a simple Mixed Linear Integer Program (MILP). Continue reading →