The Homo Economicus Rent vs. Buy Calculator

The following should not be construed as financial advice.

When people decide to rent or purchase a home, they often focus on financial liabilities (what they pay to others) and overlook the economic costs of capital. Several rent vs. buy calculators are available online, including the well-known New York Times calculator. These calculators provide valuable insights but often greatly underestimate the opportunity costs of the road not taken, from both the renter’s and homeowner’s perspectives.

Our calculator is not meant to reflect the typical behavior of renters versus homeowners, but rather considers what an optimizing homo economicus might do. Renters may have the opportunity to invest what would have otherwise gone toward a down payment and closing costs, as well as the monthly savings they gain from not having a mortgage. On the other hand, at some point, a homeowner’s monthly mortgage payment is likely to be lower than monthly rent, and it also offers the potential benefit of property appreciation.

To investigate this potential trade-off, we developed a calculator (below) that enables users to estimate the opportunity cost of taking out a mortgage under various scenarios. Values are listed in nominal terms and in inflation-adjusted (real terms) using 2025 dollars. While aggregate numbers can be inferred, users should compare apples to apples properties for best results; that is, buying a 2-bedroom house should be compared to renting a 2-bedroom house. Due to variations in how property taxes are calculated and assessed, this calculator also assumes the tax is a fixed effective rate. However, several factors can influence property taxes depending on the locality. In California, for example, Proposition 13 limits the annual increase in a property’s taxable base to 2 percent, meaning that long-time homeowners pay significantly lower rates than if they had purchased the same property today. For added accuracy, rental insurance can be added to the monthly rent cost, while homeowners’ insurance can be calculated and added to the maintenance percent. The average annual cost of rental insurance is approximately $171, or $14.25 per month. The average homeowners’ insurance cost in the U.S. is approximately $2,802 per year, or $234 per month for a dwelling coverage of $300,000.

You can view the calculator in full screen using this link, which we recommend for mobile users.

Historical Rates

For reference, here are some historical rates and figures.

• Median historical 30-year fixed mortgage rate since 1971: 7.3 percent
• Most recent median home price (Q2 2025): $410,800
• Average 1-bedroom home price (2024-2025): $245,581
• Average 2-bedroom home price (2024-2025): $265,738
• Average 3-bedroom home price (2024-2025): $325,051
• Average 4-bedroom home price (2024-2025): $475,424
• Median rent (2025): $1,300
• Average studio rent (2026): $1,694/month
• Average 1-bedroom rent (2026): $1,625/month
• Average 2-bedroom rent (2026): $1,881/month
• Average 3-bedroom rent (2026): $2,361/month
• Annualized home price growth since 1967: 5.2 percent
• S&P 500 annualized returns since 1957: 10.54 percent
• State-by-state rental prices for a 1-bedroom apartment
• Average inflation rate since 1929: 3.2 percent
• Average effective property tax rate: 0.87 percent

Primary Input Parameters:

• \( P \): Home purchase price
• \( d \): Down payment percentage (as decimal)
• \( r_m \): Annual mortgage interest rate (as decimal)
• \( T \): Loan term in years
• \( r_{pt} \): Annual property tax rate (as decimal)
• \( r_{pmi} \): Annual PMI rate (as decimal)
• \( r_{main} \): Annual maintenance cost rate (as decimal)
• \( r_h \): Annual home value growth rate (as decimal)
• \( R_0 \): Initial monthly rent
• \( r_r \): Annual rent growth rate (as decimal)
• \( r_i \): Annual investment return rate (as decimal)
• \( r_{inf} \): Annual inflation rate (as decimal)
• \( H \): Time horizon in years
• \( C_{buy} \): Buying closing costs (as percentage of \( P \))
• \( C_{sell} \): Selling closing costs (as percentage of final home value)
• \( D \): Security deposit

Derived Values

Initial Calculations:

Down payment amount:
\[ DP = P \cdot d \]

Loan amount:
\[ L = P – DP \]

Monthly mortgage payment (using standard amortization formula):
\[ M = L \cdot \frac{r_m/12 \cdot (1 + r_m/12)^{12T}}{(1 + r_m/12)^{12T} – 1} \]

Annual property tax (initial):
\[ PT_0 = P \cdot r_{pt} \]

Monthly PMI (if \( d < 0.2 \)):
\[ PMI_{monthly} = \begin{cases}
L \cdot r_{pmi}/12 & \text{if } d < 0.2 \\
0 & \text{otherwise}
\end{cases} \]

Annual maintenance cost (initial):
\[ MC_0 = P \cdot r_{main} \]

Buying closing costs:
\[ CC_{buy} = P \cdot C_{buy} \]

Mortgage Phase (Years 1 to \( T \))

For each year \( t \) where \( 1 \leq t \leq T \):

Home value appreciation:
\[ H_t = H_{t-1} \cdot (1 + r_h) \quad \text{with } H_0 = P \]

Annual property tax:
\[ PT_t = H_t \cdot r_{pt} \]

Annual maintenance cost:
\[ MC_t = H_t \cdot r_{main} \]

Annual PMI (applies until equity reaches 20% of original home value):
\[ PMI_t = \begin{cases}
PMI_{monthly} \cdot 12 & \text{if } \frac{H_t – RL_t}{P} < 0.2 \text{ and } d < 0.2 \\
0 & \text{otherwise}
\end{cases} \]

Remaining loan balance:
\[ RL_t = RL_{t-1} – (12M – RL_{t-1} \cdot r_m) \quad \text{with } RL_0 = L \]

Market rent:
\[ R_t = R_0 \cdot 12 \cdot (1 + r_r)^{t-1} \]

Renter’s Monthly Investment:

The renter invests the difference between the buyer’s monthly costs and rent:
\[ I_{rent} = M + \frac{PT_t + MC_t + PMI_t}{12} – \frac{R_t}{12} \]

Renter’s investment balance (compounded monthly):
\[ IB_{rent,t} = IB_{rent,t-1} \cdot (1 + r_i/12) + I_{rent} \quad \text{with } IB_{rent,0} = DP – D \]

Buyer’s Investment Balance:

During mortgage phase, the buyer typically doesn’t invest additional funds:
\[ IB_{buy,t} = IB_{buy,t-1} \cdot (1 + r_i) \quad \text{with } IB_{buy,0} = 0 \]

Opportunity Cost Phase (Years \( T+1 \) to \( H \))

For each year \( t \) where \( T+1 \leq t \leq H \):

Home value appreciation, property tax, and maintenance costs continue as before.

PMI is zero (mortgage is paid off).

Market rent continues to grow:
\[ R_t = R_0 \cdot 12 \cdot (1 + r_r)^{t-1} \]

Buyer’s Monthly Investment:

The buyer now invests the difference between market rent and their housing costs:
\[ I_{buy} = \frac{R_t}{12} – \frac{PT_t + MC_t}{12} \]

If \( I_{buy} > 0 \):
\[ IB_{buy,t} = IB_{buy,t-1} \cdot (1 + r_i/12) + I_{buy} \]

If \( I_{buy} \leq 0 \) (property tax + maintenance ≥ rent):
\[ IB_{buy,t} = IB_{buy,t-1} \cdot (1 + r_i) \]

Renter’s Investment:

The renter continues investing the same fixed monthly amount \( I_{rent} \) from the mortgage phase:
\[ IB_{rent,t} = IB_{rent,t-1} \cdot (1 + r_i/12) + I_{rent} \]

Final Net Worth Calculations

At time horizon \( H \):

Selling closing costs:
\[ CC_{sell} = H_H \cdot C_{sell} \]

Home equity:
\[ E = H_H – RL_H – CC_{sell} \]

Net worth for buyer:
\[ NW_{buy} = E + IB_{buy,H} \]

Net worth for renter:
\[ NW_{rent} = IB_{rent,H} + D \]

Inflation Adjustment

To express results in today’s dollars (accounting for purchasing power):

Inflation factor:
\[ F_{inf} = (1 + r_{inf})^H \]

Real net worth for buyer:
\[ RNW_{buy} = \frac{NW_{buy}}{F_{inf}} \]

Real net worth for renter:
\[ RNW_{rent} = \frac{NW_{rent}}{F_{inf}} \]

Key Assumptions

• All growth rates are compounded annually
• Investments compound monthly at the specified annual rate
• PMI applies only when equity is below 20% of original home value
• Renter invests a fixed monthly amount throughout the entire period
• Security deposit is returned in full at the end (no interest)
• No transaction costs for buying/selling investments
• No tax considerations (deductions, capital gains, etc.)

Decision Metric

The better financial option is determined by comparing the real net worth values:

\[
\text{Better Option} = \begin{cases}
\text{Buying} & \text{if } RNW_{buy} > RNW_{rent} \\
\text{Renting} & \text{otherwise}
\end{cases}
\]

The magnitude of the difference \( |RNW_{buy} – RNW_{rent}| \) indicates the financial advantage of the better option.