The Largest Contract You Will Ever Sign

The payment is an annuity, and the interest lives in the term

A mortgage payment is an annuity: a level amount that exactly exhausts the loan over the term at the contract rate. The formula is P × r ÷ (1 − (1 + r)^−n), with r the monthly rate. On $400,000 at 6% over thirty years that is $2,398; over fifteen years it is $3,375. Same rate, same lender, same house — and a total interest bill of $463,000 against $208,000. The reason the difference is so large is that early payments are mostly interest. In the first month of the thirty-year loan, $2,000 of the $2,398 is interest and only $398 reduces the balance. Shortening the term accelerates the principal, and because interest is charged on the remaining balance, the saving compounds for the life of the loan. That is why the term matters more than a small difference in rate, and why a lower rate on a thirty-year loan is not automatically better than a higher rate on a fifteen-year one. Two features of a mortgage are worth more than the rate comparison people fixate on. The first is **prepayment without penalty**, which is an option: you can make the fifteen-year payment on a thirty-year loan and get a similar interest saving while retaining the flexibility to stop. The second is **fixed versus variable**: a fixed rate removes an entire class of risk from the household’s biggest liability, and the value of that insurance is easy to underestimate until rates move. One loan, two terms — 30-year at 6.0%: $2,398 a month · $463,000 of interest · 15-year at 6.0%: $3,375 a month · $208,000 of interest · The trade: $977 a month for fifteen years, to save ≈ $255,000 ← · What protects the trade: a buffer and a payment that survives a bad year A fifteen-year payment is only better if it is genuinely affordable through a job loss or a pay cut. A payment that forces a sale or a refinancing at the worst moment is not a saving — which is exactly what the buffer in PF3 is for.

A point is a bet on how long you keep the loan

Discount points are prepaid interest: you pay cash at closing and the lender reduces the rate. One point on $400,000 costs $4,000 and, in this lesson’s numbers, cuts the rate from 6.00% to 5.75%, which is worth roughly $1,000 a year on a $400,000 balance. The payback is therefore about four years, and everything about the decision depends on whether the household will still have the loan four years later. That turns the point into a break-even problem, the same shape as the deductible in PF11. If the household stays a decade, the point is clearly profitable; if it refinances or sells in two years, the $4,000 is gone. In a period of falling rates, paying points to buy a lower rate is a bet against your own future refinancing — which is a strange position to take voluntarily. And the cash used for points cannot be used to keep the buffer intact, which is the constraint that should decide more of these questions than the rate table does. The same logic applies to the loan type. An adjustable rate trades a lower initial payment for the risk that the payment rises exactly when the household is least able to manage it; it can be right for someone who genuinely expects to move, and wrong for the household that plans to stay, because the exposure is to the one variable nobody controls. Reading the maximum possible payment rather than the introductory one is the discipline. The point, priced — Cost of one point: $4,000 at closing · Effect on the rate: 6.00% → 5.75% · Worth per year: ≈ $1,000 on $400,000 · Break-even: about 4 years ← The payback is not a subtle calculation — it is saving ÷ annual benefit. What makes it a decision is the horizon, which is why a household that may move should generally not pay points.

The method for any large purchase

Four steps carry every large decision, and they are the same four whether the object is a house, a car or a renovation. First, compare **totals, not instalments**: the fifteen-year mortgage, the car with the longer loan and the renovation financed over five years all win on the instalment and can lose badly on the total. Second, price the **alternative use of the money** — a 6% mortgage prepaid is a guaranteed 6%, which is a high hurdle for a portfolio to clear, and a low-rate loan is a much lower one. Third, make sure the purchase does not **consume the buffer**. A down payment that empties the emergency fund is a plan that has traded one risk (a shock) for another (a payment you cannot miss). The buffer is the thing that keeps the purchase survivable, which is why the affordability check belongs before the offer, not after. Fourth, decide the **contract terms** deliberately: term, fixed or variable, points, and the renewal or refinancing date diarised so it is reviewed rather than forgotten. Households routinely spend more time choosing a kitchen than choosing the loan that will outlive it, and the loan is the part that cannot be replaced cheaply. Four steps, every purchase — 1. Total cost: not the monthly payment · 2. The alternative: what else the money could do, after tax · 3. The buffer: never consumed by a purchase · 4. The contract: term, rate type, points, and a review date ← Zero-per-cent financing is rarely zero: the discount for paying cash is often larger than the interest saved. Compare the financed total against the cash price, not against the sticker.

What buying a house actually costs

The purchase price is the beginning. Closing costs run a few per cent and are paid in cash; property taxes, insurance and maintenance continue for as long as you own it, and maintenance alone is commonly budgeted at about 1% of value a year. Furnishing, moving and the first-year surprises are real line items too. A household comparing a mortgage payment against rent is usually comparing an incomplete number against a complete one. The honest comparison also has a horizon. Ownership pays off over years, because the transaction costs at both ends need time to be spread; a household that might move in two years is often better renting, even when the monthly numbers look close. And the non-financial factors are not noise: a home that fixes housing cost for decades, that cannot be ended by a landlord, and that a household wants to live in has a value the arithmetic does not capture — but it should be a reason, not a substitute for the arithmetic. Finally, affordability. The payment is one line in the household’s list (PF2), and it has to survive the rest of it. A payment that consumes nearly all the flexible line leaves nothing for saving, and the savings rate is what the whole plan depends on. The test is not what a lender will approve — it is what the household can pay in a bad year while still funding its buffer and its retirement. The costs around the price — Up front: down payment, closing costs, moving · Every year: taxes, insurance, maintenance at ≈ 1% of value · At the end: selling costs, which argue for staying several years · Against rent: which is a complete number, not a partial one ← No purchase should be judged in isolation. The house competes with the retirement contribution and the buffer for the same dollars, and the plan that loses those to keep a payment low is not a cheaper plan.

Refinancing is the same trade, entered again

A refinance replaces one loan with another, and it is the discount-point problem with a much larger fee attached. Closing costs on a refinance commonly run two to five per cent of the balance, so the decision is whether the payment saved repays those costs before the household moves again. The arithmetic is the point read generalised: break-even in months is closing cost divided by monthly saving. That same $400,000 loan refinanced from 6.00% to 5.00% saves about $239 a month, so $8,000 of costs pays back in roughly 33 months — and a household that expects to move in two years has bought nothing at all. The trap is the term. Restarting a thirty-year clock lowers the payment by more than the rate change alone implies, which makes the refinance look better than it is: the instalment falls partly because the rate fell and partly because thirty years of amortisation begin again, so more interest is paid in total and the payoff date moves out. The honest comparison holds the term constant — a loan with twenty-five years remaining should be compared against a new loan over twenty-five years, not against a fresh thirty — and it reads the two totals rather than the two payments. A lower payment spread over a longer term is not a saving; it is a smaller loan for longer, and whether that is good depends entirely on what the freed cash does. Costs can also be financed rather than paid, which raises the balance and hides the price of the transaction inside the new loan. Paying them in cash preserves the buffer test from earlier in the lesson, and financing them is defensible only when the new rate is materially below the one being retired. A **cash-out** refinance is a different instrument again: it turns home equity into cash at the mortgage rate, which can be the cheapest borrowing a household has access to and is also the fastest way to convert a buffer into a payment that cannot be missed. The rules that keep it honest are the ones from the rest of the lesson. Compare totals on a fixed term. Keep the buffer out of the transaction. And diarise the new loan’s rate, balance and review date exactly as the original was diarised, because the refinance has reset the clock — and the reviews with it. • Break-even in months is closing costs ÷ monthly saving, so the horizon decides. • Compare totals on a constant term, or the restarted clock hides the extra interest. • Keep the buffer out of the transaction, and diarise the new loan exactly as the old one was. Break-even = closing costs ÷ monthly saving. The number that decides it is not the rate you left, nor the rate you got, but how long you will actually keep the loan.

Sources

• Mortgage amortisation and the annuity payment formulaStandard annuity arithmetic: P × r ÷ (1 − (1 + r)^−n)
• Discount points and the break-even holding periodConsumer Financial Protection Bureau — mortgage points guidance
• Responsible lending and affordability measuresCFPB — ability-to-repay and qualified mortgage rules
• The buy-versus-rent comparisonStandard ownership-cost analysis; practitioner guidance