Methodology

The question

Every dollar of principal you prepay saves interest at your mortgage rate. If your loan costs 3%, paying it down early is a 3% investment. When Treasuries yield more than your loan costs, even after tax, there is a second choice: keep the cash, buy Treasuries that mature just before each monthly payment is due, and let them make the payments.

The calculator puts the two choices side by side and compares what you end up with on the loan’s original payoff date, when both mortgages are gone. The keep-the-cash choice also leaves the money accessible: you can sell a Treasury, but you can’t un-pay a mortgage.

The two options

Both options set aside the same monthly payment. Whatever isn’t going to the mortgage is invested at the “return on freed-up cash” you choose (4.50% to start), after tax.

Pay it down

Your cash goes to principal today, up to the balance. Your payment stays the same, so the loan ends early; most lenders work this way unless you ask for a recast. You keep paying the full payment until the loan is gone, then invest that amount every month. Cash beyond the balance is invested.

Keep the cash and buy the ladder

Today you buy the funding for your next payments, in order, for as long as your cash lasts (the calculator reports how many payments that is). Each month the ladder covers, the payment you would have made is freed up and invested, less tax on the interest that month’s purchase earned. After the last covered payment you resume paying the lender yourself. Cash left over after the purchases is invested too. If your cash covers every payment, the loan is fully funded.

The comparison

Each option’s result is its investments minus the mortgage balance still owed, on the loan’s original payoff date. The “gain” is the ladder option’s result minus the pay-down option’s. A gain under fifty cents is called a tie.

The rates we use

Treasury yields

We use the end-of-day Treasury constant-maturity yields published by the Federal Reserve (statistical release H.15) and distributed by FRED, for 1, 3 and 6 months and 1, 2, 3, 5, 7, 10, 20 and 30 years, and for the 4-month bill when FRED has it. They are collected on weekdays at 7:00 and 18:00 Eastern, and FRED posts them about a business day late, so the page always shows the date the yields are as of. If we can’t load today’s rates, the calculator says so and doesn’t calculate. It never falls back to sample data.

In the default funding mode the curve prices the 26-week bill and the payments from 13 onward; the first six payments are priced at the money market yield. Each of those is discounted at the yield for that point in time, found by straight-line interpolation between the published maturities, and held flat beyond the first and last. The yield is treated as an annual rate compounded twice a year, so a payment due t years from now costs (1 + yield/200)^(−2t) of its amount today.

The money market yield

FRED doesn’t carry the money market fund we use, Schwab’s SWVXX, so its 7-day yield is entered by hand from schwab.com by the site’s owner. It is shown with its own date, and marked “out of date” after 14 days; the calculation still runs with the last yield.

Mortgage averages

The weekly Freddie Mac Primary Mortgage Market Survey averages for 15- and 30-year loans are shown for reference with Freddie Mac’s permission. They are not used in the calculation, which uses the rate on your loan.

How the payments are funded

The fund’s 7-day yield is a simple annual rate compounded daily, so a month of growth is (1 + yield/36,500)^(365/12) − 1. The bill’s proceeds earn no fund growth before payment 7, which is paid at once; that is the cautious way to count it.

A money market fund is not insured or guaranteed, and its yield can change. Treasury bills and STRIPS are backed by the U.S. government; their prices move if you sell before maturity, so the plan assumes you hold each one until it matures.

What you would actually buy

• Prices are estimated from the current yield curve. Actual quotes vary by broker and by day, and the calculator counts no commissions or spreads.
• The money market deposit and the bill assume you buy at the start of the month. Buying later means slightly less money market growth. If a new 26-week bill would mature after payment 7, buy the nearest existing bill that matures before it.
• STRIPS mature quarterly, so longer rungs are bought at the nearest earlier maturity and held in T-bills until each payment.
• The CSV buy list lists each purchase with the date it should mature by, and the assumptions behind it.

Taxes

The interest each payment’s funding earns is taxed at the “tax rate on bond interest” (24% to start), in the month the payment falls due. Money market dividends and the bill’s discount in the first year are taxed at the same rate. The return on freed-up cash is taxed at that rate too.

• Treasury interest is exempt from state and local income tax, so you may enter a federal-only rate. Money market dividends are not exempt. If your rate is federal-only, state tax on them is not counted, which slightly favours the ladder.
• In practice STRIPS are taxed on accrued interest each year, even though they pay nothing until maturity. That moves some tax earlier than the calculator shows.

The mortgage-interest deduction

By default the calculator assumes you don’t deduct mortgage interest (you take the standard deduction). If you itemize, turn on “I deduct mortgage interest”. Keeping the loan then looks better, because paying it down also gives up some of the deduction.

How it is applied

For each month and each option, the interest you pay (the opening balance times the monthly rate) is multiplied by your deduction rate and by the share of the balance that is within the limit. That tax saving is added to the option’s investments in the same month, and grows from there. With the pay-down option the balance is smaller, so the saving is too. The deduction rate starts at your bond-interest rate and can be changed; use your combined federal and state rate if you deduct on both.

The $750,000 and $1,000,000 limits

Interest is deductible only on up to $750,000 of mortgage debt for loans taken out from December 16, 2017, and up to $1,000,000 for loans taken out before then. Above the limit, only the matching share of the interest counts. The calculator picks the limit like this:

• $1,000,000 if you tick “Refinanced a pre-2017 loan”, whatever the start month.
• $1,000,000 if you entered a start month (the month of your first payment) of January 2018 or earlier. A loan closed before December 16, 2017 can have its first payment as late as January 2018. A start month we worked out ourselves from your final payment month and term is not used for this.
• $750,000 otherwise, including a first payment in February 2018, which is ambiguous; we take the cautious side.

Savings are credited monthly, a simplification of getting them back at tax time. The result assumes you itemize and that all your interest is above the standard deduction. When the deduction is on, the first tile compares the ladder’s after-tax yield with what your mortgage effectively costs after the deduction. See IRS Publication 936 for the rules.

Your loan

A fixed-rate, fully amortizing loan is fixed by any three of its balance, rate, monthly payment (principal and interest) and final payment month. Enter three and the calculator works out the fourth with the standard amortization formulas. Month zero is the current month in New York, and that month’s payment counts as already made. If you enter all four, it uses your balance, rate and payment, and tells you if the payoff date they imply is more than two months from the one you entered. The original term is optional: it can help find the final payment month, and it is used as a sanity check.

The breakeven rate

The breakeven mortgage rate is the rate at which the two options tie, holding your balance and payoff date fixed. At a higher rate paying down wins. The search covers rates from 0.25% to 15%. When no rate in that range splits the outcomes, the tile says “Above 15%” or “Below 0.25%”. When paying down wins at some rates and not at others, as can happen when your cash clears the loan in a payment or two, it says there is no single rate.

What it leaves out

• Fixed-rate, fully amortizing loans only: no adjustable rates, interest-only loans, escrow, mortgage insurance, recasts or prepayment penalties.
• Tax rules beyond the rates you enter, including any state rules, and any change in the law.
• Constant assumptions: the money market yield, your tax rate and the return on freed-up cash stay the same for the whole period.
• Transaction costs and the bid-ask spread on Treasuries, and anything that happens if you sell before maturity.
• Your own situation: other debts, your emergency fund, or how comfortable you are holding bonds instead of owing nothing.

Sources and questions

• Treasury yields: Board of Governors of the Federal Reserve System, H.15, via FRED (Federal Reserve Bank of St. Louis).
• Mortgage averages: Freddie Mac Primary Mortgage Market Survey, reprinted with permission.
• SWVXX 7-day yield: Charles Schwab, entered by the site’s owner.

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