Mortgage math.
15 vs 30 year, points, and when to refinance.

Section 1 · How a mortgage actually works

A mortgage is a loan where the house serves as collateral. If you stop paying, the lender can foreclose and take the house.

The amortization schedule

• Every payment is split between principal (reducing the loan balance) and interest (the lender's fee).
• In the early years, most of each payment is interest.
• In the later years, most is principal.

The house must appreciate significantly to justify that interest cost, or you need to hold long enough that principal reduction and appreciation combine favorably.

Section 2 · 15 vs 30 year

On the same $400,000 loan:

• 30-year at 7%: payment approximately $2,661/month. Total interest approximately $558,000.
• 15-year at 6.5% (typically a lower rate): payment approximately $3,485/month. Total interest approximately $227,000. Interest savings vs 30-year: approximately $331,000.

The case for 30-year

• Lower required payment gives more cash-flow flexibility.
• You can invest the payment difference. If investments return more than your mortgage rate, you come out ahead.
• The mortgage interest deduction (limited by SALT and itemization rules) makes the effective rate slightly lower.

The case for 15-year

• Forced equity building.
• Substantially lower total interest paid.
• Paid off 15 years earlier.
• Lower interest rate.

The honest math

The 30-year-and-invest-the-difference strategy wins IF you actually invest the difference AND your investments return more than your after-tax mortgage rate. Most people do not invest the difference; they spend it. If behavioral discipline is a concern, the 15-year forced-equity approach may produce better real outcomes.

Section 3 · Mortgage points

A mortgage point is 1% of the loan amount paid upfront to reduce the interest rate.

If you plan to stay in the home longer than the break-even period, buying points makes financial sense. If you might sell or refinance before break-even, skip the points.

Rule of thumb: if break-even is over 5 years, points are a risky bet on rate stability. Get specific point-to-rate trade-offs from your lender before committing.

Section 4 · Refinancing math

When to refinance: your break-even period is shorter than your expected remaining time in the home.

Break-even calculation

• Refinancing costs: typically 2 to 5% of the loan amount ($8,000 to $20,000 on a $400,000 loan).
• Monthly savings from lower payment: $Y.
• Break-even: refinancing costs divided by $Y = months.

Cash-out refinance

Borrow more than you owe. Take out equity as cash. Higher rate than rate-and-term refinance.

• Makes sense: when you have high-interest debt to pay off (credit cards at approximately 21% APR vs mortgage at 7%) or a specific capital need (renovation that adds value).
• Does not make sense: for consumption or for investment in volatile assets where the borrowed-money risk amplifies the potential downside.

verify×DON'T TRUST, VERIFYClaim: Mortgage refinancing typically costs 2 to 5% of the loan amount.Verify at: CFPB Owning a Home guide ↗Closing-cost ranges vary by state and lender. CFPB documents typical components.

Section 5 · The 5% rule: rent vs buy on apples-to-apples math

The standard rent-vs-buy comparison is wrong. People compare a mortgage payment to rent, conclude that buying is "cheaper," and stop there. A mortgage payment is not an unrecoverable cost. Most of an early-year payment is interest, but the principal portion goes to building equity. Comparing the full mortgage payment to rent overstates the cost of owning relative to renting.

The right comparison is total unrecoverable costs of owning vs total unrecoverable costs of renting. Rent is fully unrecoverable. The unrecoverable costs of owning are property tax, maintenance, and the opportunity cost of capital tied up in the home.

The three unrecoverable costs of owning

• Property tax: roughly 1% of home value per year. Varies by state and county (Texas and New Jersey run higher; Hawaii and Alabama lower) but ~1% is a reasonable national anchor.
• Maintenance: roughly 1% of home value per year, on average. Includes roof replacement, HVAC, water heater, paint, repairs. Highly lumpy in any single year, but averages out.
• Cost of capital: roughly 3% of home value per year. This is the opportunity cost of the down payment plus equity. The money tied up in your home could otherwise be invested in stocks at a higher expected return. The cost of debt (mortgage interest) and the cost of equity (foregone stock returns) are both real economic costs.

The reverse calculation

If you are renting at a known monthly cost, you can solve for the equivalent home price. Multiply rent by 12, divide by 5%:

• $3,000/month rent × 12 / 0.05 = $720,000 equivalent home value
• $2,500/month rent × 12 / 0.05 = $600,000 equivalent home value

Renting for $3,000/month is financially equivalent to owning a $720,000 home in terms of unrecoverable costs. If similar homes in the same neighborhood are selling for more than $720,000, the rent is the better deal financially.

When the rule needs adjustment

• More conservative portfolio: if your investment alternative is bonds rather than 100% stocks, the cost of equity capital drops, lowering the rule to roughly 4%.
• Tax-advantaged investing capacity exhausted: if you have already maxed your 401(k), Roth IRA, and HSA, additional stock investments are taxed annually, reducing the after-tax cost of equity. The rule shifts toward 4-4.5%.
• High property tax states: in NJ, IL, NH, TX, the property tax piece can be 2% rather than 1%, pushing the total closer to 6%.
• Older homes or HOAs: maintenance and condo/HOA fees can push the maintenance piece above 1%.

What the rule does not account for

• Forced savings: mortgage principal is forced equity-building. A renter who fails to invest the difference loses the comparison automatically.
• Hedging: owning hedges you against rent inflation in your specific area. If you want to stay in one city, owning protects you from being priced out.
• Transaction costs: buying and selling a home costs 8-10% of the value (closing, inspection, agent commissions, transfer taxes, moving). Short holding periods make owning much worse.
• Mortgage interest deduction: for households that itemize, the deduction reduces effective unrecoverable cost. Most filers take the standard deduction post-2017 TCJA, eliminating this benefit.

The rule is an approximation, not a verdict. It is the right starting point for the financial comparison. The full decision also weighs lifestyle, geographic stability, and the behavioral fact that most renters do not actually invest the cash flow difference. See Mortgage vs Rent calculator for a per-situation projection.