You definitely have it right. Great work explaining it all out. I have an amoritization spreadsheet I obsess over (a little :) and right now in the first year of a 100% loan, it’s insane not to prepay. I get a 500% return on any payment I make. I’d have to get a 7-8% guaranteed return EVERY YEAR to beat that over 30 years.

The only point I’ve seen that’s given me something to think about is Trent’s point that once that’s paid forward I can’t use it for anything else.

If you like to take more risk, that’s fine. It is a personal decision. The problem with the CR piece is they don’t adequately disclose the risks involved, so the comparison is not as straightforward as they make it seem.

The same is true as to having the funds available. The liquidity you would like to have is also a personal decision.

I have no idea if people who are prepaying mortgages are not taking full advantage of other investments, so I won’t comment on that.

I have duplicated your Month 1 results using this formula:

Month 1: (100,000+(IPMT(6%/12,1,360,-100000)))-599.55-1000
(should equal 98,900.45)
Month 2: (98,900.45+(IPMT(6%/12,2,360,-100000)))-599.55-1000
(should equal $97,800.40)

You need to calculate the interest portion manually, so that the remaining principal includes the extra $1,000. I suggest this:

Month 1: (100,000*(100%+6%/12))-599.55-1000
(should equal 98,900.45)
Month 2: (98,900.45*(100%+6%/12))-599.55-1000
(should equal 98,795.40)

If you put these side by side, make the obvious adjustments and fill across 90+ rows or columns, you should see how paying too much interest affected your results.

The interest payments are:
month 1=IPMT(.06/12,1,360,-100000)=500.00
month 2=IPMT(.06/12,2,360,-100000)=499.50

The principal does not decrease in these interest payment calculations

In my second month principal paid increases by $5.54 and continues to accelerate. In your second month the increase is fifty cents. That can’t be right. If you pay off $1,100 of principal in the first month, that $1,100 can’t earn interest in the second month. Interest not earned by that $1,100 in one month is:

$1,100 * (.06/12) or $5.50. Since you should have had that much less interest to pay you should have paid off that much more principal.

Are you subtracting $1599.55 every month? Perhaps the number is falling. Also, you might have a decimal off, or some other error, in your interest calculator.

@Doc Econ — I like that thought. I see prudent banks trading their own accounts some, but when trading gets to be too much of the earnings disaster’s imminent.

@k — That is a good point. When people pay taxes, they usually do it out of their paycheck or their checking account, not a savings account like this one. That means compounding isn’t affected — if I earn $500 in interest and am taxed 10%, that $50 is not coming out of the $500, it’s coming out of something else. The full $500 earns interest the next year.

At a 25% rate, 3% savings account, using my above calculations and the tax payment assumptions, putting $1,000 extra into a savings account instead of prepaying costs about $2,200 in taxes. I think you’re right.

I would respond that I’m willing to take on more risk (hold a mutual fund, which is not risk-free) for 1) the probability of higher returns (I need to earn about 6% to come out ahead after taxes) plus 2) the flexibility of having funds available until I am able to pay off the mortgage balance. This seems similar to being willing to hold small value stocks over market weight — additional risk for the probability of additional return.

I would also argue that many people prepaying their mortgage have not maxed out their tax-advantaged accounts, and some may not be getting full company match on 401Ks. I personally would not pass up the ability to contribute to my 401K or Roth IRA to prepay my mortgage.

while you “save up” and invest additional $ to eventually pay off the mortage with a lump sum,

– aren’t you paying TAXES on the interest you’re earning through investments in the “saving-up fund”?

seems to me you’d need to consistently beat the whatever percentage your fixed mortgage is at, in order to compensate.

any people handy with a spreadsheet out there to comment?

If you have a mortgage at x%, then prepaying is indeed a risk-free way to earn x% (if you want to factor in the tax deduction, go ahead, it doesn’t make much difference as long as you compare it to an after-tax rate on other investments, but beware the phase out of deductions at higher incomes!).

Sure, you might earn more x% over the course of the mortgage in an alternative investment such as a mutual fund, but that usually comes with taking some risk.

The correct comparison is whether you can earn more than x% on a comparable risk basis. So, can you get a Treasury security or insured CD that yields more than x%? If yes, invest. If not, prepay.

If CR was right, then you must ask yourself why banks lend for mortgages. They can “borrow” from depositors at a rate lower than mortgage rates. For example, they borrow at 3% and lend at 6%. But why don’t they borrow at 3% and invest, as CR suggests, in a mutual fund? Because they need to have the security of low risk (in the form of collateral — the house), in case the depositors come and want their money back.

PREPAYING:
By paying $1000/mo extra to the principal of our mortgage example, you would pay it off in 89 months, and the total amount paid on the $100k loan would be ~$142,235.

SAVING OUTSIDE THE MORTGAGE:
Say you took that $1000 cash each month and stashed it under your mattress and didn’t put any extra toward your mortgage. In month 89, your loan balance would be $88,875. During those 89 months, you would have saved up $89,000 (assuming no interest). Send a check to the lender for the remaining balance. The total amount you pay on the loan is ~$88875+(89*600)=142,235

Add the effect of interest and you will come out ahead. Until very recently, I was a big proponent of prepaying. From these calculations it doesn’t seem like you make a 6% return by paying into a 6% mortgage, which doesn’t make sense. Is there something wrong with my calculations?

Paragraph 4: “I%” is a variable, not a 1. It could be 1%, 2%, 3%. I ran it up to 100% for fun.

Paragraph 7: By “$9,600 in extra payments”, I mean six months of $600 regular loan payments and six months of $1,000 additional payment to the savings account.

Also, I switched my method since the “Michael @ 12:57 pm January 31st, 2008″ post, but it makes no difference because so long as either method is consistently applied to both the loan and the savings account. I just tried it to be sure.

That’s not what I get. Here is my method. Please tell me how yours differs.

$100,000 loan at 6% compounded monthly, $600 loan payments. Each month the spreadsheet subtracts $600 from the previous month’s balance, then multiplies that by 106%/12.

$100,000 loan at 6% compounded monthly, $1600 loan payments. Same method as above, except more is subtracted before each month’s interest is applied.

Several savings accounts paying 0%, 1%, 2%, etc., all compounding monthly. In each one, $1,000 is added to the previous month’s total, and then the sum is multiplied by (100%+I%)/12.

Using this method, if you pay $1,600/month into the mortgage, you pay off the loan in March of the 7th year with $524.97 to spare.

If you pay $600/month and put $1,000/month into a 6% savings account, the savings account wipes out the remaining principle in March of the 7th year, with $524.97 to spare. It makes no difference. This would be a good option if 6% savings accounts existed.

With 3% interest, it happens in September of the 7th year — six months later than if the loan were prepaid, or $9,600 in extra payments. By my method, that $9,600 is the cost of Kathryn’s security.

1. The money you pay toward your mortgage is guaranteed during the time frame you do so. For example, I got my 6 percent mortgage in 2000 and paid it off in 2005. The S&P 500 during that time had a slightly negative return which made a guaranteed 6 percent rate of return pretty darn nice!

2. Not having to make a mortgage payment is imputed income. What’s imputed income? It’s money you don’t have to earn and pay taxes on. Not having to pay $1,000 a month on a mortgage is the same as making $1,333 (before taxes in the 25 percent tax bracket). Did you ever wonder how many retirees can make ends meet on just Social Security? They own their houses free and clear.

3. Building on #2, not having to pay a mortgage gives you a very precious non-monetary commodity…and that is freedom of choice. Want to take a lower paying but more satisfying job? Do you desire to cut back on your work to help take care of children or grandchildren? Fed up working for “Da Man” and want to start your own business? No mortgage=less monthly expenses=more choice in life.

4. And finally, life is never either/or. Everybody should have several months of liquid emergency money and everyone who works for a company which matches money in a 401(k) needs to do that before thinking about paying off the mortgage.

But that was a few years ago. Within the last six months I bought a pint of it just to get a test color and found it covered better.