Questions that come up in scenarios related to buying or refinancing a home:
- Is mortgage A better than mortgage B?
- Each mortgage may be amortized over a different duration (e.g., 15 vs. 30 years)
- Given that I'm part-way through mortgage C, should I refinance to mortgage D?
Setting aside the emotional aspects, there is almost always a clear answer based on the Net Present Value (NPV) calculation of the cashflows related to the principal, interest, and loan fees.
For question #1, the Loan Estimate document would include an APR value that can be the basis for a comparison if the loan durations being compared are identical. It's not immediately obvious how to use the APR to compare loans of different durations. Also, the APR cannot be used to answer question #2 related to a refinance.
Sometimes the total (undiscounted) cashflow of interest payments over the span of the loan is used for the comparison, but as you'll see below that may give you the wrong answer.
I've made available a Mortgage Comparison Template.ods file that implements the calculations referred to in this post.
Discount rate
For the NPV calculation you'll need an appropriate discount rate (aka, opportunity cost). This would be the expected gains on an investment that you'd funnel your cash into if you didn't have to pay the mortgage.
I use a conservative 7.1 %/year (nominal rate which includes inflation).
If your investments are more aggressive, then a nominal rate of 9-10 %/year may be a reasonable choice.
Buying a house
Inputs needed:
- Starting principal
- Interest rate (%/year)
- Amoritization duration (years)
- Amortization period (usually monthly; to wit 12 periods/year)
- Loan fees (origination fees, title/insurance/deed fees, recording fees, etc.)
- Do not include any escrow amounts for home insurance and/or property taxes as they are not pertinent to the cost-benefit analysis
Set-up your amortization table for each mortgage and then calculate:
Present value of the loan =
NPV of cashflows for principal +NPV of cashflows for interest +Loan fees
Choose the loan that has the lowest present value. That's it.
What if two loans have the same present value?
If I knew I would never refinance again then I could argue that either loan is equally viable; it's a true coin toss.
However, practically speaking, there is always a higher chance that I'll refinance again if it's an environment of falling interest rates. Ergo, personally, I would go with the option that has the lowest fees as that meaningfully lowers the opportunity cost.
To get more confidence, you can run the NPV calculation for 1-yr, 3-yr, 5-yr etc. periods and you will see that the loan with the lowest fees will always be ahead of its competitors (since we assumed that the NPV at the end of the loan period was identical across the options).
Example 1 (30 year loans).
Consider the following two loans for a starting principal of \$332,000.00 which I was offered in Jan-2026. Both loans were for a 30 year duration, with monthly payments.
- Loan #1: 5.875 %/year; loan fees of \$4,717
- Loan #2: 5.990 %/year; loan fees of \$0
- The bank is willing to absorb the loan fees in order to charge me a higher interest
After setting up the amortization tables, the total interest payments (undiscounted) were:
- Loan #1: \$375,003.08
- Loan #2: \$383,817.08
So, I'm paying more in interest with Loan #2 (which would be obvious looking just at the interest rate). Even if I include the \$4,717 of loan fees in Loan #1, it still looks better than Loan #2. Why should I pay more to the bank with Loan #2? Sure looks like I should pick Loan #1.
What about looking at discounted cashflows for the interest? The NPV calculation (using a discount rate of 7.1 %/year) for interest alone is:
- Loan #1: \$190,714.11
- Loan #2: \$194,946.08
Now, if I include the loan fees (\$4,717), Loan #1 is starting to look less attractive than Loan #2. But, to be honest, it's almost even. The difference is only \$485.03.
Adding in the discounted cashflows for the principal in addition to the interest and loan fees gives the full picture:
- Loan #1: \$296,999.29
- Loan #2: \$295,874.45
IOW, Loan #1 is going to cost me \$1,124.84 extra in today's dollars over the course of the mortgage. Thus, Loan #2 wins even though it has a higher interest rate.
Yes, it's still close but the point of this real-life example is that a simplistic view of looking only at (undiscounted) interest payments does not always give the right result.
Example 2 (15 vs. 30 year loans)
The general idea doesn't change if the two mortgages being compared are over different durations. You would still do the same NPV calculation for principal, interest, and loan fees and compare the two products to determine which is better. This is where the oft-repeated notion that a shorter duration mortgage is preferable over one with a longer duration can fail.
Consider the following loan terms for a principal of \$332,000.00 which I was offered in Jan-2026. Both loans had the same loan fees of \$4,717 and were subject to monthly payments.
- Loan #1: 15 year, 5.500 %/year
- Loan #2: 30 year, 5.875 %/year
In terms of (undiscounted) interest payments only:
- Loan #1: \$156,288.79
- Loan #2: \$375,002.93
I would be paying almost twice the amount of interest with Loan #2, suggesting that I should go for Loan #1. This is usually the argument for the shorter duration loans.
However, comparing the NPV of cashflows for principal, interest, and loan fees over the duration of each loan (using a discount rate of 7.1 %/year):
- Loan #1: \$304,655.02
- Loan #2: \$296,947.33
IOW, Loan #1 will cost me \$7,707.69 extra in today's dollars. Thus, Loan #2 is objectively the winner.
Refinancing a mortgage
The idea is the same as before, except here you want to compare the NPV of the remaining cashflows on your current mortage to those of the new (refinanced) mortgage.
When calculating the remaining cashflows on the current mortgage you must ignore past cashflows that have already happened. So, the amortization table should be set-up only for all cashflows pending on the remaining portion of the loan. This should then be compared with the full duration of the refinance option.
Example 3
My current loan is on an initial principal of \$400,000.00 at an interest of 6.490 %/year that I've been paying down for the last 10 years. The outstanding balance is now \$339,019.74 with 20 years left on the mortgage.
I want to compare this to a refinance option on the outstanding balance at 5.875 %/year with refinance fees of \$4,717. (This is the same as Loan #2 from Example 1 above.) A refinance will reset my payment schedule; to wit, I'll carry the mortgage for another 30 years.
From the amortization tables, total interest payments (undiscounted) were:
- Current loan (pending payments only): \$267,136.17
- Refinance option: \$382,934.74
Even without counting the refinance fees, it might look like I should continue with my current loan. However, looking at the NPV (using a discount rate of 7.1 %/year) for principal, interest, and loan fees:
- Current loan (pending interest + principal): \$323,256.49
- \$0 in fees to continue my current loan
- Refinance option (interest + principal + loan fees): \$303,129.85
Now it's obvious that my current loan will cost me \$20,126.64 more in today's dollars. Thus, refinance is the objectively better option here.
If I have the opportunity to refinance again in the future, I would run the exact same calculation. It totally doesn't matter what loan fees were paid in the past as we only look at future cashflows - and that's all that matters.
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