Mortgage Comparison Calculator

Two offers, one table

You have two mortgage quotes in front of you. One has a slightly better rate, the other has a slightly better something else, and staring at two PDFs is not helping.

This puts them in one table. Give it the amount, term and rate for each, and it lays out the monthly payment, the number of payments, the payoff date, the total interest and the total paid for both, in adjacent columns.

Seeing them side by side does something that reading them one after the other does not. A quarter point of rate is abstract on its own. Next to the alternative, with the total interest printed underneath, it stops being abstract.

Filling in both columns

Three boxes per mortgage, six in total.

1. Mortgage Amount. What you would be borrowing under that offer. The loan, not the house price.
2. Mortgage Term. Years to repay.
3. Interest Rate. The quoted interest rate for that offer, as a percentage.

Fill in Mortgage 1, fill in Mortgage 2, press Calculate. The results table appears with both columns filled and a Total Savings row at the bottom.

The most useful discipline here is to change exactly one thing between the two columns. If the amount and the term are identical and only the rate differs, every row in the output is telling you about the rate. Change two things at once and you have a result but no explanation.

What it runs on each side

Both columns get the same treatment, run independently. For each one:

Monthly payment = L × i ÷ (1 - (1 + i)^-n)

where L is that mortgage amount, i is that rate divided by 100 and then by 12, and n is that term multiplied by 12.

Then total paid is the payment multiplied by the number of months, and total interest is that total minus the amount borrowed.

The payoff date starts from today's month and counts forward by the number of payments, which is why the two columns show different payoff dates when the terms differ.

The Total Savings row subtracts one total paid from the other and puts the difference under whichever offer is cheaper overall. That row has a subtlety worth its own section, and it is coming up next.

The comparison it does best

Same loan, same term, two rates. This is the question the tool answers most cleanly, and it is also the most common one, because it is what happens when you get quotes from two lenders on the same house.

Take 300,000 over 30 years, quoted at 6.5 percent by one lender and 6.0 percent by another.

Half a percentage point is 97.55 a month. Which sounds like the cost of a phone contract, and it is easy to shrug at.

Across the full term it is 35,118.90.

That gap between how small the monthly difference feels and how large the lifetime difference is turns out to be the single most useful thing this table does. Rate shopping is boring and it is worth doing anyway, and the bottom row is the argument.

Reading the Total Savings row properly

The bottom row shows the difference between the two totals and places it under the cheaper column. It is a straight subtraction, and it means exactly what it says only when the two offers are otherwise identical.

Here is where it gets slippery. Suppose you put a 300,000 loan in one column and a 200,000 loan in the other. The table dutifully reports a Total Savings of around 227,544.

Nothing is wrong with that arithmetic. Borrowing 100,000 less does cost around 227,544 less across thirty years, which is a genuinely interesting fact about compound interest. It is just not a comparison of two offers. It is a comparison of two different amounts of debt.

So the row is doing what it says: total paid on one side, total paid on the other, difference between them. Whether that difference is a saving depends entirely on whether you were choosing between the two things in the first place.

The rule of thumb: if the two Mortgage Amount boxes hold the same number, the Total Savings row is a real answer. If they do not, read it as a difference and think about what is producing it.

When the two columns are different lengths

Comparing a 30 year offer against a 15 year offer is a legitimate thing to want, and the table handles it, but the bottom row needs reading with your eyes open.

Take 300,000, offered at 6.5 percent over 30 years or 6.0 percent over 15 years, which is roughly how lenders price the two.

Total Savings comes out at 226,950.78 for the 15 year deal, which is true and is not the whole story. The 15 year option also costs 635.37 more every month for fifteen years.

So read those two rows together. The bottom row tells you which is cheaper overall. The payment row tells you which you can actually live with. When they disagree, the payment row usually wins, because a cheaper mortgage you cannot afford in month seven is not cheaper.

The payoff date row is worth a glance here too. Same start month, and the two dates fifteen years apart, which makes the trade concrete in a way the numbers alone do not.

Getting the inputs to match

Both columns want the interest rate rather than the APR. The interest rate drives the payment. APR is a wider figure that folds in points, origination charges and broker fees, and typing it here produces a payment higher than the one you will be billed.

Which raises the obvious question: if APR captures fees and the interest rate does not, how do the fees get into this comparison?

Through the Mortgage Amount box, when the fees are financed. If one lender rolls 4,000 of charges into the loan and the other does not, then the two offers genuinely have different loan amounts, and putting 304,000 against 300,000 is the honest comparison rather than a mistake. That is one of the few cases where the two amount boxes should differ on purpose.

If the fees are being paid in cash at closing instead, they never touch the loan, so they never touch this table. Note them separately and add them to whichever side is charging them.

Two more things that live outside these six boxes. Mortgage insurance, if one offer needs it and the other does not, which can be worth more per month than the rate difference. And escrow for taxes and insurance, which is the same house either way and so cancels out.

What decides it once the table is a tie

Sometimes both columns come out close enough that the numbers stop deciding. A few things then matter more than the last hundred of total interest.

The APR on each Loan Estimate. This is the figure designed for exactly this comparison, since it folds each lender's own fees into a single rate. It sits on page three. If the interest rates are near identical and the APRs are not, the gap is fees.

Whether the rate is locked, and for how long. A quote that expires in ten days and one that holds for sixty are not equivalent offers even at the same rate.

Prepayment terms. If you expect to overpay or to move within a few years, the offer that lets you do so without penalty may beat the one with a marginally better rate.

Run the table first, because it tells you whether the difference is large enough to care about. If half a percentage point is worth 35,000 to you, that is worth another phone call to the lender who came second.

Questions people ask

Should both mortgage amounts be the same?

Usually yes. Matching amounts is what makes the comparison meaningful. The exception is when one lender is financing fees into the loan and the other is not, in which case the different amounts are the real difference between the offers.

What does the Total Savings row actually mean?

It is the difference between the two total paid figures, shown under the cheaper one. It is a genuine saving when the two offers are otherwise identical, and simply a difference when they are not.

Do I enter the interest rate or the APR?

The interest rate, since that is what the payment is calculated from. Keep the APRs to one side and use them as a separate check on fees.

How much is half a percentage point worth?

On 300,000 over 30 years it is 97.55 a month and 35,118.90 across the full term. Small monthly, large lifetime, which is exactly why it is worth shopping.

Does this include mortgage insurance or property tax?

No. Both columns show principal and interest. If one offer requires mortgage insurance and the other does not, add that separately, because it can outweigh a rate difference.

Can I compare a 15 year offer against a 30 year one?

Yes. Read the monthly payment row alongside the total, because the shorter term will nearly always win on total cost and lose on monthly affordability.

Why do the payoff dates start from this month?

The table counts forward from the current month for both offers, so they share a start date and the difference between the two payoff dates is purely the difference in term.

What if I have three offers?

Run the best two, then run the winner against the third. Two rounds and you have your answer, and it is a fast way to shortlist.

References

The payment relation used in both columns is the standard actuarial amortisation equation, with the quoted annual rate treated as a periodic rate multiplied by the number of periods in a year, as set out in Regulation Z. The guidance on comparing competing offers using principal and interest, on the distinction between an interest rate and an APR, and on where each appears in the standard disclosures follows the Consumer Financial Protection Bureau.

1. Consumer Financial Protection Bureau (CFPB), Regulation Z, Appendix J to Part 1026: Annual Percentage Rate Computations for Closed-End Credit Transactions. https://www.consumerfinance.gov/rules-policy/regulations/1026/j/
2. Consumer Financial Protection Bureau (CFPB), Regulation Z, § 1026.22 Determination of Annual Percentage Rate. https://www.consumerfinance.gov/rules-policy/regulations/1026/22/
3. Consumer Financial Protection Bureau (CFPB), On a Mortgage, What Is the Difference Between My Principal and Interest Payment and My Total Monthly Payment? https://www.consumerfinance.gov/ask-cfpb/on-a-mortgage-whats-the-difference-between-my-principal-and-interest-payment-and-my-total-monthly-payment-en-1941/
4. Consumer Financial Protection Bureau (CFPB), What Is the Difference Between a Mortgage Interest Rate and an APR? https://www.consumerfinance.gov/ask-cfpb/what-is-the-difference-between-a-mortgage-interest-rate-and-an-apr-en-135/
5. Consumer Financial Protection Bureau (CFPB), When Can I Remove Private Mortgage Insurance (PMI) From My Loan? https://www.consumerfinance.gov/ask-cfpb/when-can-i-remove-private-mortgage-insurance-pmi-from-my-loan-en-202/