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Starting with:

  • \$0 in savings and \$50000 in debt
  • the savings earns 2.5% interest and the debt loses 5% interest yearly
  • you gain \$2000 of income each month to distribute among either savings or debt (fully committed to either so there is \$0 in cash at the end of the month)

  • the minimum debt payment each month is \$200

    1. What is the optimal percent contribution of the \$2000 to savings and paying off debt each month assuming the goal is to maximize net worth in 120 months?

    2. What is the solution for arbitrary interest rates/income levels/starting balances/time periods/minimum payments? Would it require a numerical solver?

    3. Does maximizing short term net worth (picking a percentage each month that maximizes your net worth for that particular month) lead to a poor global solution (net worth at the end of N months)?

EDIT: Assume interest for both debt and savings is compounded monthly at the end of the month, and the income is received and immediately paid towards one and/or the other at the 1st of the month.

AAC
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  • Can you clarify a precise formula for the loan schedule: if the debt this month is $D$ and I pay off $Y$ towards the debt, what is my new debt $D'$ at the following month? And how frequently is the savings interest compounded? I.e., if my savings is valued at $S$ and I put $X$ towards it, what is the new value of my savings $S'$ at the following month? – pre-kidney Sep 12 '19 at 04:44
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    If the net worth at any point in time is savings minus debt, the obvious optimal strategy in this scenario is to maximize debt payments until the debt is zeroed and then contribute to the savings account simply because 5 > 2.5. In real life, however, there are other choices than a savings account that pays 2.5% interest, and one has to also pay for expenses (rent, food, etc.). – parsiad Sep 12 '19 at 04:52
  • @parsiad The way i read the question is that $$2000$ is what remains of the monthly income after having paid for food and rent. Anyway, the main point of your comment is correct (obviously correct in the sense of making this a non-question). – Jyrki Lahtonen Sep 12 '19 at 04:57
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    @JyrkiLahtonen the main point of the previous comment may be "obviously correct" by I believe there is value to showing why it is correct, which can perhaps be done most simply by starting with a concrete formula for the loan and compounding schedules and mathematically proving that the best strategy is to save. I believe that is the value of this question, and in particular it is not a non-question. – pre-kidney Sep 12 '19 at 05:08
  • I believe this is a duplicate of several questions asked on the SE site dedicated to money. – Jyrki Lahtonen Sep 12 '19 at 05:28
  • I am looking for some kind of proof that it is best to zero debt first in all cases and then contribute to savings. It is not obvious to me that, for instance, starting with 20000 in savings and 10000 in debt that zeroing out the debt is the best strategy because you can still end up with net positive gain each month by contributing 200 to debt and 1800 to savings. – AAC Sep 13 '19 at 23:41

1 Answers1

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It is as simple as get the best interest rate you can. Paying down debt earns $5\%$ while savings only pays $2.5\%$. Both are compounded monthly.

The real life thing your model does not capture is the value of liquidity. If you put all the money toward reducing debt and do not have any savings, a bad event may force you to borrow at higher than $5\%$ or not be able to borrow at all. Keeping a reserve fund in savings costs you net worth in the model, but is insurance against disaster.

Ross Millikan
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