Mortgage Observation  when it's better to invest at lower rate

 Posts: 3
 Joined: Tue Oct 09, 2018 12:34 am
Mortgage Observation  when it's better to invest at lower rate
Hello all 
Apologize for this long winded post but I thought some might find these calculations helpful  they weren't obvious to me until I ran them and please point out errors if you see them.
Intuition would say it's always better to reduce your mortgage vs. invest the extra cash  as long as your mortgage rate is higher than your forecast investment rate. I wanted to share an important scenario in which this is not true, it's when you are choosing your down payment.
Assume a 4.3% rate, 30yr mortgage, $500k house (you can adjust these and run different scenarios  also note I'm just using nominal #s for simplicity):
 Put down 20% ($100k), equals $312,615 in interest over the 30yr term
 Put down 30% ($150k), equals $273,538 in interest over the 30yr term.
You save $39,077 in interest by putting an down an extra $50k. If you instead invest that $50k in a 30yr bond (today's yield ~3.1%, 1.2% less than the mortgage rate we're assuming), you get an extra $74,948 at maturity.
You've earned as extra ~$36k ($74,948  $39,077) over 30yrs by investing in the 30yr bond vs. putting that $50k towards your initial down payment.
This is despite the materially lower rate on the 30yr vs. your mortgage rate.
The rationale I saw after doing this is that the smaller down payment results in a larger monthly payment (incl. larger payment towards principal).
So over the course of the mortgage term, the mortgage debt outstanding with the smaller down payment vs. the larger down payment becomes less than $50k. That is, you aren't saving 1.2% (the difference between your mortgage rate and investment rate) on $50k, rather it's on something less then $50k (and less and less as the mortgage term goes on).
There is a very important qualifier here  with the larger down payment, your monthly payments are $247/mo less. If you invest this extra money every month at the same 3.1% investment rate quoted above, you''ll make ~$58k at the end of the 30yr period. Easily wiping out the excess profits from putting the extra down payment into the 30yr bond. Of course  many people might choose to make a larger down payment for budget flexibility  namely, being able to spend some of the extra monthly income they have due to a smaller mortgage payment. But if you saved only $100 of the $247/mo you're saving due to the larger down payment  you still come out ahead in the smaller down payment scenario.
Apologize for this long winded post but I thought some might find these calculations helpful  they weren't obvious to me until I ran them and please point out errors if you see them.
Intuition would say it's always better to reduce your mortgage vs. invest the extra cash  as long as your mortgage rate is higher than your forecast investment rate. I wanted to share an important scenario in which this is not true, it's when you are choosing your down payment.
Assume a 4.3% rate, 30yr mortgage, $500k house (you can adjust these and run different scenarios  also note I'm just using nominal #s for simplicity):
 Put down 20% ($100k), equals $312,615 in interest over the 30yr term
 Put down 30% ($150k), equals $273,538 in interest over the 30yr term.
You save $39,077 in interest by putting an down an extra $50k. If you instead invest that $50k in a 30yr bond (today's yield ~3.1%, 1.2% less than the mortgage rate we're assuming), you get an extra $74,948 at maturity.
You've earned as extra ~$36k ($74,948  $39,077) over 30yrs by investing in the 30yr bond vs. putting that $50k towards your initial down payment.
This is despite the materially lower rate on the 30yr vs. your mortgage rate.
The rationale I saw after doing this is that the smaller down payment results in a larger monthly payment (incl. larger payment towards principal).
So over the course of the mortgage term, the mortgage debt outstanding with the smaller down payment vs. the larger down payment becomes less than $50k. That is, you aren't saving 1.2% (the difference between your mortgage rate and investment rate) on $50k, rather it's on something less then $50k (and less and less as the mortgage term goes on).
There is a very important qualifier here  with the larger down payment, your monthly payments are $247/mo less. If you invest this extra money every month at the same 3.1% investment rate quoted above, you''ll make ~$58k at the end of the 30yr period. Easily wiping out the excess profits from putting the extra down payment into the 30yr bond. Of course  many people might choose to make a larger down payment for budget flexibility  namely, being able to spend some of the extra monthly income they have due to a smaller mortgage payment. But if you saved only $100 of the $247/mo you're saving due to the larger down payment  you still come out ahead in the smaller down payment scenario.
Re: Mortgage Observation  when it's better to invest at lower rate
Sorry but you are overthinking this. It’s pretty simple really. Just a spread between the rates. If you have investments that yield less than your mortgage rate, you are not coming out ahead by investing.
You are including return of bond principal as a “return” but not considering the 50k down payment as equity in the house. And you are not considering that you are paying down mortgage principal each payment.
You have to compare apples to apples.
You are including return of bond principal as a “return” but not considering the 50k down payment as equity in the house. And you are not considering that you are paying down mortgage principal each payment.
You have to compare apples to apples.
Re: Mortgage Observation  when it's better to invest at lower rate
I assume you're talking 30 year treasury bonds here? Aren't they simple interest and not compound interest?frostyblue wrote: ↑Sat Jan 19, 2019 2:56 amYou save $39,077 in interest by putting an down an extra $50k. If you instead invest that $50k in a 30yr bond (today's yield ~3.1%, 1.2% less than the mortgage rate we're assuming), you get an extra $74,948 at maturity.
Re: Mortgage Observation  when it's better to invest at lower rate
And, it's really just as simple as once you put the extra $50k down, you never once pay 4.3% interest on that money.
The total interest paid on a mortgage over 30 years is important to look at. But, it's on a shrinking balance mortgage. That's not the same as a constant balance or purchase amount like a bond. You're paying interest on $350k, and then $349k, and so on.
I'm sure others can explain what I'm trying to say better than I... I'm pretty simple.
The total interest paid on a mortgage over 30 years is important to look at. But, it's on a shrinking balance mortgage. That's not the same as a constant balance or purchase amount like a bond. You're paying interest on $350k, and then $349k, and so on.
I'm sure others can explain what I'm trying to say better than I... I'm pretty simple.
Re: Mortgage Observation  when it's better to invest at lower rate
I would select option 1 above  20% down. I rather have the 50K liquid in Taxable/Roth IRA for flexibility than in the real property that I cannot access easily. I would try to trim the interest by paying down 30 year note sooner.frostyblue wrote: ↑Sat Jan 19, 2019 2:56 amHello all 
Apologize for this long winded post but I thought some might find these calculations helpful  they weren't obvious to me until I ran them and please point out errors if you see them.
Intuition would say it's always better to reduce your mortgage vs. invest the extra cash  as long as your mortgage rate is higher than your forecast investment rate. I wanted to share an important scenario in which this is not true, it's when you are choosing your down payment.
Assume a 4.3% rate, 30yr mortgage, $500k house (you can adjust these and run different scenarios  also note I'm just using nominal #s for simplicity):
 Put down 20% ($100k), equals $312,615 in interest over the 30yr term
 Put down 30% ($150k), equals $273,538 in interest over the 30yr term.
Re: Mortgage Observation  when it's better to invest at lower rate
That's one reason the analysis is wrong. It's not that you can't reinvest treasury interest or buy a zero coupon which 'reinvests' for itself. It's that the calculation implicitly assumes reinvestment (compounding) on the treasury side but compares that to the difference in total simple interest paid over the life of a $350k v $400k mortgage.chevca wrote: ↑Sat Jan 19, 2019 9:55 amI assume you're talking 30 year treasury bonds here? Aren't they simple interest and not compound interest?frostyblue wrote: ↑Sat Jan 19, 2019 2:56 amYou save $39,077 in interest by putting an down an extra $50k. If you instead invest that $50k in a 30yr bond (today's yield ~3.1%, 1.2% less than the mortgage rate we're assuming), you get an extra $74,948 at maturity.
The other error is using 30 yrs as the term of the investment when the average maturity of principal in a level payment 4.3% mortgage is around 18.5 yrs. The rough but apples to apples comparison to the $39k savings in simple interest w/ the smaller mortgage would be 18.5*.0294*$50k=$27k more simple interest from the treasury with the larger mortgage. 2.94% being the approximate 18.5 yr point on the treas curve expressed as APY. A more sophisticated calc would take into account reinvestment on *both* sides, would give a fairly similar relative result...because you lose money borrowing at 4.3% to invest at 2.94%.
As a partial aside, in less obvious cases some people would immediately respond 'what about the tax deduction?' but even before the recent tax changes that wouldn't reverse such a big negative spread. However now a lot of averageish income people will not longer get any *effective* deduction on mortgage interest. If a couple had $6.8k in nonmortgage federal income tax deductions, they'd get no effective federal deduction adding a 4.3% $400k mortgage. The max interest first year would be a little less than .043%*$400k=$17.2k, $24k total, but they could get that using the standard deduction. Even with $16.8k in nonmortgage deductions adding the mortgage would only generate a net $10k benefit over the standard deduction, 10/17.2=58% effective deductibility of mortgage interest, but 100% of the treasury interest would be taxable. State tax could change the picture but typically fairly slightly, sometimes not at all (my state has no mortgage int deduction, several states have no income tax).

 Posts: 3
 Joined: Tue Oct 09, 2018 12:34 am
Re: Mortgage Observation  when it's better to invest at lower rate
Yes, sorry I used compound interest with the 30yr bond example, not simple. Even if you use a 3.1% simple return, the $50k delivers $46,500 in interest over 30yrs (before tax, which is an important point to note), exceeding the $39,077 saved by putting the $50k towards a larger down payment.
At a 2.5% compound rate over 30years, which is probably pretty reasonable (converts to a ~3.46% simple return, still ~84bps below the 4.3% mortgage rate), the result is $51,852 in investment profit (again, before tax) at the end of the 30yr term  exceeding mortgage interest savings by ~$12.8k
Note that I'm not advocating for either scenario here. I personally would rather put the extra money towards a bigger down payment. The scenarios I've run above were just counterintuitive to me.
JackoC  I see your point regarding the average maturity of principal on the mortgage being less then 30yrs. But the point of this analysis is just to compare the amount of interest you'll end up paying on the 30yr mortgage in the larger vs. smaller down payment scenarios. The difference is $39,077 (at least with the example I'm using). My point is only that if you take the extra down payment money (in this case $50k) and put it into an investment that has a lower return than your mortgage rate  you can potentially still come out ahead.
The rationale being that with the smaller down payment, you end up making larger principal payments due to your larger mortgage and your mortgage paydown is catching up with the larger down payment/smaller mortgage scenario.
But again  as noted in the original post  if you reinvest the majority of the money you save from making smaller payments on the smaller mortgage, you will come out ahead by putting down more money. You just have to make sure you will be reinvesting the majority of this money, if you opt to spend a big chunk of it, you might have been better off with the smaller down payment
At a 2.5% compound rate over 30years, which is probably pretty reasonable (converts to a ~3.46% simple return, still ~84bps below the 4.3% mortgage rate), the result is $51,852 in investment profit (again, before tax) at the end of the 30yr term  exceeding mortgage interest savings by ~$12.8k
Note that I'm not advocating for either scenario here. I personally would rather put the extra money towards a bigger down payment. The scenarios I've run above were just counterintuitive to me.
JackoC  I see your point regarding the average maturity of principal on the mortgage being less then 30yrs. But the point of this analysis is just to compare the amount of interest you'll end up paying on the 30yr mortgage in the larger vs. smaller down payment scenarios. The difference is $39,077 (at least with the example I'm using). My point is only that if you take the extra down payment money (in this case $50k) and put it into an investment that has a lower return than your mortgage rate  you can potentially still come out ahead.
The rationale being that with the smaller down payment, you end up making larger principal payments due to your larger mortgage and your mortgage paydown is catching up with the larger down payment/smaller mortgage scenario.
But again  as noted in the original post  if you reinvest the majority of the money you save from making smaller payments on the smaller mortgage, you will come out ahead by putting down more money. You just have to make sure you will be reinvesting the majority of this money, if you opt to spend a big chunk of it, you might have been better off with the smaller down payment
Last edited by frostyblue on Sat Jan 19, 2019 1:04 pm, edited 1 time in total.
Re: Mortgage Observation  when it's better to invest at lower rate
The return on making extra mortgage principle payment is the interest rate of the loan. Period. This has been discussed hundreds of times on here. Every once in a while someone will post a thread trying to prove against it even though the math is quite simple.
The direct comparison is straight between the interest rates on the investment and the mortgage. You are twisting the math much more than it needs to be. Mortgages are simple interest calculation. For some reason people get confused with amortization schedules and think that mortgages are alien math.
The direct comparison is straight between the interest rates on the investment and the mortgage. You are twisting the math much more than it needs to be. Mortgages are simple interest calculation. For some reason people get confused with amortization schedules and think that mortgages are alien math.
Re: Mortgage Observation  when it's better to invest at lower rate
OP, what you're really doing is comparing a $350k vs a $400k debt pay down to buying a 30 year bond. Those aren't really comparable, but they are... if that makes sense.
When you put an extra $50k down, you really save 4.3%. I.E. you never, never pay any interest on that money. You save that on closing day. Do you know anything that comes close to that in one day?
It's often called a return, but you really save the interest you would have paid when you throw any extra at a mortgage. The return or saving is simply the interest rate of the mortgage for that money. There's no way 4.3 loses to 3.1... and a taxable 3.1. I forget where I saw the saying but it was something like, you almost always pay taxes on the interest you earn... you never pay taxes on the interest you save.
Not to mention, I don't think buying a 30 year bond at 3.1% right now is a very wise decision anyway.
When you put an extra $50k down, you really save 4.3%. I.E. you never, never pay any interest on that money. You save that on closing day. Do you know anything that comes close to that in one day?
It's often called a return, but you really save the interest you would have paid when you throw any extra at a mortgage. The return or saving is simply the interest rate of the mortgage for that money. There's no way 4.3 loses to 3.1... and a taxable 3.1. I forget where I saw the saying but it was something like, you almost always pay taxes on the interest you earn... you never pay taxes on the interest you save.
Not to mention, I don't think buying a 30 year bond at 3.1% right now is a very wise decision anyway.
Re: Mortgage Observation  when it's better to invest at lower rate
This is a net present value problem. You cannot get the right answer without doing an NPV spreadsheet. The mortgage professor site has lots of calculators that may help.
Among other things:
The original analysis seems to either ignore the $50,000 put into the house altogether, or assume the rate of return on that will be zero. The presentation is too simple to tell. You are not "paying" $50,000 to save on interest. You are investing $50,000 in the house, avoiding the interest on the mortgage and getting the rate of return on the house.
Taxes:
Depending on the rest of your finances, the mortgage interest may be deductible. But even if it is not, there are other tax considerations.
The return on the Treasury bond will be taxable every year.
The capital gain on the extra $50,000 that you put into the house will not be taxed until you sell the house. Meanwhile, all the gains compound pretax, so they are worth more than the T bond return, which is reduced each year by the income taxes you pay every year.
At the worst, you could end up paying taxes at the capital gains rate when you sell. Since you can exclude $250,000 in capital gains ($500,000 for a couple) you might be able to sell without paying any taxes at all. All that compound interest completely escapes taxation. If you keep the house to death your heirs get a stepped up basis.
Rates of return:
You can oversimplify and assume that you can reinvest the annual AFTER TAX interest income from the T bond at the same rate as the current rate. But since you are reinvesting only a part of the T bond interest, your rate of return will be well below the nominal rate paid by the bonds.
If you get the same rate of return (after tax) on the bond as you do (tax deferred and perhaps tax free) on the house and the mortgage interest rate (after tax) was the same rate, then it would be a wash.
If the mortgage rate is higher than the pretax return on the T bonds, you cannot get there.
Do an NPV spreadsheet or look for a calculator.
Among other things:
The original analysis seems to either ignore the $50,000 put into the house altogether, or assume the rate of return on that will be zero. The presentation is too simple to tell. You are not "paying" $50,000 to save on interest. You are investing $50,000 in the house, avoiding the interest on the mortgage and getting the rate of return on the house.
Taxes:
Depending on the rest of your finances, the mortgage interest may be deductible. But even if it is not, there are other tax considerations.
The return on the Treasury bond will be taxable every year.
The capital gain on the extra $50,000 that you put into the house will not be taxed until you sell the house. Meanwhile, all the gains compound pretax, so they are worth more than the T bond return, which is reduced each year by the income taxes you pay every year.
At the worst, you could end up paying taxes at the capital gains rate when you sell. Since you can exclude $250,000 in capital gains ($500,000 for a couple) you might be able to sell without paying any taxes at all. All that compound interest completely escapes taxation. If you keep the house to death your heirs get a stepped up basis.
Rates of return:
You can oversimplify and assume that you can reinvest the annual AFTER TAX interest income from the T bond at the same rate as the current rate. But since you are reinvesting only a part of the T bond interest, your rate of return will be well below the nominal rate paid by the bonds.
If you get the same rate of return (after tax) on the bond as you do (tax deferred and perhaps tax free) on the house and the mortgage interest rate (after tax) was the same rate, then it would be a wash.
If the mortgage rate is higher than the pretax return on the T bonds, you cannot get there.
Do an NPV spreadsheet or look for a calculator.
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Re: Mortgage Observation  when it's better to invest at lower rate
I just want to say that I find these threads very helpful when trying to learn how to calculate these things myself. Thanks to OP for asking, and thanks to the responders who have explained where the initial calculation was incorrect.
Re: Mortgage Observation  when it's better to invest at lower rate
It was an interesting one to bring up. At first, I scanned quick, looked at the numbers and thought, really, that's awesome. Then I thought about it more and, nah, 4.3 to 3.1, can't be...
Re: Mortgage Observation  when it's better to invest at lower rate
No, you don't make money because of the point you say you see. A given extra dollar you borrow via the mortgage is available to finance other investments for an average of around 18.5yrs, not 30 yrs. Now that you've corrected for compound v simple interest, you are still making the mistake of calculating interest paid on a borrowing for 18.5 yrs (that's the 39k) but comparing it to interest earned for 30 yrs. Of course that's going to look good...but it isn't reality. You can't borrow money for 18.5 yrs and invest it for 30 yrs.frostyblue wrote: ↑Sat Jan 19, 2019 12:56 pm
JackoC  I see your point regarding the average maturity of principal on the mortgage being less then 30yrs. But the point of this analysis is just to compare the amount of interest you'll end up paying on the 30yr mortgage in the larger vs. smaller down payment scenarios. The difference is $39,077 (at least with the example I'm using). My point is only that if you take the extra down payment money (in this case $50k) and put it into an investment that has a lower return than your mortgage rate  you can potentially still come out ahead.
The rationale being that with the smaller down payment, you end up making larger principal payments due to your larger mortgage and your mortgage paydown is catching up with the larger down payment/smaller mortgage scenario.
Or, back to the very simple conclusion you can draw from looking at the rates, you can't make money borrowing at 4.3% to invest at 3.1%. There's no double secret reverse thing about mortgages that makes that obvious principal not apply. Borrowing at a higher rate than you invest at loses money.