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Thread: Refinancing debt (mortgage) with a new loan

  1. #1 Refinancing debt (mortgage) with a new loan 
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    Hello mathematicians, I hope you can and want to help us. My wife and I can't agree how to most effectively refinance our current mortgage. Bear in mind that we live in Denmark, so the banking details might not apply to the US or other countries. We only need help with the math behind this.

    So, some background info:

    We have a debt of DKK 475,000 with an interest rate of 6.45% in Bank A. We have the option to take a new loan of DKK 200,000 with an interest rate of 3.95% in Bank B. We can deduct the interest rate from our taxes, and we also have to pay taxes from any interest earned.

    We can do this in two ways:


    Option 1

    We can simply pay off DKK 200,000 of our current debt to Bank A, leaving us with a loan of DKK 275,000 with an interest rate of 6.45% to Bank A and a loan of DKK 200,000 with an interest rate of 3.95% to Bank B. Both loans have to be repaid in 120 months.


    Option 2

    We can keep the entire debt to Bank A, that is DKK 475,000 with an interest rate of 6.45%, and a debt of 200,000 with an interest rate of 3.95% to Bank B. However, Bank A leaves us with the opportunity to put up to 475,000 into a savings account with an interest rate that matches the interest rate on our mortgage. So we can put the DKK 200,000 into the savings account and get 6.45% interest rate on them. We will pay off the loan to Bank B from that account.


    My wife claims that option 1 saves us the most money, while I claim that it doesn't matter at all which option we use.

    So, who of us are right? :-)


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  3. #2  
    Forum Radioactive Isotope MagiMaster's Avatar
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    Compound interest - Wikipedia, the free encyclopedia

    Well, ignoring taxes and assuming your stated interest rates are compounded monthly, with option 0 (not taking the second loan) you would pay 30,654.40 a month for a total of 3,678,530.

    Option 1 leaves you with two separate loans with payments of 17,747.30 and 7,976.36 for a total of 3,086,840.

    Option 2 leaves your with the same payment as option 1, but for a while you'd also be getting interest. Just putting the numbers in a table shows that the savings account would run out part way through the 9th payment. You should be able to work out whether that's a good deal or not pretty easily.

    Edit: The answer is significantly different if those interest rates are yearly rates compounded monthly. You'd have to redo the numbers using a monthly interest of 0.522% and 0.323% which means that the savings account in option two runs out part way through the 42nd payment. Either way, it makes a difference which option you pick.


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    Forum Radioactive Isotope zinjanthropos's Avatar
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    Quote Originally Posted by Bob Loblaw View Post
    Hello mathematicians, I hope you can and want to help us. My wife and I can't agree how to most effectively refinance our current mortgage. Bear in mind that we live in Denmark, so the banking details might not apply to the US or other countries. We only need help with the math behind this.

    So, some background info:

    We have a debt of DKK 475,000 with an interest rate of 6.45% in Bank A. We have the option to take a new loan of DKK 200,000 with an interest rate of 3.95% in Bank B. We can deduct the interest rate from our taxes, and we also have to pay taxes from any interest earned.

    We can do this in two ways:


    Option 1

    We can simply pay off DKK 200,000 of our current debt to Bank A, leaving us with a loan of DKK 275,000 with an interest rate of 6.45% to Bank A and a loan of DKK 200,000 with an interest rate of 3.95% to Bank B. Both loans have to be repaid in 120 months.


    Option 2

    We can keep the entire debt to Bank A, that is DKK 475,000 with an interest rate of 6.45%, and a debt of 200,000 with an interest rate of 3.95% to Bank B. However, Bank A leaves us with the opportunity to put up to 475,000 into a savings account with an interest rate that matches the interest rate on our mortgage. So we can put the DKK 200,000 into the savings account and get 6.45% interest rate on them. We will pay off the loan to Bank B from that account.


    My wife claims that option 1 saves us the most money, while I claim that it doesn't matter at all which option we use.

    So, who of us are right? :-)
    Do you have deferred tax retirement savings that surpass the amount your mortgage is worth? Not sure about Danish law but it may be possible to hold your own mortgage using those funds. Set it up with a lawyer and the bank, then pay yourself back. You get to use the interest rather than having it go to a mortgage holder. Pay back your savings to everyone's satisfaction and the house is eventually paid off and your retirement savings remain intact. Can be done here in Canada (RRSP Mortgage), there are some fees to get started but it's something people with enough retirement savings and who are still saddled with a mortgage might consider.
    All that belongs to human understanding, in this deep ignorance and obscurity, is to be skeptical, or at least cautious; and not to admit of any hypothesis, whatsoever; much less, of any which is supported by no appearance of probability...Hume
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