Lesson 6 of 16 · Level 2: Intermediate
Rent or Buy a Home? How to Run the Numbers on a Mortgage
- ⏱ 12 min read
- ❓ 4 review questions
- ✍️ Exercise with solution
In this lesson
- How a mortgage works: amortization, 15- vs. 30-year terms, fixed vs. adjustable rates.
- What goes into your real housing payment: principal, interest, taxes, insurance, PMI and HOA dues.
- How much house you can afford using the 28/36 guideline and your down payment.
- How to compare buying and renting fairly with the "unrecoverable costs" method.
- Whether to make extra principal payments, and when PMI goes away.
"Renting is throwing money away" might be the most repeated line in personal finance, and it's only half true. Owning has costs you never get back too: mortgage interest, property taxes, insurance, maintenance and the return your down payment could have earned elsewhere. The right answer depends on the numbers, your job stability and how long you plan to stay. This lesson gives you a method to run them yourself.
Mortgage rates, property taxes, insurance premiums and closing costs vary a lot by state, by lender and over time. The rates in this lesson (6.5% for a 30-year fixed and 5.75% for a 15-year fixed) are illustrative, chosen to teach the method. Always use the actual Loan Estimate a lender gives you, and compare offers by APR, not just the interest rate.
How a mortgage works
A mortgage is a long-term loan secured by the home. Most U.S. buyers choose a fixed-rate loan with a fixed monthly principal-and-interest payment. Early on, most of each payment is interest; over the years, more and more goes to paying down the balance (principal). That schedule is called amortization.
Example: a $400,000 home with 20% down ($80,000) and a $320,000 loan.
| Loan | Rate (illustrative) | Monthly principal and interest | Total interest over the loan |
|---|---|---|---|
| 30-year fixed | 6.50% | $2,022.62 | ≈ $408,142 |
| 15-year fixed | 5.75% | $2,657.31 | ≈ $158,316 |
The 15-year payment is $634.69 a month higher (about 31%), but you'd pay roughly $250,000 less interest, partly because 15-year loans usually carry lower rates and mostly because you owe the money for half as long. The 30-year loan buys flexibility: a lower required payment, with the option to pay extra when you can.
Look at where the 30-year payment goes in year one:
- Interest (85.3%) $20,695The bank's fee for lending you the money. You never get it back.
- Principal (14.7%) $3,577Pays down the loan. It becomes home equity, a kind of forced savings.
You can calculate any payment in Excel or Google Sheets. U.S. mortgage rates are annual rates divided by 12:
=PMT(6.5%/12, 360, -320000) → $2,022.62 a month1. What happens if you choose a 30-year mortgage instead of a 15-year one for the same loan amount?
You pay less each month but for twice as long, on a balance that shrinks more slowly. In our example, total interest jumps from about $158,000 to $408,000.
Fixed or adjustable?
- Fixed rate: principal and interest never change. Predictable and the most common choice.
- Adjustable rate (ARM): for example, a 5/6 ARM is fixed for 5 years, then adjusts every 6 months based on an index, within caps. It often starts lower. Ask yourself: could I afford the payment if the rate rose to its cap?
Your real monthly payment: PITI and friends
Lenders look at PITI: principal, interest, property taxes and homeowners insurance, usually collected monthly through an escrow account. Add PMI if you put down less than 20% on a conventional loan, and HOA dues if there's a homeowners association. With $4,000 a year in property taxes and $1,800 in insurance, our 30-year example costs $2,022.62 + $333.33 + $150 = $2,505.95 a month.
How much house can you afford?
- The 28/36 guideline: keep housing costs (PITI) under about 28% of gross monthly income and all debt payments, housing included, under about 36%. To keep $2,505.95 under 28%, you'd want gross income of about $8,950 a month. Lenders may approve more; that doesn't mean you should borrow more.
- Down payment: 20% avoids PMI on a conventional loan. Many buyers put down less: some conventional programs allow as little as 3%, and FHA loans as little as 3.5% with a qualifying credit score, but you'll pay mortgage insurance.
- Closing costs: lender fees, title insurance, appraisal, prepaid taxes and insurance often add 2% to 5% of the loan amount, on top of the down payment.
- Keep your emergency fund intact. Don't drain it for the down payment. A house comes with surprises, starting with the water heater.
2. Your gross income is $7,500 a month. Under the 28% guideline, what's the most you'd want to spend on PITI?
28% × $7,500 = $2,100. $2,700 is the 36% ceiling for all debt payments combined, not just housing.
Buying vs. renting: compare unrecoverable costs
To compare fairly, don't put the mortgage payment next to the rent. Compare what you don't get back in each case:
- Interest
- Mortgage interest (not principal: that's savings).
- Carrying costs
- Property taxes, homeowners insurance, PMI, HOA dues.
- Upkeep
- Maintenance and repairs, often estimated at about 1% of the home's value per year.
- Opportunity cost
- What your down payment and closing costs would earn if invested.
- Rent
- The full monthly rent.
- Insurance
- Renters insurance, usually inexpensive.
- Upkeep
- Usually nothing: major repairs are the landlord's job.
- Flexibility
- You can move at the end of a lease with no selling costs.
Year one of our example ($400,000 home, $80,000 down, $12,000 closing costs, 30-year loan) against renting a similar home for $2,300 a month:
| Unrecoverable cost, year 1 | Buy | Rent |
|---|---|---|
| Mortgage interest | $20,695 | |
| Property taxes (1%) | $4,000 | |
| Homeowners insurance | $1,800 | |
| Maintenance (1%) | $4,000 | |
| Opportunity cost of $92,000 at 5% | $4,600 | |
| Rent ($2,300 × 12) | $27,600 | |
| Renters insurance | $180 | |
| Total | $35,095 | $27,780 |
In year one, renting costs about $7,300 less. So should no one ever buy? Not so fast:
- If the home appreciates 3% a year ($12,000 in year one), buying's net cost drops to about $23,100, below rent.
- Rents tend to rise; your fixed principal and interest don't.
- Each year, the interest share of your payment shrinks and the principal share grows.
- Owning brings stability and the freedom to renovate, which don't show up in the table.
- But selling costs (agent commissions, transfer taxes, closing costs) take a meaningful slice of the price, which is why buying rarely pays off if you move within a few years.
If renting a comparable home costs clearly less than the unrecoverable costs of owning, and you're not confident you'll stay at least five to seven years, renting and investing the difference is usually the more flexible choice, and often the cheaper one. If you plan to stay many years, the payment is comfortable and your job is stable, buying tends to make more sense.
3. In a rent-vs-buy comparison, which part of the mortgage payment is NOT an unrecoverable cost?
Principal works like forced savings: it increases the share of the home you own. Interest, taxes and insurance are gone for good.
Extra payments and PMI
Most U.S. mortgages let you pay extra principal; check your loan documents for any prepayment penalty. Extra payments shorten the loan and cut total interest. Your payment stays the same unless you ask the lender to "recast" the loan. Before prepaying a 6.5% mortgage, make sure your emergency fund is complete, you're getting any 401(k) match, and you have no higher-rate debt.
If you put down less than 20%, know your PMI rights: you can ask your servicer in writing to cancel PMI once your balance is scheduled to reach 80% of the home's original value (or earlier through extra payments), and it must generally end automatically when the balance is scheduled to hit 78%, as long as you're current on payments.
4. You have a credit card at 24% APR and a mortgage at 6.5%. You get a $3,000 bonus. Which should you pay first?
Each dollar that pays down the card saves 24% a year; each dollar on the mortgage saves 6.5%. That's the avalanche method from lesson 4.
Practice exercise
Jasmine and Luis, in Raleigh, North Carolina, earn $9,000 a month gross. They're looking at a $350,000 home with 10% down. The loan: $315,000, 30-year fixed at 6.5%. Estimated property taxes are $3,150 a year, insurance $1,500 a year and PMI 0.5% of the loan per year (illustrative).
- Calculate the monthly principal and interest with
PMT, then the full payment. - Does it pass the 28% test? How much room is left for other debt under 36%?
- When could they first request PMI removal, and when would it end automatically?
See solution
=PMT(6.5%/12, 360, -315000)= $1,991.01. PMI: 0.5% × $315,000 ÷ 12 = $131.25. Taxes: $262.50. Insurance: $125. Total: $2,509.76 a month.- 28% of $9,000 = $2,520, so it passes, just barely. Under 36% ($3,240), all their other debt payments combined should stay under about $730 a month.
- 80% of the original value is $280,000; on schedule, the balance reaches it around payment 95 (almost 8 years), when they can request cancellation. Automatic termination at 78% ($273,000) comes around payment 109 (about 9 years). Extra principal payments, or a higher appraisal in some cases, can get them there sooner.
Takeaway: the payment fits on paper, but with almost no margin. A smaller loan or a bigger down payment would make the budget far less fragile.
Summary
- A 30-year mortgage lowers the payment but can more than double the total interest of a 15-year loan.
- Your real payment is PITI, plus PMI and HOA dues if they apply.
- Keep housing near 28% of gross income and all debt near 36%, and budget for closing costs.
- Compare buying and renting by unrecoverable costs, not by mortgage payment vs. rent.
- Extra principal payments save interest; PMI can be canceled at 80% and generally ends at 78% loan-to-value.
Next lesson: Compound Interest and Inflation: Why to Invest and Why to Start Early. You'll see the two forces acting on your money every day, and why time is your biggest advantage.
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