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Math Help - Debt Optimization problem

  1. #1
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    Debt Optimization problem

    I've taken Calc I, II, and III but the fact that I've taken these does not imply that I know them well. That being said, I understand the concepts fairly easily and know one of the functions that can be acheived is optimization.

    I'm trying to determine some method by which to optimize debt payments.

    Take for instance the following 3 debts
    CreditCard balance: $2400 APR: 18% (compunds atthe daily rate of 18/365 = 0.0493...%) min payment due: $35
    Car balance: $7000 APR: 4% fixed min payment due: $400
    Mortgage balance: $180,000 APR: 6.75% fixed min payment due: $1300
    Savings Account balance $3000 APR: 3% fixed

    Lets assume I have $2000 to make payments and would like to balance apply the difference to one ore more of the debts or deposited in the savings account.

    I'm not looking for a solution, but rather a process. As this data is arbitrary if I am missing something necessary for your response, feel free to make it up for your example.

    Thanks! Randy
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  2. #2
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    A smooth mathematical algorithm will suggest, without fail, that earning 3% is utterly foolish compared to paying 18%. For this reason, without other considerations, the solution will ALWAYS be:

    A) Maximum Payments on the Highest Credit Rate
    B) Minimum Payments on everything else.

    If you have an Earning Rate higher than a Credit Rate, then the problem gets interesting. As long as your Earning Rate is lower than ALL your Credit Rates, there is no confusion.

    Having said that, the concept of NO savings generally is considered socially unacceptable. Defining a minimum payment for the savings account will solve this social problem.

    Note: Loans can be tricky. You must read the terms very carefully. There may be punitive clauses for early payment. Car loans are notorious for using the "Rule of 78s". This packs interest into the beginning of the loan and you may not calculate it correctly.

    Note: Credit Cards can be tricky. Transferring balalces at a tempting interest rate, maybe 1.5% is likely to be a surprise. 1) There probably is a fee to do this. Accounting for future interest costs against this fee is non-trivial. 2) If you pay more than the minimum, the additional amount probably will be allocated to the lowest interest rate portion of the balance. This is NOT what is wanted by the consumer.

    Note: Unless you have a really stupid mortgage, such as one that increases for quite a while (negative amortization) or simply never decreases (interest only payments), mortgages tend to behave rather well, but keep your eyes on escrow charges. Do NOT assume the bank has a clue. Prove it!
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  3. #3
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    Certainly the financial advice you give above is sound but this is less about the actual finances and more to the point of the math behind the calculations required to determine the most optimal debt reduction strategy on any given day. Each of the elements listed was done specifically to represent a different scenario - daily compounding rates, large balances, small balances, and interest earning. My personal financial situation was not represented above.

    A one-time payment of $250 toward the credit card scenario saves $800 in one repayment scenario over the balance of the payments, whereas that same payment paid on the first payment of a standard 200,000 mortgage would save over $1,600 over the life of that loan.

    Both of these scenarios represent a moment in time - a single one time payment. Is there a method by which to calculate this at "any moment" in time?
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  4. #4
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    I wasn't giving financial advice. I was building your algorithm. Read it again in that light, particularly the fundamental parts before I started writing notes.
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