Mortgage math.
15 vs 30 year, points, and when to refinance.
A 30-year mortgage at 7% on a $400,000 loan costs approximately $558,000 in total interest. Here is how the math works, when a 15-year makes sense, what points actually buy you, and the break-even on refinancing.
US-only. 30-year fixed-rate mortgages are a US-specific product. Other countries use variable-rate, shorter-term, or balloon-payment structures that change the math.
Every mortgage payment is split between principal (reducing the balance) and interest (the lender's fee). Early years are mostly interest. The 30-year buys flexibility; the 15-year saves enormous interest. Mortgage points are a prepaid rate buy-down with a break-even period in years. Refinancing is worth it only when the cost recoups within your remaining time in the home.
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.
- Monthly payment: approximately $2,661 (principal + interest)
- Total paid over 30 years: approximately $958,000
- Total interest: approximately $558,000
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 SALTState and Local Tax (SALT)The federal deduction for state income taxes, property taxes, and local taxes, currently capped at $10,000 per year.Full definition 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.
- 1 point = $4,000 paid at closing.
- Typical rate reduction: approximately 0.25% per point (varies by lender and market).
- Break-even: $4,000 divided by monthly payment savings = months to recoup.
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.
- Current rate: 7%. New rate: 5.5%. Remaining balance: $380,000.
- Refinancing costs: $9,000.
- If monthly savings = $400: $9,000 / $400 = 22.5 months (about 2 years).
- If you plan to stay 5+ years, refinance makes sense. If you are moving in 2 years, do not.
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% APRAnnual Percentage Rate (APR)The yearly cost of borrowing money, shown as a percentage.Full definition 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.
- Consumer Financial Protection Bureau. Owning a Home. · consumerfinance.gov/owning-a-home/process.
- Freddie Mac. Primary Mortgage Market Survey · freddiemac.com/pmms. Weekly average mortgage rates.