Check the math on my 15-vs.-30-year mortgage calculators?

I've received some fantastic help on this forum before, so I thought I'd try again, by submitting my two newest calculators for peer review.

And if that doesn't work then I guess I'll hire someone to check my results. :)

The first of my two calculators comparing 15- to 30-year mortgages does something that no other calculator of the same type does (at least not that I've seen): show the results in real dollars (adjusted for inflation). That's important, because the 15-year mortgage looks a lot less attractive once you look at the results in real dollars. I think most folks have been misled into thinking that 15-year notes are a much better deal than they actually are, since all the other calculators out there don't adjust for inflation.

The second calculator shows what happens if you take a 30-year mortgage and then invest the difference in payments (vs. a 15-year mortgage). Likewise, on the 15-year side once we no longer have a payment to make starting in year 16, we invest the payment amounts into something else. And like with the first calculator, the results are (optionally) reported in real dollars. This calculator shows that in most cases, it's a better deal to take a 30-year mortgage and invest the difference.

Here's the link to the calculators.

wow, the second calculator's conclusion surprised me by how much it is, even though I am a great believer in "big mortgage/big investments"

I will never pay off my house, for example, I'll keep getting long mortgages as long as the rates are low and the banks let me. That 'thing' about paying off your house that people get from their parents or grandparents [Great Depression Thinking] is a huge mistake. You must agree.

Here's somebody else who agrees:

http://www.ricedelman.com/cs/ordinary_people_extraordinary_wealth/excerpts

Quote:

show results in real $

Some won't know what you mean. I would instead use the expression "constant dollars"

Quote:

(results may be inaccurate)

let's hope somebody can verify. Is it assumptions that have to be checked?

Quote: MichaelBluejay

I've received some fantastic help on this forum before, so I thought I'd try again, by submitting my two newest calculators for peer review.

IRS Publication 936:The total amount you can treat as home acquisition debt at any time on your main home and second home cannot be more than $1 million ($500,000 if married filing separately).

I haven't gone over the numbers, but the assumption is undoubtedly true. Mortgage rates are reasonable, and interest is tax deductible up to a million dollars .

It used to be very common to extend interest only balloon mortgages for very expensive homes. These are bank notes that do not reduce principal at all, but must be renegotiated or financed after a given length of time (usually 7-10 years). The purchasers could often afford to pay cash, but they chose to invest their money elsewhere.

The decision to pay off a home mortgage early is usually emotional. My brother is a chaplin in a nursing home, and he is about to pay off his mortgage in less than 10 years. He always is afraid of being laid off and he thinks that his wife's part time salary or pulpit fill will always give him enough money to pay the taxes insurance and utility bills ($400-$500).

The conclusions surprised me too!

The real dollars values are already labeled as being "Adjusted for inflation", which is easy to understand. But in the parenthetical, I went one better, and changed it from "real dollars" to "today's dollars".

Ideally, someone would check the results from a set of assumptions that provides a tax break on each side. The default values don't trigger a mortgage interest deduction, because the interest rate is so low and the house so cheap. If someone gets the same results as I do for a given set of assumptions that provides a tax break on both sides, then it's likely that we'll get the same results for all given sets of assumptions.

pacomartin, thanks for the reminder about the limit on deductible interest. I added a field for that.

I like the calculator; very informative. If I have one nitpick, it's that the top calculator and the bottom calculator don't populate with the same numbers, in only one field, which is the loan amount. (Top calculator populates with $150,000, bottom one with $175,000.) I think it would be nice if those populated identically, so that someone just looking at the page, prior to putting in their own information, would be viewing identical data.

In the past, I had always opted for the shorter mortgage loans. But this was because I was buying property to rent out, and I couldn't qualify to have two mortgages. I intuitively knew that a longer mortgage, with smaller payments, meant that I would have the money for a down payment on the next house quicker, it didn't do me a lot of good, since I couldn't get a mortgage on a second property. Thus, it was better for me to pay off one house, then buy another. Using shorter mortgages meant an ability to do that quicker.

Quote: odiousgambit

Some won't know what you mean. I would instead use the expression "constant dollars"

"Real" is a term that is used in economics. "The nonimal interest rate is 6%, but inflation is 5% so the real interest rate is 1%."

konceptum, thanks for the suggestion. I made the default loan amount in each calculator the same.

Everyone else, the discussion is very interesting, though let me ask that we return to the original topic. A discussion about the relative merits of paying off or not paying off a mortgage should probably go in a new thread.

Quote: EvenBob

We love the peace of mind that comes from knowing we actually own the things we own, not the bank.

Like I said it is an emotional issue, and not really about mathematics. But dead equity usually qualifies for a low interest rate. Factoring in the tax deduction you can almost "predict on paper" doing better elsewhere. Using a similar argument people always take the upfront cash value of a lottery win.

Very rich people who can afford to buy homes outright, often invest in some securities offered by the bank. In turn the bank extends them a home mortgage acquisition loan for up to a million dollars which does not pay down principal, so that they qualify for the tax deduction. But even then, the principal is often invested in stocks which may actually go down in value so that they don't earn enough to make the interest payment.

Peace of mind is worth a lot. Now in order to use your home equity you actually have to make a conscious decision to out a loan against your house. A big thing about money is the ease in which it is available.

Like I said, let's move discussions about the relative merits of mortgages to a new thread, and keep this one focused on reviewing the math behind the calculators. Thanks.

A couple of other ideas. Would it be possible to automatically populate date into the 2nd calculator based upon information put into the 1st calculator? My idea is that the average person putting in his mortgage and interest rate information into the 1st calculator is also going to be interested in seeing the same data in the 2nd calculator, and it would be nice if they didn't have to type it all in again. Even a button copying the information down would help.

Second, what about adding a button to restore the default numbers? I was playing around with the calculator entering all kinds of weird numbers and information. Ok, I admit I was trying to break your calculator. :) When I decided to look at more serious numbers, I couldn't remember what information you had in all the fields, especially with the 2nd calculator. Yes, I can reload the webpage, but why give the user a chance to move their cursor to their menu bar where they might also be tempted to just go to another website?

Finally, depending on who your target audience is, you might consider adding something more visually oriented, such as a graph. Even a simple line graph showing the growth of the invested monies over the 30 yr period, with one line representing the 15 yr loan option, and the other the 30 yr loan option, would be nice. The majority of people are drawn to the visual as opposed to just strictly numbers.

Those are all good suggestions (thank you), and I'll take some of them, but I wasn't really seeking feedback on the calculators in general. I was hoping that someone would check my math. Any takers?

Quote: MichaelBluejay

Those are all good suggestions (thank you), and I'll take some of them, but I wasn't really seeking feedback on the calculators in general. I was hoping that someone would check my math. Any takers?

Yes.

So far, I've only taken a look at the first calculator. I think the numbers are off a little when you account for inflation. I calculated my numbers using excel's built in function for present value "=pv(..." with monthly compounding and I also calculated using continuous compounding. So, I took a look at your source code and I saw that you are assuming annual payments and you do not discount the first payment. If you assume annual payments, the first payment will be at the end of the year, and should be discounted by the inflation rate. I would recommend running the loop from 1 to 360 and using the monthly payments and 1/12 of the interest rate.

Thanks for the help! I didn't think compounding monthly rather than yearly was important, since it makes only a tiny difference in each column's results (and nearly no difference in the bottom line of 15 vs. 30 comparison), but since you're helping me, I went ahead and rejiggered both calculators to compound monthly. I'm now converting to real dollars starting with the very first payment. How do the results look to you now?

You're welcome.

In your source, I see this:
infRate=Math.pow(1+infRate,1/12);

I was initially using a calculation that would look like "infRate=1+infRate/12", which is how mortgages compound monthly, but upon second thought, I think that your method is a better way to model inflation.

When I change my monthly interest rate to your method, we get the same numbers. I think I'll take a look at the second calculator tomorrow.

On the second calculator, I unchecked the box to account for inflation to verify the numbers for "Investing the difference for years 1-30" and "Investing the difference for years 16-30."

I had quite different numbers, so I looked into it. I found that you are assuming annual contributions to the investment, which I think is OK, but you are also assuming that the contribution to the investment is made at the beginning of the year.

For instance, with the 30 year mortgage, you are paying a monthly mortgage of $856 plus a single payment of $4743 at the beginning of the year. Also, for the 15 year mortgage, you are making an investment contribution of $15012 (12 regular payments) at the beginning of year 16.

If you assume annual payments, I would change them to be at the end of the year, because it is not likely that the borrower has the cash at the beginning of the year. In the case of the 15 year mortgage, the borrower would need to save the $15012 for 12 months after the final mortgage payment and then invest the money. Likewise, the 30 year borrower would need to save the $4743 throughout the year and make the investment at the end.

Also, when you check the inflation box, the final investment balances do not discount by the same amount. It should discount both by 1/(1.03)^30.

I found an issue with the capital gains tax as well. At the end of the 30 years, you are assuming that 100% of the investment balance is taxable. This isn't the case, because you first get to deduct your basis in the investments.

If we look at the 30 year case, and use the numbers from the calculator as they are now, the investment balance is $422,303 at the end, but the basis is all of the contributions made, which is $395 * 360 = $142,200. So, the taxable amount is $422,303 - $142,200 = $280,103. The tax paid is 25% of $280,103 = $70,026, for a net of 422,303 - 70,026 = 352,227.

In the 15 year case, the investment balance at the end is 367,799, and the basis is 1251*180 = 225,180. This gives a taxable amount of 142,619 and a tax paid of 35,655. This gives a net of 367,799 - 36,655 = 331,144.

Thank you again for your continued help!

I changed the 2nd calculator so that no return on investment is applied the first year, which is what I think you were suggesting.

Whoops on applying tax to the principal, good catch. I fixed it.

Are you sure the real dollars calculation for investments is really wrong? I'm having a hard time wrapping my head around it, but here's my thinking: If we had a lump sum of money today, and we wanted to see how much it was worth 30 years from now, then we'd indeed discount the current sum by doing lumpSum =/ 1.03^30. However, we're not really looking at how much a lump sum of money today would be worth in the future. Our total is actually being built over 30 years, and the value of dollars going into that sum decreases each and every year. That's why I'm tallying the contributions to the total sum as I go, rather than waiting until the very and then applying a conversion factor. What do you think? If I'm wrong about this then I'm not sure where the error actually lies...

You're welcome, and thanks.

About the real dollars calculation: if you put 2.666666 in for the 15 year mortgage rate, uncheck the inflation box, and set the marginal tax rate to 0, the investments will be worth the same amount of money in 30 years (at whatever value a dollar is in 30 years). So, does it stand to reason that $347,104 in future money is always going to be worth $347,104 / (1.03)^30 in current money? I opine that it doesn't matter the distribution in which we invested the money, only the final value.

I'm not saying you're wrong, but I'm not quite convinced...yet.

Let's say today you put $10,000 in a box. In 30 years, its nominal value is $10,000, and its real value is X.

In another scenario, 29 years from now you put $10,000 in a box. After one more year (30 years from today), its nominal value is $10,000, but is its real value also X as in the first case? It doesn't seem to be, because the Year0 dollars were worth a lot more than the Year29 dollars.

But let's assume I'm wrong about this. If so, then I don't know where the error in the calculator lies, since the code is pretty simple and it appears to be calculating correctly. What do you think?

Quote: MichaelBluejay

I'm not saying you're wrong, but I'm not quite convinced...yet.

Let's say today you put $10,000 in a box. In 30 years, its nominal value is $10,000, and its real value is X.

In another scenario, 29 years from now you put $10,000 in a box 29. After one more year (30 years from today), its nominal value is $10,000, but is its real value also X as in the first case? It doesn't seem to be, because the Year0 dollars were worth a lot more than the Year29 dollars.

But let's assume I'm wrong about this. If so, then I don't know where the error in the calculator lies, since the code is pretty simple and it appears to be calculating correctly. What do you think?

OK. I also couldn't understand why you would be wrong either, so I calculated the present value of the investment by discounting the investment amounts based on when they are made, then discounting the balance of the investment every month. Doing this in excel yields the same present value for both scenarios that I presented (2.666666 interest for the 15 year note), and it equals what I said above (final value/(1.03^30).

So, I think there is an error somewere in the script. If you want to PM me your email, I'll send you what I have in excel so you can see if this is the calculation that you intended.

Thanks again for your help. I think you identified the problem: You said you discounted the investment when made *and* the value of the investment every month. I wasn't doing the second part. That made me think about the nature of inflation a little more:

I gave you my example of putting $10,000 in a box either today or 29 years from now, and thinking that the future values should be different. Well, maybe the future values should indeed be different, but I'm not really trying to compute future values, am I, I'm trying to figure the *present* value of a future sum. In the scenarios I described, say someone finds both boxes and opens them. S/he'd have nominal $10k in each box. It wouldn't matter when the boxes were funded, to figure either the values the future person held, or what that values would be worth in today's dollars. Both boxes would have to be the same.

So if it doesn't matter when the contributions are made, then I can simplify my code by just ignoring inflation, and computing in nominal dollars each year, and then at the end converting the total to real dollars, which is in fact what I just did. So maybe I've got it right now. What do you think?

Monthly mortgage payment $1,251 $856
Total cash out ($298,277) ($298,277)

I must not understand what you mean by "total cash out"
I usually think of "total cash outlay"=(# of months)*(monthly mortgage payment)

I am not sure what you are calculating. Also your figure is the same for both a 15 and 30 year mortgage.

The number calculates to -$450,376 if you put in 0% inflation, but I am still not sure what it means.


In any case it is considered standard to indicate how much you pay for the life of the mortgage (in unadjusted dollars). You can adjust it later to account for other factors.

Total Cash Out is defined explicitly in the notes right under the calculator.

I think you should calculate inflation rate on a monthly basis instead of an annual basis.
For example (1+3.5%/12)^12=3.556695%
So if I put 3.556695% in for the inflation rate, the "total paid" in inflation adjusted dollars is $175,000. The inflation rate cancels out the mortgage rate even without considering taxes or investing the difference.

It would be better if you put 3.5% in the box, and it said "amount paid"=$175,000. Mortgages are calculated by interest rate on a monthly basis (i.e. 3.5%/12), but you should be consistent and calculate inflation the same way.


My calculator below compares 15 vs. 30-year loans, and it's the only one I know of which takes the important step of accounting for inflation.-MichaelBluejay

I think you are making an important point, and it is often overlooked. But I think it would help drive home the point if you first did the full calculation without accounting for the time value of money.
$175,000 @ 3.50%/yr for 15 years = $1,251.04 per month or -$225,188.00 over life of the loan (-$50,188.00 in total interest)
$175,000 @ 4.20%/yr for 30 years =$855.78 per month or $308,080.82 over life of the loan (-$133,080.82 in total interest)
which shows that the 15 year loan saves you $82,892.82 in interest.

With the 30 year note after 15 years principal is reduced to $114,142.00 while the 15 year note is already paid in full.

Then make your point that when you calculate the time value of money the $82,892.82 is reduced to some value as a function of assumed inflation rate. Given a high enough interest rate, the 30 year mortgage will be more beneficial using inflation adjusted dollars even without considering tax benefits or alternative investments.

BTW, wealthy people often get interest only loans, partly because they are assuming that inflation will make the principal easier to pay in the future,

Quote: pacomartin

Mortgages are calculated by interest rate on a monthly basis (i.e. 3.5%/12), but you should be consistent and calculate inflation the same way.

I disagree. Standard practice is to calculate mortgages on a monthly basis, and to quote inflation on a yearly basis. If I made them both monthly, my handling of inflation completely *inconsistent* with what the rest of the world commonly uses.

If readers want to see the difference with and without accounting for inflation, they can uncheck the "Account for Inflation" box, which is why it's there.

Quote: MichaelBluejay

I disagree. Standard practice is to calculate mortgages on a monthly basis, and to quote inflation on a yearly basis. If I made them both monthly, my handling of inflation completely *inconsistent* with what the rest of the world commonly uses.

If readers want to see the difference with and without accounting for inflation, they can uncheck the "Account for Inflation" box, which is why it's there.

$225,188.00 = amount pad for 0.0% inflation for 3.5% per year note for 15 years.

$175,662.00 = amount paid in present year dollars assuming 3.5% per year inflation calculated on a yearly basis
$175,000.00 = amount paid in present year dollars assuming 3.556695% per year inflation calculated on a yearly basis
$182,654.78 = amount paid in present year dollars assuming 3.0% per year inflation calculated on a monthly basis of 3.0%/12 .
$181,670.00 = amount paid in present year dollars assuming 3.0% per year inflation calculated on a yearly basis

You are correct, that normally inflation is quoted on a yearly basis, but then so are mortgage rates. I think it would be more intuitive if a 3.5% inflation rate cancelled out a 3.5% mortgage rate. In either case it is not a significant amount of money.

I would be interested if someone else has an opinion.

The other solution is to put the explanation in the FAQ section. If I look at the powerball website it gives me the odds of winning a prize based on correctly winning a prize by selecting the correct powerball number as 1 in 55.41. Since the obvious question is Why isn't the chance of winning 1 in 35 (since there are 35 number)?, they put it as the first question in the FAQ.

You could put it in your FAQ section. Why doesn't a 3.5% inflation rate balance out a 3.5% mortgage rate?

Yes, I realize that the user can uncheck the box, but it is also standard practice to quote amounts both in inflation adjusted dollars and again in unadjusted amounts. Since it costs you no effort to list both numbers, then why not do it? The whole purpose of the exercise is to be educational, so why not spell things out?

Quote: pacomartinYou are correct, that normally inflation is quoted on a yearly basis, but then so are mortgage rates[/b

.

As you know, banks actually charge mortgage interest monthly. So that's how I calculate it.

As you know, inflation rates are widely reported is annual rates. So that's what I use.

Quote: pacomartin

Since it costs you no effort to list both numbers, then why not do it?

There is a cost. The cost is making things more cluttered and more confusing. I think most of my readers want a bottom-line, realistic number, and so that's the default. For those who want to dig deeper, I give them the tools to do that. I'm not going to force something on the majority of my readers that they don't want.

In any event, as I've said before, the purpose of this thread is my seeking a check on my calculations, *not* seeking feedback of various other ways I can change the calculators' user interface.

Quote: MichaelBluejay

In any event, as I've said before, the purpose of this thread is my seeking a check on my calculations, *not* seeking feedback of various other ways I can change the calculators' user interface.

Well without access to your equations, I was checking the calculations the only way I know how, by experimentation. I figured that 3.5% inflation would cancel 3.5% mortgage. When it didn't I tried 3.556695% inflation rate to see if it cancelled out a 3.5% mortgage rate so I understood the calculation.


If I set all the return to zero
Return on investments 0%

Using 3% inflation index for both calculators, I am not sure I understand the differences between 1st and 2nd calculator. If there is no return on investments, then these numbers should be the same.

$22,367 Total saved over 30 years by taking a 15-year instead of a 30
$34,151 15-year loan is better than a 30 year loan by ...

I just checked the calculator this morning, and I get essentially the same numbers as you (within about $5, a meaningless difference).

I'll add in the ability to deduct mortgage interest into my calculator and I'll try to verify that aspect of the calculator.

Very odd, there was a post from PacoMartin here this morning that I was going to respond to. Unfortunately, I remember the gist of the question, but no details.

So, to attempt to answer the question that is no longer here:

If you take the 30 year mortgage and invest the difference between a 15 year payment and the 30 year payment, assuming the rates on MichaelBluejay's website, that you will have an investment balance of $116,203.83 at the end of 15 years. With a basis of $71,146.80, the total value after the 25% capital gains tax is $104,939.57. The balance of the mortgage will be $114,142.00, so the investment cannot pay off the mortgage after 15 years.

This seems to contradict the previous answer that a 30 year is better than a 15 year, but it doesn't, because the investment power of the $116,203.83 will outweigh the cost of the mortgage payments in years 16-30.

PacoMartin had a different result, showing that the mortgage could be paid off and have some money left in the investment (about 10K). I think the difference is how we calculated the rate of return. If you compound the investment like you do a mortgage (i.e. monthly ROR = .0667/12), you will over estimate the investment balance. Instead, to change the ROR to a monthly amount, I used monthly ROR = (1.0667)^(1/12)-1.

I checked the calculator when changing the "Amount of deductions besides mortgage interest" and there are a few problems, but I can't quite pin them down.
1. When I put in $4000 or $11900, we get the same numbers when not accounting for inflation. The numbers accounting for inflation are off by a factor of 1.03. I think maybe the last year doesn't adjust for inflation, but I'm not sure exactly where the error is. For the rest of the testing, I did not account for inflation.
2. When I put in a value between $4607 (minimum to qualify for itemized deductions with a 30 year loan) and $11900, we get different values. We must have a discrepancy when we calculate how much benefit the borrower gets. I think that we are adjusting the standard deduction the same way (*1.03 every year), but I think that we are adjusting the other deductions differently. I'm increasing them by the inflation rate, but it looks like you might be keeping the difference between the other deductions and the standard deduction constant.
3. When I put in a number above $11900, my tax savings do not increase, but yours do. My calculation is something like this:

deductible interest that will benefit the borrower = interest paid + other itemized - standard deduction, but this is bound by $0 and interest paid. I think that you are not capping this value by the interest paid.

Quote: CrystalMath

PacoMartin had a different result, showing that the mortgage could be paid off and have some money left in the investment (about 10K). I think the difference is how we calculated the rate of return. If you compound the investment like you do a mortgage (i.e. monthly ROR = .0667/12), you will over estimate the investment balance. Instead, to change the ROR to a monthly amount, I used monthly ROR = (1.0667)^(1/12)-1.

That's not what I did.

I took down the post because I realized I had been fiddling with the mortgage rates and had set both the 15 and 30 year mortgage rates to 3.5% . I posted an overly optimistic rate at required to pay off the balance in only 15 years. I realized my mistake afterwards.

Recalculating I get 7.177% as the required rate of return on the investment (using the other default parameters), so that there is enough money to pay your taxes and still pay off the mortgage balance.

Let me be clear, that rate is higher than the rate required to make the 30 year mortgage better than a 15 year mortgage. But I think it is still a significant breakpoint. Should you be lucky enough to have an investment at that rate, you have the option of paying off the balance. Of course, you are still better off continuing the payments on the mortgage, and allowing the other investment to keep on accumulating.

=================
In general, the "be safe" emotional argument will always favor paying off mortgages as fast as possible. But if someone wants to sell you some investment, possibly one that costs $400 a month, he can almost always show you numbers that favor keeping the mortgage as long as possible so that you have money for the investment. He only needs to present an example with investment rates that are optimistic, but not rates that are outrageous.

Schwab is posting "interest only" rates of under 3%. That allows you to borrow a million dollars for the low $2000's, The catch is that after 10 years you have to pay off the balance at a 20 year rate, which can push your payment up threefold. But people go for those mortgages because they assume that they will either sell the house or condo, refinance, or strike it rich.

I am nowhere near as sophisticated as you guys, but could someone please explain why "risk" isn't used in any if the formulas? Doesn't matter what the real money value is, if the rate is low enough, or the tax break, if you cannot pay the bill. Risk never seems to be factored in. I love being debt free!

OK. So how on Earth do you remove a post?

Quote: avargov

I am nowhere near as sophisticated as you guys, but could someone please explain why "risk" isn't used in any if the formulas? Doesn't matter what the real money value is, if the rate is low enough, or the tax break, if you cannot pay the bill. Risk never seems to be factored in. I love being debt free!

I agree, but we cannot quantify risk. I think that the 30 year mortgage is actually better for risk because it keeps your assets liquid. If you have an emergency, a call to your broker is a lot easier than getting a second mortgage to tap into your equity.

I disagree, but I look at it from the other side, loss of income. A deal is only worth getting into if you keep you shirt when it goes bad. Easier to survive an emergency if you have no payments. ;-)

CrystalMath, thanks as always for your continued help.

(1) I wasn't adjusting the tax savings for inflation in the first year. I didn't think it needed to be. But I just went ahead and did so, and that decreases the tax savings by 1.03, so I think we're in line on that one now.

(2,3) I think the problem was that if the user turned off "Account for inflation?", then the other & standard deductions also stopped inflating. But they should inflate, even if we're not accounting for real dollars. So I fixed that, and clarified in the notes that deductions inflate no matter what.

What does your Crystal[Math] Ball show now?

Quote: MichaelBluejay

What does your Crystal[Math] Ball show now?

It shows that we are still off when the other deductions exceed $11,900 and I have the adjust for inflation box checked or unchecked, but we match for all values <=$11,900. Entering an amount of $11,900 ensures that all interest paid throughout the life of the loan is deductible, and this should result in the maximum interest savings.

Quote: MichaelBluejay

I wasn't adjusting the tax savings for inflation in the first year. I didn't think it needed to be.

I decided to adjust it because the tax savings are delayed until the following year. Of course, we are both assuming that the mortgage begins in January, but to do otherwise would be a waste of time. But, if you plan on buying a house, closing the mortgage in January is often best because it maximizes the tax deductibility of the interest, points, up front MIP (for FHA), and annual MIP/PMI. It would stink to close in December and have none of those things deductible.

Quote: avargov

I am nowhere near as sophisticated as you guys, but could someone please explain why "risk" isn't used in any if the formulas? Doesn't matter what the real money value is, if the rate is low enough, or the tax break, if you cannot pay the bill. Risk never seems to be factored in. I love being debt free!

I think "risk" is inherently quantified in the interest rates. Generally, you aren't going to get 6.67% on your investment if you don't risk some fluctuation in your principal. It is also inherent in that the calculation assumes that you faithfully put the money into your investment even though you don't have to do so without risking default.

The term "dead equity" was very popular at one time to refer to value that was simply dormant in your house, and not "working for you". With so many millions of people underwater on their mortgages, many people would kill for "dead equity".

============
For instance if you take an interest only loan at 3% on a million dollars (maximum amount allowable for tax deduction), the interest payments are $2,500 per month. Now, no bank is going to give you a loan like that unless you remove some of their risk. They're preference is that you purchase a home for $1.5 million and put $500K down (possibly from the sale of your previous residence). Normally the interest rate is adjusted by some index, so it could go up or down every year.

Now typically, the bank will not let you pay "interest only" for more than 10 years. After that you must pay down the principal on a 20 year schedule at a minimum. Now principal and interest amounts to $5,546 per month at 3%. That is still broken down into $2500 interest and $3046 principal the first month.

Now do you consider this loan "risky"? After a decade of payments you still owe a million dollars. If high end real estate takes a nasty turn during that decade you may not be able to refinance easily.

Compare that to the maximum allowable Fannie Mae conventional loan ($417,000 since 2006). Following the previous mortgage where the buyer puts a downpayment of 33.33% assume the house was purchased for $625K. Now you finance this amount at 4.0% for 20 years which means "principal and interest are -$2,527 per month (almost the same as the previous loan). But you are now paying down your debt every month! In fact after 10 years into the 20 year mortgage you have reduced the $417,000 to $249,586 paying down over $167.4K. You didn't get as big as a tax deduction as the "interest only" borrower.

But in many cases the interest only loan customer has a much more expensive house to live in for a decade. In some cases the more expensive house will have increased in value so much more than the cheaper house that the increase will dwarf the $167.4K that the conventional buyer reduced his debt.

Before the late 19th century, these interest only loans with a balloon payment for the principal were the only kind of loans that existed. The idea of mortgage didn't exist.
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On a final note, let's look at Michael's an CrystalMath's comment:
So why wouldn't you always just take the 30 and try to pay it off in 15? Two reasons: First, the interest rate on the 30 is higher. And second, if you're not diligent about making the extra payments, there goes your interest savings. I recommend the 15 for those who can afford it because the savings are automatic, and you can't blow it by failing to make the prepayments.

Quote: CrystalMath

I think that the 30 year mortgage is actually better for risk because it keeps your assets liquid. If you have an emergency, a call to your broker is a lot easier than getting a second mortgage to tap into your equity.

What is missing is any mathematical analysis. For the example given, if you take the 30 year mortgage at 4.2%, and voluntarily make the calculated 15 year payment (-$1,251.04 at the 3.5% interest rate), the consequences are that it will take you 16 years to pay off the principal.

Personally, I agree with CM that the extra year is a reasonable compromise to legally binding yourself to the higher payment, or the need to take a second home equity line of credit.

I'm reviving this thread to seek more help with my calculator (the one that compares a 30-year loan to a 15-year loan + "investing the difference"). I'm overhauling the code now and upgrading the output, which presents a problem...

Calculating without any adjustment for constant dollars, I'd simply keep the loan payment and the PMI payment static, and increase everything else by inflation (property taxes, standard deduction, other deductions).

Doing it with an adjustment for constant dollars, there seem to be two ways to do it:
(1) Run through all 30 years without adjusting any values, and then apply an adjustment factor to the bottom line. Or,
(2) Reduce the loan payment & PMI amounts each year, and hold everything else static.

#1 is simpler, but I'd like to display the results in a table, which shows all the various values year-by-year. If I don't apply the adjustment factor until the end, then all the numbers in the table will look the same whether I'm adjusting for inflation or not. If I do #2, then I'm confused about how to calculate the value of the investment. The amounts feeding the investment have already been adjusted for inflation, but I have the feeling that the amounts earned from the investment also need to be further adjusted for inflation...somehow.

Thoughts?

What makes the most sense to me is to run through the 30 years without adjusting any values. Store them all in an array as you go, then apply the adjustment to each year.

I'm sure there is a way to calculate as you go, without storing an array, as in option 2, but it is not intuitive. If I were to come up with a method, I would need to start with option 1 and then make sure option 2 matches those results.

Thank you very much for your help! I was thinking the same things when I posted -- make a table of the values, and compare the bottom line in my RD-adjusted version to the RD-adjusted bottom line in the non-adjusted version. (Wow, I hope that makes sense.)

So, I posted the overhauled calculator. (Scroll down to get to the 2nd calc.) The good news is that since I put all the results in a table, it's extremely easy to check the values year-by-year, and to compare the RD-adjusted values with the non-adjusted values with just a click. The bad news is that I don't have any confidence in the bottom line of the RD-adjusted version.

What do you think?

I haven't checked the discount for inflation yet and I only looked at the 15 year calculation, but here is what I have so far:

1. When the buyer starts investing, you are crediting the full deposit at the beginning of the year. It would be more likely for the deposit to occur monthly or at the end of the year.
2. When I change the down payment, it doesn't update results.
3. Mortgage insurance deductibility phases out between an AGI of 100,000 to 110,000 (half that for married filing separately).
4. I would prefer to have an input box for property tax rather than having it fixed at 3,500 (plus inflation).
5. I would set the default investment tax rate to 15%, since these are long term investments that would be taxed at the capital gains rate.

I would make it more clear that the amount paid and savings figures are based on current the value of money, which I assume is the case. Personally, I would show it both ways.

I do agree with the advice to generally go with a 15-year mortgage if you can afford it. That is what I have.

Thanks guys for the help!

2. I fixed the Down Payment selector.
5. I set the default Capital Gains tax rate to 15%.

4. The Property Tax amount isn't fixed, it's 2% of the purchase price. In any event, adjusting that amount would rarely make a significant difference in a 15 vs. 30 decision, since property taxes are paid on both sides. The property tax amount affects only the tax savings, which are already not much different between 15 and 30 year loans. And like last time, I'm not really seeking input on the interface at this point, I just want to make sure the calculations are correct.

1,3. The difference in (1) is negligible, and (3) applies to maybe only 2% of U.S. residents, and even if it applies to the reader, the difference will be small for a 15 vs 30 decision. I'll save the more trivial tweaks for a future update. For now, I just want to make sure the calculator works.

Quote: Wizard

I would make it more clear that the amount paid and savings figures are based on current the value of money, which I assume is the case. Personally, I would show it both ways.

I don't follow. I do have a prominent "Account for inflation" checkbox in the calculator (though the figures it shows are probably wrong, which was the whole point of my posting here).

Okay, I *think* I have the real dollars calculation correct now, but I'm not 100% sure. What do you think?

I saw the page and it looks OK, tax-wise and perhaps interest-wise. The actual formula not shown. So I would have to ask about accelerated depreciation, ARM, or other variable-interest rate.

A "straight" mortgage generally is compounded monthly.

let's say 3%... .03/12=.0025
Add 1... 1.0025
the number of monthly payments... 15yr=180 and 30yr=360
so the 15 yr total is 1.0025^180 or 1.56743* mortgage amt. divided by # of Mon. payments

For 200,000 borrowed 313,486.34 / 180 =1741.59/month
Using 30 years...1.0025^360 = 2.45684*200,000 / 360 = 1364.91
Total saved with 15 yr boils down to net difference of amt. paid =177,882.10
total interest 15 yr =113,486.34 / 180 =630.48 per month
total interest 30 yr = 291,368.44 / 360=809.36 per month

I know how to figure mortgage interest. The big question is whether the "Account for inflation" button in the second calculator accurately reports real-dollars figures (both line-by-line for each year, as well as the bottom-line result).