Mortgage vs Rent: The Mathematical Decision Framework (With Real Numbers)

This is not a "follow your heart" decision. This is a spreadsheet decision. Let me show you the math.

I've analyzed the buy-vs-rent question across New York, London, and Tokyo. The answer depends on exactly 5 variables. Get these right and the decision becomes obvious.

The 5 Variables

1. Home price — What you'd pay
2. Mortgage rate — Your borrowing cost
3. Rent for equivalent property — What you'd pay to rent
4. Investment return — What your down payment could earn elsewhere
5. Time horizon — How long you plan to stay

The Price-to-Rent Ratio

The quickest way to evaluate: divide home price by annual rent.

Price-to-Rent Ratio = Home Price / Annual Rent

Ratio	Verdict
< 15	Strong buy signal
15-20	Neutral — depends on other factors
> 20	Strong rent signal

Real Market Examples

City	Median Home Price	Annual Rent	Ratio	Verdict
Detroit	$180,000	$14,400	12.5	Buy
Austin	$450,000	$24,000	18.8	Neutral
San Francisco	$1,200,000	$36,000	33.3	Rent
London	£650,000	£24,000	27.1	Rent
Tokyo	¥45,000,000	¥1,800,000	25.0	Rent

The Full Calculation

Use a Mortgage Calculator to determine monthly payments, then compare:

Buying Costs (Monthly)

• Mortgage payment (principal + interest)
• Property tax (1-2% of home value / year)
• Insurance ($100-300/month)
• Maintenance (1% of home value / year)
• HOA fees (if applicable)

Renting Costs (Monthly)

• Rent
• Renter's insurance ($15-30/month)
• Opportunity cost of down payment (invested elsewhere)

The Break-Even Horizon

The critical question: how long do you need to stay for buying to beat renting?

At 7% mortgage rate, $500K home, 20% down, $2,500/month rent:

• Break-even: 7.3 years
• After 10 years: buying saves $47,000
• After 30 years: buying saves $312,000

But at 7% mortgage, $1.2M home, $4,000/month rent:

• Break-even: 14.2 years
• After 10 years: renting saves $89,000
• After 30 years: buying saves $156,000

The Hidden Costs of Buying

1. Closing costs — 2-5% of home price (buyer side)
2. Selling costs — 5-6% agent commission when you sell
3. Moving costs — $500-5,000 per move
4. Maintenance surprises — New roof: $15K. New HVAC: $8K.
5. Property tax increases — Can rise 3-5% per year

The Hidden Benefits of Renting

1. Flexibility — Move for a job, lifestyle, or relationship
2. No maintenance responsibility — Call the landlord, don't pay
3. Predictable costs — Rent increases are capped in many markets
4. Investment diversification — Down payment invested in index funds

The Decision Framework

Buy if:

• Price-to-rent ratio < 15
• You plan to stay 7+ years
• You have 20% down payment
• Your total housing cost < 28% of gross income

Rent if:

• Price-to-rent ratio > 20
• You might move in < 5 years
• You prefer investment diversification
• Your market has rent control

Run your specific numbers with our free Mortgage Calculator — includes property tax, insurance, and break-even analysis.