Archives for April 2009

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.

I’ve been tinkering around with my mortgage. Have you ever wondered how the monthly payment was determined? It’s called amortization. An amortization schedule is a way to make equal payments over a period of time, but have the payments split between principal and interest so that the interest paid over time decreases over time along with the loan amount remaining. It is a balancing act to be fair to both borrower and lender, and you can find a mathematical derivation here.

The most direct way to see where you are on your amortization schedule is to ask your lender to send you a copy. Alternatively, you can generate one yourself by using a mortgage calculator with this feature. Here is the amortization schedule for a $200,000 loan with a fixed interest rate of 5% over 30 years.

As you can see, in the beginning most of your payment goes towards interest, and only a little reduces your principal, or outstanding loan amount. As time goes on, your payment stays the same, but the chunk going towards interest decreases as the principal shrinks.

Mortgage Principal Prepayment
If you want to pay off the loan in less than 30 years, you’ll have to pay more than required. This is known as principal pre-payment. The effect of making such additional payments can be visualized by imagining that it moves you “ahead” in the amortizaton schedule.

Here’s an example using the schedule shown above. Let’s say you’re just getting ready to make your first payment of $1,074. At this rate, you still have 359 out of 360 monthly payments left to go! How much money would it take to shave off one extra payment off the end? To find that, you just have to look at the principal portion of Month #2, which I highlighted orange: $241.

If you pay $241 additional with your first payment now, you’ll won’t have to pay the $1,074 due on Month #360. Why is this? Working backwards, you can confirm that this is pretty much a 5% compounded return on $241 for 30 years, as expected. In addition, you’ll be shifted forward to Month #3 on the schedule. So next month your (still required) payment of $1,074 will have a bit more applied towards principal, and a bit less towards interest.

Making a 30-year Mortgage into a 15-year Mortgage
This actually creates an interesting way to shorten your mortgage. What if you kept paying the next month’s principal payment on top of your required $1,074 each month. You’d add on $241, then $243, then $245, and so on. Every month you’d shave off one month off the end, leaving you with a 15-year mortgage! You can also imagine this as skipping every other payment by just paying the principal and saving the interest.

This can work out nicely because the extra required will start out reasonably low at $241, and increase gradually with time along with your income and/or cashflow.

An alternative is to add $510 to every payment each month to shorten the term to 15 years. Although if you’re sure you want to do that, you might want to just get a 15-year fixed mortgage at a lower interest rate.

Read on in Part 2: Return on Investment Verification.