Calculator overview
Inputs and outputs
This summary comes from the calculator's published input and output contract.
Inputs
- Mortgage Rate (required)
-
Unit fraction Default 0.06 Range At least 0
About this input
The rate on the loan, as an annual percentage. Held constant for the whole period.
- Property Tax Rate (required)
-
Unit fraction Default 0.012 Range 0 to 1
About this input
Annual property tax as a share of the home's value. It scales with the value as the home appreciates, which is why it is a rate rather than a dollar amount. Rates vary by county, not just by state.
- Maintenance Rate (required)
-
Unit fraction Default 0.01 Range 0 to 1
About this input
What you spend keeping the home up, as a share of its value each year. One percent is the usual rule of thumb and is optimistic for an older house. This is the cost renters do not carry and owners routinely forget.
- Monthly Rent (required)
-
Unit currency/month Default 2200 Range At least 0
About this input
What the comparable rental costs today. Comparable matters: a rental you would actually accept, not the cheapest listing you can find.
- Selling Cost Rate (required)
-
Unit fraction Default 0.06 Range 0 to 0.99
About this input
What it costs to sell, as a share of the sale price: agent commission, transfer taxes, repairs asked for at inspection. Five or six percent is usual, and omitting it is the second most common way a calculator flatters buying.
- Years Held (required)
-
Unit years Default 7 Range 1 to 40
About this input
How long before you sell or move. The answer is more sensitive to this than to anything else, because selling costs are paid once and are spread over however long you stayed.
- Purchase Price (required)
-
Unit currency Default 400000 Range At least 0
About this input
What the home costs. Tax and maintenance are computed against the home's value as it changes, so this figure drives more than the loan.
- Return Volatility (required)
-
Unit fraction Default 0.08 Range 0 to 1
About this input
The same, for the return on money not tied up in the house. Eight percent is in the range of a diversified equity portfolio and is far larger than the appreciation uncertainty, which is most of the reason the answer is a range at all: the renter's side of this comparison is the volatile one. Zero means certain.
- Annual Insurance (required)
-
Unit currency/yr Default 1800 Range At least 0
About this input
Homeowner insurance for a year, as a dollar amount. Held flat rather than scaled, because premiums track rebuild cost rather than market value.
- Annual Rent Growth (required)
-
Unit fraction Default 0.03 Range At least -1
About this input
How fast rent rises each year. Applied once a year on the anniversary rather than smoothly, because that is how a lease renewal works.
- Annual Appreciation (required)
-
Unit fraction Default 0.03 Range At least -1
About this input
How fast the home gains value. Applied continuously through the year. Over a long run this has tracked inflation more closely than most people expect, so a large number here should be a deliberate assumption, not a default.
- Annual HOA
-
When omitted Blank
Unit currency/yr Default Not set Range At least 0
About this input
Optional. Association or condo dues for a year. Leave blank if there are none. They do not build equity and they rise, so on a condo they can decide the comparison on their own.
- Investment Return (required)
-
Unit fraction Default 0.06 Range At least 0
About this input
What money you do not tie up in the house would earn each year. It applies to the down payment and to every month's difference in cost, whichever side is cheaper that month. Setting it to zero answers a different question: what if the money simply sat there.
- Loan Term Years (required)
-
Unit years Default 30 Range 1 to 40
About this input
How long the mortgage runs. It does not have to match how long you stay; the model sells the home and repays whatever is left.
- Appreciation Volatility (required)
-
Unit fraction Default 0.03 Range 0 to 1
About this input
How unsure you are about the home's yearly gain, as one standard deviation. This is as much a part of the answer as the gain itself, which is why it is asked for rather than assumed. The model runs the whole comparison across eleven appreciation levels and eleven return levels and reports how often buying wins. Quote it per YEAR: it is scaled to your holding period by the square root of time, because the model applies one constant rate across the period and a long-run average is less uncertain than a single year. Three percent is a reasonable starting point for a residential market. Set it to zero to say you are certain, and the grid collapses along that axis.
- Down Payment (required)
-
Unit currency Default 80000 Range At least 0
About this input
Cash you put in. It is the single most important input here, because if you rent it stays invested instead, and that is the comparison most calculators leave out.
Outputs
- Sale Proceeds After Costs
-
Unit currency
About this output
What the sale actually puts in your pocket: the value, less the costs of selling, less the loan.
- Table1 Futures Column Axis
-
No unit declared
About this output
The values across the top of the grid: what the money you do not tie up earns each year. Read a column to hold this fixed. The middle entry is your own figure.
- Table1 Futures Column Input
-
Unit fraction
About this output
Machinery, and NOT an input. The same for the column axis: Excel substitutes into it while filling the grid, and the rest of the time it mirrors Investment_Return.
- Owner Side Account
-
Unit currency
About this output
Money the OWNER invested, in any month where rent cost more than owning. Usually zero, and worth watching when rent is high: a model that credits only the renter is quietly assuming this money went nowhere.
- Probability Buying Wins
-
Unit fraction
About this output
The share of the simulated futures in which buying leaves you better off. Blank until you enter both uncertainties. Read it as a shape rather than a forecast: it is the chance under YOUR assumptions about how uncertain those two numbers are, and it says nothing about whether those assumptions are right.
- Renter Net Worth
-
Unit currency
About this output
The down payment, invested, plus every month's saved cost, invested, compounded to the same date. This is what renting leaves you with, and it is the figure most calculators never compute.
- Table1 Futures Values
-
Unit currency
About this output
The body of the grid: the advantage of buying, recomputed for every combination of the two axes. One hundred and twenty-one cells, each one the whole calculation run again. It is a component of the table rather than a result on its own.
- Total Paid Owning
-
Unit currency
About this output
Cash out of pocket while owning, including the down payment. Not a measure of who is better off, because some of it came back as equity; shown so the cash-flow story is visible next to the wealth story.
- Total Paid Renting
-
Unit currency
About this output
Cash out of pocket while renting over the same period.
- Table1 Futures Corner
-
Unit currency
About this output
Machinery. Excel requires the formula being tabulated to sit in the grid's top-left corner, where it means nothing to a reader, so it is formatted away. It holds Advantage_Of_Buying.
- Table1 Futures Row Axis
-
No unit declared
About this output
The values down the left of the grid: how much the home gains each year. Read a row to hold this fixed and vary the other axis. The middle entry is your own figure.
- Table1 Futures Row Input
-
Unit fraction
About this output
Machinery, and NOT an input. Excel substitutes each value from the row axis into this cell while it fills the grid; the rest of the time it mirrors Annual_Appreciation. Change Annual_Appreciation above, never this: the axis is derived from it, so editing the mirror moves the axis while the table walks and the grid comes out meaningless.
- Advantage P90
-
Unit currency
About this output
The advantage in a lucky tenth. The gap between this and the unlucky tenth is the honest width of the answer, and on most inputs it is wide enough to be the finding.
- Break Even Month
-
Unit months
About this output
The first month from which buying is ahead and stays ahead for the rest of the table. Not the first month it merely edges in front: a crossing that later reverses is not a break-even, and this figure is built backward from the last month so one cannot be reported as one. Zero means buying never overtakes renting within the period the table covers.
- Break Even Years
-
Unit years
About this output
The same figure in years, for reading against how long you actually expect to stay. Blank when buying never overtakes.
- Advantage Of Buying
-
Unit currency
About this output
The two differenced. Positive means buying comes out ahead over this period on these assumptions. It is often a smaller number than people expect, and it can change sign on a one-point change in any of the three forecasts.
- Advantage P10
-
Unit currency
About this output
The advantage of buying in an unlucky tenth of the simulated futures: weak appreciation, strong investment returns, or both. If this is comfortably negative, buying carries real downside on your own assumptions.
- Advantage P50
-
Unit currency
About this output
The middle of the simulated futures. It sits near the single-point answer rather than on top of it, because the comparison is not symmetric in the two forecasts.
- Model Status
-
No unit declared
About this output
Reads OK, or explains why the inputs are not valid or why the answer deserves a second look.
- Monthly Payment
-
Unit currency/month
About this output
Principal and interest only. Tax, insurance, maintenance and dues are added separately in the monthly table.
- Owner Cost First Month
-
Unit currency/month
About this output
Everything owning costs in the first month. Compare it against the rent to see how far apart the two choices start.
- Buyer Net Worth
-
Unit currency
About this output
The sale proceeds plus that side account. This is what buying leaves you with at the end of the period.
- Home Value At Exit
-
Unit currency
About this output
What the home is worth on the day you sell, at the appreciation you assumed.
- Loan Balance At Exit
-
Unit currency
About this output
What is still owed then, from the closed-form balance rather than an accumulated schedule.
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Methodology
Purpose and model boundary
Use this calculator to compare buying and renting over the number of years you expect to stay. The common measure is ending net worth, not monthly housing cost. The renter starts with the down payment invested, and each month whichever choice costs less invests the difference. The uncertainty analysis evaluates a weighted grid around the appreciation and investment-return assumptions; entering zero for both volatility inputs makes that analysis deterministic.
This is a comparison model, not a prediction of home prices, rent, or investment returns. Those rates are inputs because they are local and uncertain.
Inputs and units
| Input | Unit | Accepted range | What it means |
|---|---|---|---|
| Purchase Price | $ | Above 0 | Home price at purchase. |
| Down Payment | $ | 0 through Purchase Price | Cash paid toward the purchase. |
| Mortgage Rate | percentage | 0% or more | Annual fixed mortgage rate. |
| Loan Term Years | years | 1–40 | Mortgage term. |
| Property Tax Rate | percentage | 0–100% | Annual property tax as a share of modeled home value. |
| Maintenance Rate | percentage | 0–100% | Annual maintenance as a share of modeled home value. |
| Annual Insurance | $/year | 0 or more | Homeowners insurance. |
| Annual HOA | $/year | 0 or more, or blank | Optional association or condominium dues. |
| Selling Cost Rate | percentage | At least 0% and below 100% | Selling cost as a share of exit value. |
| Monthly Rent | $/month | 0 or more | Starting rent. |
| Annual Rent Growth | percentage | Greater than -100% | Annual change in rent. |
| Annual Appreciation | percentage | Greater than -100% | Expected annual home-price change. |
| Investment Return | percentage | 0% or more | Expected annual return on the renter and owner side accounts. |
| Years Held | years | 1–40 | Time before sale or move. |
| Appreciation Volatility | percentage | 0–100% | Required one-year standard deviation around appreciation; 0% means no appreciation uncertainty. |
| Return Volatility | percentage | 0–100% | Required one-year standard deviation around investment return; 0% means no investment-return uncertainty. |
Annual HOA is optional and ships blank; blank association dues mean no dues. The two volatility inputs are required. Set both to 0% for a deterministic comparison, or enter their one-year standard deviations to model uncertainty.
Governing relationships
Loan principal is Purchase Price minus Down Payment. A level-payment mortgage supplies the monthly principal-and-interest payment, with a zero-rate branch that divides principal evenly across the loan months.
For each month, ownership cash cost is mortgage payment plus property tax, insurance, maintenance, and association dues. Property tax and maintenance scale with that month's modeled home value; insurance and dues remain annual nominal amounts divided across twelve months. Rent grows annually.
The renter's portfolio starts with the down payment. Each month the renter invests any amount by which owning costs more than renting; if renting costs more, the owner invests that difference instead. Both side accounts compound monthly at the entered Investment Return.
At exit:
- sale proceeds after costs = home value × (1 − Selling Cost Rate) − remaining loan balance;
- buyer net worth = sale proceeds after costs + owner side account;
- renter net worth = renter portfolio; and
- advantage of buying = buyer net worth − renter net worth.
The break-even month is durable: it is the first month from which buying stays ahead through the end of the 40-year table, not the first temporary crossing.
Calculation sequence
- Validate price, down payment, terms, rates, costs, holding period, and the two required volatility inputs.
- Calculate loan principal and the monthly level mortgage payment.
- Run the monthly comparison through the holding period, growing home value and rent and crediting the lower-cost choice's side account.
- Accumulate cash paid by each choice and calculate the remaining loan balance.
- Deduct the selling cost and remaining loan from exit value, then calculate buyer and renter net worth.
- Calculate buying advantage and scan the full 480-month comparison backward to find the first durable break-even month.
- Divide each required one-year volatility by the square root of the holding period and evaluate the complete weighted 11 × 11 grid. A zero volatility collapses its axis onto the centre rather than disabling the grid. Report the weight where buying wins and the weighted P10, P50, and P90 advantages.
- Evaluate the status conditions below in order; the first matching condition is returned.
Outputs and interpretation
| Output | Role | Unit | What it means |
|---|---|---|---|
| Advantage Of Buying | headline | $ | Buyer net worth less renter net worth at exit; positive favors buying. |
| Break Even Month | headline | months | First durable month buying stays ahead; zero means no durable crossing within 40 years. |
| Buyer Net Worth | headline | $ | Sale proceeds after debt and costs plus the owner's side account. |
| Model Status | status | text | OK, CHECK, or NOT VALID, using the ordered rules below. |
| Renter Net Worth | detail | $ | Invested down payment and accumulated monthly savings. |
| Break Even Years | detail | years | Break-even month divided by twelve; blank when Break Even Month is zero. |
| Monthly Payment | detail | $/month | Mortgage principal-and-interest payment. |
| Owner Cost First Month | detail | $/month | First month's total ownership cash cost. |
| Home Value At Exit | detail | $ | Modeled home value at sale. |
| Loan Balance At Exit | detail | $ | Mortgage principal remaining at sale. |
| Sale Proceeds After Costs | detail | $ | Exit value after selling cost and loan balance. |
| Owner Side Account | detail | $ | Monthly renting-cost advantage invested by the owner. |
| Total Paid Owning | detail | $ | Down payment plus cumulative ownership cash outflow. |
| Total Paid Renting | detail | $ | Cumulative rent through the same month. |
| Probability Buying Wins | detail | percentage | Weighted share of uncertainty-grid futures with a positive buying advantage. A fully collapsed grid yields 100% or 0% by construction. |
| Advantage P10 | detail | $ | Weighted 10th-percentile buying advantage. It equals the deterministic centre when both volatility inputs are 0%. |
| Advantage P50 | detail | $ | Weighted median buying advantage. It equals the deterministic centre when both volatility inputs are 0%. |
| Advantage P90 | detail | $ | Weighted 90th-percentile buying advantage. It equals the deterministic centre when both volatility inputs are 0%. |
The four charts use the same workbook outputs. The first compares buyer and renter net worth by year. The second compares cumulative cash paid by owning and renting; cash paid is context, not the decision measure, because ownership cash can also build equity. The third shows the weighted distribution of buying advantage across the uncertainty grid. The fourth shows how buying advantage changes as appreciation and investment return move above or below the entered assumptions.
Validation and status logic
| Condition | Returned status |
|---|---|
| Purchase Price <= 0 | NOT VALID: the price has to be above zero |
| Down Payment < 0 or Down Payment > Purchase Price | NOT VALID: the down payment has to be between nothing and the whole price |
| Mortgage Rate < 0 | NOT VALID: an interest rate cannot be negative |
| Years Held < 1 or Years Held > 40 | NOT VALID: the holding period has to be between one year and 40 |
| Loan Term Years < 1 or Loan Term Years > 40 | NOT VALID: the loan term has to be between one year and 40 |
| Monthly Rent < 0 | NOT VALID: rent cannot be negative |
| Selling Cost Rate < 0 or Selling Cost Rate >= 100% | NOT VALID: selling costs have to be between nothing and the whole price |
| Property Tax Rate, Annual Insurance, Maintenance Rate, or Investment Return < 0 | NOT VALID: none of the annual rates or costs can be negative |
| Annual Rent Growth <= -100% or Annual Appreciation <= -100% | NOT VALID: rent and the home cannot lose more than all of their value in a year |
| Nonblank Annual HOA < 0 | NOT VALID: association dues cannot be negative |
| The uncertainty grid was requested but its center does not match the live deterministic answer | CHECK: the simulation grid has not recalculated against these inputs, so the probability and the band are withheld rather than shown stale |
| Years Held > Loan Term Years | CHECK: you plan to hold the home longer than the loan runs, so the later years carry no mortgage payment and the comparison flatters buying |
| Break Even Month = 0 | CHECK: on these assumptions buying never overtakes renting within 40 years |
| Break Even Month > Years Held × 12 | CHECK: buying does overtake renting, but not until month <month>, after you plan to leave |
| Advantage Of Buying < 0 | CHECK: over this period renting and investing the difference comes out ahead |
| None of the preceding conditions applies | OK |
Assumptions and limitations
- The mortgage is a fixed-rate level-payment loan. Private mortgage insurance, loan points, buyer closing costs, and refinancing are not modeled.
- Property tax and maintenance are proportional to modeled home value. Insurance and association dues are held flat in nominal dollars.
- The model omits income tax, itemized deductions, investment tax, rent deposits, moving costs, purchase closing costs, and transaction-specific concessions.
- Selling cost is one entered percentage of exit value. Actual commissions, transfer charges, and other sale costs vary.
- Appreciation, rent growth, and investment return are constant at the grid centre; the required volatility inputs define the surrounding sensitivity range.
- The uncertainty grid varies only appreciation and investment return, treats their weights independently, and is a sensitivity analysis rather than a forecast distribution.
- A renter's modeled portfolio assumes the down payment and every monthly saving are actually invested. The owner receives the same treatment when renting is the more expensive choice.
- Results are nominal and do not adjust for inflation.
Restrictions and non-computing states
All required inputs must be present. Price must be positive; down payment must be between zero and price; rates and costs subject to nonnegative constraints cannot be negative; the holding period and loan term must each be 1–40 years; and rent growth and appreciation must stay above -100%. Selling cost must remain below 100%.
Both volatility inputs are required and each accepts 0% through 100%. Zero means certainty on that axis; setting both to 0% collapses all scenarios onto the deterministic centre. Negative values and values above 100% are rejected. When the grid does not recalculate to the live centre value, its probability and percentile outputs are withheld rather than returned stale.
Errors and warnings
NOT VALID means at least one input state cannot be evaluated. CHECK retains deterministic figures but identifies a stale uncertainty grid, a holding period beyond the mortgage term, no durable break-even within 40 years, a break-even after the planned move, or a negative buying advantage. Probability and percentile outputs are withheld only when the returned grid fails its live-centre consistency check.
References
The calculator's mortgage-cost categories are aligned with the Consumer Financial Protection Bureau's explanation of mortgage and homeownership costs, which distinguishes principal and interest from property tax, homeowners insurance, and association dues.
The holding-period warning reflects the CFPB's guidance on financial considerations when buying a home, including the cost of buying and selling and the responsibility for taxes, insurance, repairs, and maintenance.
The renter and owner side accounts use monthly compounding. For general background on initial investments, recurring contributions, time, and estimated returns, see the U.S. Securities and Exchange Commission's Investor.gov compound interest calculator.
These sources provide consumer context; they do not supply the calculator's assumptions or certify its result. This calculator is informational and is not financial, investment, tax, mortgage, or real-estate advice. Results are highly sensitive to holding period, local costs, and future growth assumptions.
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