On Mortgages and the Time Value of Money

I’m in an interesting situation. After discussing it with some friends, some folks over at Reddit, and a great mortgage calculator here. I’ve decided to share it with the Internet because a choice I make this weekend may mean saving or losing $4,000 and I’m sure this information will be useful to other people as well. I’ll attach a spreadsheet at the end with the exact numbers I’ve used for these calculations.

In a nutshell: I bought a home last year. To make things simple let’s say the loan was for $70k and payments started November 1st (30 years, 4.75%). In January I had to buy a car, auto loan payments started February 1st ($10k, 5 years, 6.9%).

I happen to have $200/mo that I can spare and I want to pay down my loans, so I started thinking. Conventional wisdom says to always pay down the loan with the higher interest first. “But I took some accounting classes in college!” So I probably know just enough to hurt myself.

One of the things you learn in accounting is the “time-value” of money. Tiny fractions can add up to millions of dollars when you compound interest over time, and the longer the time the more powerful it gets. Even though the home interest rate is lower I had a sneaking suspicion that paying it down would be wiser because of how long the loan is for.

Let’s say next month I start putting an extra $200/mo towards the auto loan until it’s paid off. I’ll save $920 and cut the term of that loan down by 28 months. The auto loan would end in May of 2015 (an important date we’ll come back to later). Will putting those 28 payments of $200 towards my home loan save me even more money? Absolutely, because knocking down the principal on my home loan will change how interest is accrued for the next 30 years. Putting 28 payments of $200 towards the principal on the home loan will save me $12,978. A $13,000 difference!?! That’s more than I paid for my car. Doing that alone would save me enough to get my car for free.

But here’s the thing: the question is bigger than what to do with those 28 payments of $200. I could stop making additional payments at that point, but would I? Probably not. So I need to look at what happens after the car loan is paid off.  My options are:

  •  Take the money I had been paying towards the auto loan and apply it towards the home loan (in which case I’ll now be paying an extra $400/mo).
  • Start paying $200/mo extra towards the home loan and pocket the money I’d been paying on the auto loan.

Many people take life as it comes. In 2015 when my car loan is paid off I might be tempted (or have) to spend the money I’d been paying towards the auto loan on other things … but that actually puts me in a worse situation.

If I start paying $200/mo extra towards the home in May 2015 I save $29,316. If I start paying $400/mo extra I save $37,552. (When you add the $920 I saved from paying down the car the savings add up to $30,237 or $38,472 respectively.)

But we’ve already shown that payments towards the house pay off better than payments towards the car. So what happens if I just pay $200/mo towards my house from the start and not pay anything extra towards the car? That will save me $34,093. That’s $4,379 less than if I pay $400/mo towards my home after the car is paid off … but it’s $4,777 more than if pay off the car then put $200/mo towards the home.

Let me say that again: If I pay $200/mo towards the car and then $200/mo towards the home I’m actually losing $4,777 compared with putting $200/mo towards the house from the start.

Once I’m done paying off the car loan I have to roll that money into the home loan payment or I’ll lose almost five grand. If I think I’ll want (or need) to use those funds for something else after 2015 I’m better off paying down the home from the start.

It’s a $4k – $5k decision, and I think I was right: the conventional wisdom is only perfect when applied to loans of similar length. If you have loans that are of greatly different lengths you need to look at it more closely. If you want to run some numbers of your own, I’d point you to  this mortgage calculator, and if you want to check my numbers you’ll need that and this spreadsheet.

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6 responses to “On Mortgages and the Time Value of Money

  1. While the math may make sense, it seems to me you are looking at two different classes of assets. Cars are a depreciating asset and you are unlikely to make a profit if you sell it, whereas a home is usually an appreciating asset that is more likely to be sold at a profit. Cars also have a more unpredictable ownership tenure. Accidents happen and car repairs can be prohibitively expensive. In both cases I would always prefer to have a paid-off vehicle so I have more options and choices as to my next course of action. I would vastly prefer any insurance payout on a totaled vehicle be made out to me rather than a finance company, and I never again want to be faced with a large repair invoice and a monthly car payment. These circumstances are much less likely to happen with a home.

    • I’m not sure they’re less likely to happen with a home. I’ve already got a Christmas Club account set up to save for a new roof. Please don’t jinx me ;)

      • No jinxing here! I bought a foreclosure at the end of 2012 and had significant maintenance and repairs to make it comfortably inhabitable, including a new roof. Yours was a curious question and reminds me how much I hate car payments. Mortgage I can live with. Car payments are to be disposed of as quickly as possible even with a 0.9% interest rate.

      • I see. Based on your first comment I was thinking of noting that you were bringing up subjective points that other people would also take into account (but as you pointed out may or may not be the best mathematically/financially). I’d say that your last sentence would definitely indicate an emotional reaction. I might not like the depreciating asset but if paying down the home instead of the car can save me $20k … that’s two new cars to me. Maybe not immediately, but eventually. But maybe I have an emotional connection to deferred gratification.

      • Definitely true. Do you plan to keep this home until the mortgage is completely paid, thus realizing the savings? We could go round and round on the fine points of savings, etc., but in reality personal finance is just that, personal. I always appreciate a different, thoughtful perspective.

      • Honestly I’m not sure. I think it’s smarter to pay down the principal either way though. More equity for me regardless of whether I sell it sooner or later.

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