finance-business · personal-finance · housing

Rent vs Buy Calculator

Compares renting with buying on the net worth each leaves you with at the end of the period you expect to stay, rather than on monthly cost. The renter's down payment and every month of saved cost are invested at a return you set, the owner's spare cash is invested in any month rent costs more, and the sale at the end pays selling costs and repays the loan. It also reports the month from which buying goes ahead and stays ahead.

Last updated
Decision Canvas

Calculator overview

Inputs and outputs

This summary comes from the calculator's published input and output contract.

Inputs

Mortgage Rate (required)
About this input

The rate on the loan, as an annual percentage. Held constant for the whole period.

Unit fraction Default 0.06 Range At least 0
Property Tax Rate (required)
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.

Unit fraction Default 0.012 Range 0 to 1
Maintenance Rate (required)
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.

Unit fraction Default 0.01 Range 0 to 1
Monthly Rent (required)
About this input

What the comparable rental costs today. Comparable matters: a rental you would actually accept, not the cheapest listing you can find.

Unit currency/month Default 2200 Range At least 0
Selling Cost Rate (required)
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.

Unit fraction Default 0.06 Range 0 to 0.99
Years Held (required)
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.

Unit years Default 7 Range 1 to 40
Purchase Price (required)
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.

Unit currency Default 400000 Range At least 0
Return Volatility (required)
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.

Unit fraction Default 0.08 Range 0 to 1
Annual Insurance (required)
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.

Unit currency/yr Default 1800 Range At least 0
Annual Rent Growth (required)
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.

Unit fraction Default 0.03 Range At least -1
Annual Appreciation (required)
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.

Unit fraction Default 0.03 Range At least -1
Annual HOA
When omitted Blank
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.

Unit currency/yr Default Not set Range At least 0
Investment Return (required)
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.

Unit fraction Default 0.06 Range At least 0
Loan Term Years (required)
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.

Unit years Default 30 Range 1 to 40
Appreciation Volatility (required)
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.

Unit fraction Default 0.03 Range 0 to 1
Down Payment (required)
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.

Unit currency Default 80000 Range At least 0

Outputs

Sale Proceeds After Costs
About this output

What the sale actually puts in your pocket: the value, less the costs of selling, less the loan.

Unit currency
Table1 Futures Column Axis
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.

No unit declared
Table1 Futures Column Input
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.

Unit fraction
Owner Side Account
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.

Unit currency
Probability Buying Wins
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.

Unit fraction
Renter Net Worth
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.

Unit currency
Table1 Futures Values
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.

Unit currency
Total Paid Owning
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.

Unit currency
Total Paid Renting
About this output

Cash out of pocket while renting over the same period.

Unit currency
Table1 Futures Corner
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.

Unit currency
Table1 Futures Row Axis
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.

No unit declared
Table1 Futures Row Input
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.

Unit fraction
Advantage P90
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.

Unit currency
Break Even Month
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.

Unit months
Break Even Years
About this output

The same figure in years, for reading against how long you actually expect to stay. Blank when buying never overtakes.

Unit years
Advantage Of Buying
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.

Unit currency
Advantage P10
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.

Unit currency
Advantage P50
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.

Unit currency
Model Status
About this output

Reads OK, or explains why the inputs are not valid or why the answer deserves a second look.

No unit declared
Monthly Payment
About this output

Principal and interest only. Tax, insurance, maintenance and dues are added separately in the monthly table.

Unit currency/month
Owner Cost First 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.

Unit currency/month
Buyer Net Worth
About this output

The sale proceeds plus that side account. This is what buying leaves you with at the end of the period.

Unit currency
Home Value At Exit
About this output

What the home is worth on the day you sell, at the appreciation you assumed.

Unit currency
Loan Balance At Exit
About this output

What is still owed then, from the closed-form balance rather than an accumulated schedule.

Unit currency
This page is provided by LogicCommons for informational purposes only. Results are model outputs computed from the inputs you supply and are not financial, investment, tax, accounting, or legal advice, and no advisory relationship is created. Verify all inputs and results independently before relying on them in any decision.

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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

  1. Validate price, down payment, terms, rates, costs, holding period, and the two required volatility inputs.
  2. Calculate loan principal and the monthly level mortgage payment.
  3. Run the monthly comparison through the holding period, growing home value and rent and crediting the lower-cost choice's side account.
  4. Accumulate cash paid by each choice and calculate the remaining loan balance.
  5. Deduct the selling cost and remaining loan from exit value, then calculate buyer and renter net worth.
  6. Calculate buying advantage and scan the full 480-month comparison backward to find the first durable break-even month.
  7. 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.
  8. 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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