# Should we try to make additional mortgage payments if we want to sell the home after 5 yrs?

In this question: Why making additional payment to mortgage counts towards principal? Why does it matter? it is explained why making additional payments towards your mortgage will bring down the total time in which you can pay it off.
My question is: if I buy with the exclusive purpose of selling after 5 yrs., does the additional payments still make sense?
After all, I am selling it after 5 yrs, so why does it matter if the total term is reduced from 35 yrs to 30 yrs by making extra payments?

Much of the interest on a loan comes in the first years of a mortgage, so the sooner you can pay that off, the better. But let's see what the numbers say.

If you have a loan at 4%, principal of \$100,000, a term of 30 years, then this gives monthly payments of \$477.42 (using the Excel PMT function).

If you sell the house after precisely 5 years worth of payments, then you have made \$28,644.92 in payments, you still owe \$90,924.93.

Suppose you sell the house for \$100,000. That means you will be in the hole for:

\$100,000 - \$90,924.93 - \$28,644.92 = -\$19,569.85

Now, suppose you pay an extra \$50 per month over the five years. The same calculation becomes:

\$100,000 - \$87,659.98 - \$31,644.92 = -\$19,304.90

So in this scenario, which is a little simplistic, you are \$264.95 better off.

The question you have to ask is whether you could have done better investing the \$3,000 in extra payments somewhere else. The CAGR in doing this is 1.7%, so you might be better off putting the money away.

Running the same numbers for a 6% mortgage the CAGR you have is about 2.7%.

Edit 2 OK, so I've had a look at what JoeTaxpayer is saying in the comments below, and now I agree: The CAGR should be 4%.

Where I want wrong was to assume that the \$50 per month payments over the five years are worth \$50 * 5 * 12 = \$3000.

This neglects the "time value of money" --- having small amounts of money periodically, rather than all of it in a lump sum.

Including this makes the "effective" value of the monthly \$50 payments \$2714.95 written as `=PV(0.04/12,60,-50)` in Excel or Google Docs.

I've added a tab to the original spreadsheet to show the different calculations. Note that it still doesn't quite come to 4%, but I guess it's a minor error in the sheet.

NB: I know, I'm leaving out mortgage interest tax relief, costs for selling etc. etc.

• Good analysis. IIRC, when I did a similar analysis when I purchased my home, it really made financial sense after taxes, etc after 10-12 years of ownership. My time horizon was a 10 years, so I chose the extra payment route. Another factor to me is that the schools in my city suck. So paying off the mortgage in 20 years vs. 30 means that I can choose to stay in the house and pay for private school when my future children are at that point. – duffbeer703 May 26 '11 at 15:39
• @duffbeer703: Thanks! Over a 10 year time-frame, the CAGRs are 2.0% (4% IR) and 3.0% (6% IR). – Peter K. May 26 '11 at 16:06
• Peter, the CAGR For a prepayment is exactly the mortgage rate. No more no less. In Canada, the interest is not deductible. If you calculate a 1.7% CAGR for prepaying a 4% mortgage, the calculation is incorrect. – JTP - Apologise to Monica May 26 '11 at 20:27
• @JoeTaxpayer: I agree that it's counter-intuitive. I'm not sure where the fault (if any) in my reasoning is. Pointers or additional comments to pinpoint the problem appreciated! – Peter K. May 26 '11 at 20:29
• At first glance, it appears your calculation for CAGR ignores the fact that the money isn't there the whole time. Best I can explain - If I give you a dollar a day for 20 days, you have an average \$10 over that time, or \$20 over an average 10 days. Forgive me, but I think you missed that completely. I can read excel equations, but google docs is a bit different. There can be penny error or rounding, but the result should clearly look like it wants to be exactly the rate of the mortgage. Also the google sheet doesn't permit users to change anything. – JTP - Apologise to Monica May 26 '11 at 20:52

Regardless of how long the mortgage has left, the return you get on prepayments is identical to the mortgage rate. (What happens on your tax return is a different matter.) It's easier to get a decent financial calculator (The TI BA-35 is my favorite) than to construct spreadsheets which may or may not contain equation errors. When I duplicate John's numbers, \$100K mortgage, 4% rate, I get a 60 mo remaining balance of 90,447.51 and with \$50 extra, \$87132.56, a diff of \$3314.95. \$314.95 return on the \$3000. \$315 over 5yrs is \$63/yr, over an average \$1500 put in, 63/1500 = 4.2%. Of course the simple math of just averaging the payment creates that .2% error. A 60 payment \$50 returning \$314.95 produces 4.000%.

@Peter K - with all due respect, there's nothing for me about time value of money calculations that can be counter-intuitive. While I like playing with spreadsheets, the first thing I do is run a few scenarios and double check using the calculator. Your updated sheet is now at 3.76%? A time vaule of money calculation should not have rounding errors that larger. It's larger than my back of envelope calculation.

@Kaushik - if you don't need the money, and would buy a CD at the rate of your mortgage, then pay early. Nothing wrong with that.

It is important to consider your overall financial goals (especially in the 3-5 year range). If you have another financial goal which cannot be met without that additional money then meeting that financial goal might take priority over what I am about to say.

Your mortgage rate is another important factor to consider when answering this question. Extra mortgage payments are equivalent to investing that money in a VERY low risk investment with an equivalent yield of the mortgage rate because you will be paying that much less per year in interest. (Actually, when you consider that mortgage interest is often tax-deductible the equivalent yield should be reduced by your income tax rate.)

Typically it is not possible to find such a low risk investment with a yield as high as your mortgage rate. For example current mortgage rates are over twice as high as the yield of a one year CD.

Also keep in mind that additional mortgage payments help you build equity. This equity will most likely be applied to your next home purchase. If so their effect will be in place throughout the life of your next mortgage too.

• How home equity for home #1 will count towards purchase of home # 2? is it state dependent? I am in ontario in canada – Victor123 May 26 '11 at 18:32
• @Kaushik: I think the point is that the extra payments will increase the amount of money you will get when you sell the house, by reducing the amount you owe the bank. If you take this extra money and put it into the down payment on your next house, you will have a smaller mortgage on that house. – bstpierre May 27 '11 at 12:38