Theoretical Question about Mortgage Interest Rate

I hope you guys can confirm whether I am missing anything. I had a discussion in Reddit with Fatezeroking, who claimed to have a Master's in Finance, CFA, and Institutional investor. $10 billion in assets under management. Whether that is true is not relevant.

Please judge who is right. I am not talking about whether it is good or bad to pay off mortgage early. I am asking whether it makes any sense to convert a 30 year mortgage at 3.0% interest rate, and convert it to a an effective rate of 1.4%. The conversation below described how he got to the 1.4% (In brief, n = 30; pv = 300000; pmt = 0; fv = -(300000 + 155332.36); Compute Interest rate = 1.40%).
He is using that 1.4% rate and basically said you can get higher return than 1.4% in treasuries today and thus even if your portfolio is 100% treasury securities, you would be better off not paying off a 3.0% mortgage early but instead invest in treasury securities. My point is the 1.4% is meaningless. It does not consider the timing of the payments, rather it assumes you are making one lumpsum payment at the end of the 30 years. The actual interest rate would be very close to 3.0% (monthly interest rate: n = 360; pv = 300000; pmt = 1,264.81; fv = 0)

It was a heated discussion, but now I really just want to know if he has a point.

HERE IS A SUMMARY OF THE DISCUSSION
Fatezeroking:
Fully paying off a mortgage early is silly.
Earth…
Only an idiot pays off a 3% amortizing mortgage early. Would you invest $150,000 at 1.5%? No then don't pay off a mortgage early, because that's what you're doing. I can get a better return in treasuries.
Finance 101.
R30871
Mortgage interest rates are almost always higher than treasury yields. Finance 101.
fatezeroking
I'm talking about right now. Mortgage rates are 3% on an effective basis, 3% is 1.5% effective rate. At 1.5%… You can earn more in treasuries. Don't like treasuries? No worries, you have a S&P 500 ETF with a 40 year average return of 11.83% which is always higher than mortgage rates.
I have a Master's in Finance. CFA. Institutional investor. $10 billion in assets under management.
Do I need to school you in math? I'd be more than happy to. I love speaking high level finance to commoners.
You probably don't even know what an effective rate is. Huh? That's finance 102.
R30871
You cannot get to 1.5% effective rate from 3% mortgage rate. Stop humiliating yourself. Perhaps go back to elementary school. LOL
fatezeroking
4%. Ready to get schooled. This is the difference between a high school education and a master's in finance.
Ex: $300,000 mortgage at 3% over 30 years.
Step 1. Compute total interest over 30 year.
n = 360
I = 3/12
pv = 300000
fv = 0
Compute payment = $1,264.81
Amortize total interest = $155,332.36
Step 2. Compute annual simple interest
($155,332.36 / 300,000) / 30 = 1.7259%
Well look at that, based on simple interest we are already at 1.73% interest. You can verify this by simply taking 1.73% of $300,000 and multiplying my 30. It'll match the total interest over the life of the loan.
But wait! there's more, formed as an investment, we must take into account the effects of compounding.
Step 3. Compute rate at which $300,000 will earn total interest over 30 years.
n = 30
pv = 300000
pmt = 0
fv = -(300000 + 155332.36)
Compute Interest rate = 1.40%
Therefore, by paying off a 300,000 mortgage to save $155k in interest, you will have invested your money at a 1.4% rate.
If you want to verify 1.4% is right you use the FV formula. 300000 * (1 + 0.014)30 = $455,260.43 - $300,000 = $155,260.43 off by a $100 from rounding.
Sorry buddy, I really didn't want to have to do that to you.
R30871
You are a complete idiot. Business transactions are all done using compound interest. Simple interest is mainly used for easy calculations, especially those for as single period or less than a year. We are talking about a 30 mortgage. It is ridiculously stupid to convert to simple interest. Don't tell anyone where you got your master degree. It is really going to embarrass your school. LOL.
fatezeroking
You didn't read the post huh. It's in both simple and compound.
Buying a home is never done in compound interest btw. It's always simple. Lol which is why the buy side is simple and the investing side is compound.
You sir have been schooled. You literally have no defense. Take this FAT L
Oh and all interest rates are ALWAYS quoted as simple interest lmfaooooooooo.
This clown just got schooled online bad. If you don't know how mortgages work, you shouldn't be commenting. You clearly didn't understand how amortization worked. Rookie mistake
fatezeroking
Just to laugh at you harder than I am. I have another formula for you.
Say you have $300,000 to pay off your entire mortgage. Do you invest or pay the mortgage and invest the savings?
Invest scenario: $300,000 * (1 + (.11/4))^ 30 * 4 = $7.78 million
VS pay off mortgage and invest $1264.81 * ((1+(.11/4))4 * 30) / (.11/4) = $1.15 million.
I guess you should have took that cheap leverage huh?
R30871
You are just making the numbers up. ~11% return. You forgot one thing. We are not here to chase returns. It is the combination of return and risk that is important. There is no free lunch in investing. If yes, everyone would put their money on the stocks with the highest expected return. However you have to remember every investment out there in this world has an investor. The bond market is actually significantly bigger than the stock market. Investors are dominated by institutional investors. If return is all it matters, why are there so much investments (and mostly institutional investors) in the bond market. We all know the stock market is expected to have higher return. the answer is higher expected return comes with higher rosk. You don't seem to even consider risk in your comments. You really should just stop, take a loss, and stop humiliating yourself.
fatezeroking
11% is the average return of the S&P 500 over the past 40 years. It's not a made up number lol....  Stocks are less risky over a long horizon. Its extremely hard to lose money in the long-run.
I'm an institutional investor btw. I'm managing a $10 billion portfolio. I'm a bond trader. Most investors are in bonds because they are use for wealth management. You can't invest $10 billion in stocks easily... there's no liquidity. A pension fund can easily buy $10 billion in fixed income assets in a single day.
Don't humiliate yourself any further...
You would rather invest at a 1.4% rate rather than stocks and bonds? You can only blame yourself on why you're broke.
R30871
I have already demonstrated multiple times your 1.4% is complete garbage. If you haven't got it by now, you probably will never understand. LOL.

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Comments (4)

  • Partner in RE - Comm
Nov 17, 2021 - 3:05am

the only reason to pay off a mortgage early is psychological imo. Not having a mortgage will compel you to take bigger risks and reap bigger rewards. this assumes you have enough cash flow to do both, but if you don't, I would get on a IO LIBOR+125-200bps floater, get your payment down, and pile the difference between that and what your payment would be on a 15-30 year fixed into the market every month.

Nov 17, 2021 - 5:20pm

r30871

Step 2. Compute annual simple interest
($155,332.36 / 300,000) / 30 = 1.7259%
But wait! there's more, formed as an investment, we must take into account the effects of compounding.
Step 3. Compute rate at which $300,000 will earn total interest over 30 years.
n = 30
pv = 300000
pmt = 0
fv = -(300000 + 155332.36)
Compute Interest rate = 1.40%

This makes zero sense, it totally ignores time value of money. There is a correct way to do this type of comparison (present values or IRR of the differential cash flows), this is just silly. The interest is paid over the life of the loan, and the first calculation to find PMT using 3% confirms 3% as the IRR of the loan (by definition). No way to get around the cost of the loan being 3% annualized, that's literally how the PMT is calculated.  

Nov 17, 2021 - 5:38pm

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