On the usefulness of concrete numbers

This post was last modified in 2011!  We’re digging into the deep history of drafts to bring you things!

Remember when our personal finance Mondays were hardcore personal finance?  And not just updates on our own personal finances?

Sometimes it’s hard to visualize what numbers are when the information you are given is in percents, even if you’re good at math.  APR and APY aren’t the same thing.   Amortization, or how loan repayments are structured can make a big difference on the effects of paying off a loan early.

APR doesn’t take into account compounding.  That is, it doesn’t take into account the idea that if you don’t pay off all your interest each month, some of that interest becomes principal and starts accruing interest of its own, compounded monthly.  APY does take that into account.

When we’re talking about prepayment for revolving loans like credit cards or cars it gets even more tricky because the interest is generally calculated every month based on how much you owe at that point in time and you’re usually paying some required amount in addition to the prepayment.

Auto loan at 5% APY => each $1000 you prepay at the beginning of the year is $50/year you’re not paying in interest.  At 5% APR, that’s going to be a bigger difference.  How much bigger?  Well, you could put the numbers into the compound interest formula, or you could go online and plug into a debt payoff calculator and just look at the numbers to give you a realistic idea of how much you’ll be saving each month or each year or the life of the loan or how much more quickly you will retire your debt.  There are a lot of different calculators out there, each one giving you different inputs and outputs, so you may want to play around with different ones.  Here’s one from nerd wallet.

These numbers are different if you’re talking about something structured like a mortgage.  They’re amortized differently.  For that a spreadsheet is useful.  The way mortgages work, the percent doesn’t directly translate with prepayment savings the same way that it does with a credit card or auto loan. Prepayments early on are worth a lot more than prepayments later.  This is because when you pre-pay a mortgage, your monthly payment does not change, instead the term of your loan changes.  You’re paying your loan off earlier, not changing the amount paid each month.  Additionally, you cut more months off with early pre-payments than you do with later pre-payments because pre-payments pay down principal and early in your loan, you’re mostly paying back interest, not principal with your regular payments.  With later pre-payments you’ve already paid off most of the interest and your regular payments are mostly attacking principal.  In order to truly understand the percent savings from prepayment, it is helpful to use a mortgage amortization calculator or spreadsheet. We like the one from get rich slowly.

Looking at the actual dollar amounts can also tell you that something isn’t worth doing because it saves/makes less money than you initially thought it did.  Like that $1K Chase bonus that was really less than $600 when all was said and done, and not worth the hassle of opening and closing accounts and back again.

Has looking at the concrete numbers ever gotten you to change your mind?

10 Responses to “On the usefulness of concrete numbers”

  1. revanche @ a gai shan life Says:

    I try to make my money decisions based on concrete numbers and projections but it’s still tough to stick to when they go against my gut. For example, since we only make enough to work on making a lot of contributions to our retirement OR paying down mortgage principal, I had to pick one. I don’t want to pick just one! But I must. At least I did already make some serious payments to principal early on and have also refinanced to get a decently low interest rate. I just hate debt so much. But the utility of a 3/4 paid off mortgage is lower than having a decent stack of cash saved up to pay the bills in ten plus years. I’d love to have one less bill of course, but we can’t be positive that this is the place we’re staying forever either. Last year I was on the other side of the fence. I wanted that mortgage gone very much.

    • nicoleandmaggie Says:

      With the chase bank account, we would still have been making some money over our other online savings accounts options, just not enough to be worth the hassle! I think the numbers help inform feelings– we can put prices on things.

  2. FF Says:

    I had previously been opposed to the idea of high-deductible health plans as too risky, but a few years ago, I needed to switch to a less expensive plan and so I spent a lot of time crunching numbers and came to the conclusion that I should switch to a specific high-deductible Gold plan. I found that if my medical needs in the next year were similar to those of the prior year, I would save ~$2000 vs my then-current Platinum plan. Even in the worst-case scenario of maximum out-of-pocket costs, I would still save a few hundred dollars. My calculations also indicated that this plan would be cheaper by at least a few hundred dollars (if not more) than all of the other gold plans I was considering, as well as the silver plans. This was pretty surprising to me, but my calculations have been the same every time I’ve repeated them and I would not have guessed it without actually doing the math.

    • Katherine Says:

      I had a similar experience. I crunched the numbers and the high-deductible plan is cheaper if we don’t need much healthcare and also cheaper if we need a lot of healthcare. There is a middle area in which if we need a medium amount of healthcare mostly in office visits (that would have copays in the “low”-deductible plan) the lower-deductible plan is cheaper, but that was a fairly narrow window.

      My only concern with the high-deductible plan was that we might avoid non-preventive doctor visits knowing that we have to pay the full cost (a pretty big concern for me – I don’t want to decide my kid doesn’t REALLY *NEED* to go to the doctor for that ear and then have them lose their hearing because we didn’t treat an infection). To mitigate that, we’re maxing out the HSA, keeping enough in cash in the HSA to cover the entire annual deductible, paying all out-of-pocket costs with the HSA debit card, and pretending that medical care doesn’t cost money.

      • FF Says:

        I do exactly the same thing–max out the HSA and use the debit card.

      • Debbie M Says:

        Katherine, that is awesome, making a plan for your psychological reality (and most people’s, on this issue) that is also based on the numbers. So many people don’t even get that both are even important, let alone have the ability to find multi-faceted solutions like yours!

    • Debbie M Says:

      That’s very interesting. I never would have guessed these answers either. When I had a choice, I just chose them figuring that if I saved enough of the cost differential, then over several years (most of which would be low-cost), I would come out ahead. I didn’t think you come out ahead in high-cost years, too. Cool!

  3. Debbie M Says:

    The only example I can think of is also the mortgage. When I first got one in ancient times, my principal and interest payment was around $500, but only $30 of that was going toward principal. Which seemed just sickening until I realized that paying an extra $100 per month would cut off over three months of payments (from the end). (Then I refinanced to a 15-year mortgage, which cut quite a bit more off the end!)

    Oh, once my brother calculated that with the amount he’d spent on cigarettes, he could have bought a car. Sobering!

    Oh, sometimes I’m appalled by my property taxes and repair bills, and so I check how much a similar apartment would rent for (specifically, the ones right next to me and the ones I moved from), and those are even more appalling. Nobody’s salary is doubling that fast!

    And there are other situations where I don’t actually do the calculation, but do remind myself that prevention and catching things early is pretty much always the best idea.


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