Amortization Schedules and Principal Prepayment, Part 2: Verification

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Yesterday in Part 1, we talked about the basics of amortization and mortgage prepayment. In this post, I just wanted to share some other interesting results I got when tinkering around with the amortization schedule.

Are you always paying the same amount of interest?

As I noted before, amortization is a way to make equal payments but still preserve the right ratio of principal paydown and interest. You can check this using the same schedule of payments as before, except now I’m just looking at it broken down by 12 years instead of 360 months. ($200k mortgage, 30-year fixed at 5%).

If you have a loan of $200k at 5% interest, simple arithmetic will lead you to guess you’ll pay around $10,000 of interest the first year. As you see above, during the first year you actually pay $9,933 towards interest, as your loan balance went from $200,000 down to $197,049 over time. If you simply divide the $9,933 by the average of $200,000 and $197,049, again you’ll get 5%.

This just provides a rough estimate, but you can see that you’re always paying 5%, even as the principal shrinks. Only at the very end does it vary slightly, not sure why exactly, but I’m guessing due to smaller numbers. The lender isn’t ripping you off by having you pay a ton of interest in the first year. You just have a lot of interest to pay! Kind of neat, actually.

Is your investment return from paying extra towards principal really the mortgage’s interest rate?

When you pay down your mortgage at 5% interest, it is often assumed that this is the same as investing that cash elsewhere and earning 5% per year. (Ignoring tax issues.) But is it?

Again, a quick check on the spreadsheet confirms this. Let’s say I am just starting Year 2. If I prepay the entire equity portion of $3,102, this will advance me to Year 3 of the schedule, and I will be shaving off one year from my mortgage. In other words, my $3,102 will be worth an entire year’s worth of payments, or $12,884, in 29 years. This works out to be the same as a 5.03% annualized return. Close enough for me. Again, if you prepay near the very end of the term, the percentage starts to drop off a bit. But remember, if you’re prepaying, you’ll probably be finished with your mortgage well before reaching that point.

I’ve plotted both the effective interest rate paid and the paydown investment return (gain) below:

You can play with the spreadsheet yourself at Google Docs or in Microsoft Excel format.

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  1. Google docs version seems to be non public at the moment.

    We’re sorry, does not have permission to access this spreadsheet.

  2. Google docs version seems to be non public at the moment (2nd to last link), but I can see the embedded copy.

    We’re sorry, does not have permission to access this spreadsheet.

  3. It’s calculus. The estimate always varies from 5%, but not noticeably at the beginning because at the beginning you are changing the principle by very small amounts. At the beginning, the remaining balance can be approximated by a line. Near the end, it becomes more decidedly nonlinear (it always was, but that becomes obvious at the end) so your approximation quits working. Your approximation is based on an assumption of linearity.

  4. Interesting post…

    Also of note, your home interest deduction gets to be less over time. Your standardized deduction will likely go up over the years (inflation) while the amount of interest you can itemize will go down.

    I’ve found that writing off interest is only a benefit for people who tend to have bought a LOT of house. (or are single…) I’ve yet to be able to itemize as I’m married and the standard deduction is always more than the interest I’m paying.

  5. Thank you for this information. I have a 207K mortgage that we refinanced in January for 4.875% so these charts workout great for us. We have 20% equity so we are not paying PMI. We are considering paying down our mortgage because we are hoping to stay in the house for a while. This information is helpful! Can you consider doing a post on the benefits of putting an extra 300 towards principle or putting 300 in a total stock fund?

    Also any posts on escrowing or not escrowing would be helpful…we are now at that point too.

  6. Thanks Don, I thought it was something like that but I no longer have the skillz to do calculus. 😉

    I have changed the permissions on the Google Doc, I could have sworn I did it last night. To edit, you’ll have to File > Export into your own .csv or .xls file.

  7. I also just re-financed my home and even though it hurt to give up my 20 year, for a 30 (I needed cash for various reasons), I just think of the term is a variable-term, not necessarily 30 years. I have 30 years to drag out my payments, which is very affordable, but if I have more money, I’ll pay it early. Taking a 30 year rate is just buying the flexibility to pay over 30 years, so it costs a little more. It’s interesting how the math works, thanks for showing me that. I’m more simple-minded in that I just know you pay less interest when you pay early. It’s very hard to calculate precisely what you save, because like other posters said, your deductions can change from year-to-year, so can your income. Not to mention the fact that you pay down your mortgage with after-tax dollars, and you have to consider this too — because you could diverted that same amount pre-tax to a 401K.

  8. Has anyone ever looked into NACA? Seems like a bizzare approach to home mortgages. The finance 100% and cover closing costs. You can use what you would have used as a DP to buy down your interest rate as low as 0%. I did some math on a 200k condo and my 20k I would have used as a DP to buy down the interest rate to 1.87% over the life of the loan I would pay only 61k in interest.

  9. You may have already mentioned this, there is another interesting piece to the 15 year mortgage. Because the principal portion paid is equal to the PV of an investment that would yield a FV of the loan balance that the 15-year mortgage the principal paid in the 1st month of a 15-yr mortgage is equal to the amount that would have been paid in the 1st and 181st months of a 30-yr. Thus combining the two PV into one principal payment. This holds true for each additional month down the line as well (2 & 182, 3 & 183, etc).

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