What the model is trying to answer

The calculator answers a narrow question: under the assumptions you enter, which path is projected to leave more net worth after a chosen number of years? It does not answer whether you will enjoy owning a home, whether you can qualify for a loan, or whether a particular property is a good investment.

That distinction matters because a mortgage payment is not the same thing as a housing cost. Part of the payment reduces principal and becomes equity. At the same time, ownership adds property tax, insurance, maintenance, HOA dues, PMI, and a future selling cost. Renting avoids many of those costs but leaves the renter responsible for rent increases and the opportunity cost of cash that could have been used as a down payment.

Core formulas

Mortgage paymentM = P × r(1+r)n / ((1+r)n − 1)

P is the loan amount, r is the monthly interest rate, and n is the number of monthly payments.

Buyer net worthInvestment balance + home value − mortgage balance − selling costs

Selling costs are applied to projected home value at the end of the horizon.

Renter net worthInvestment balance + refundable security deposit

The initial investment includes cash that would otherwise have funded the down payment and buying costs, less the modeled deposit.

Net worth advantageBuyer net worth − renter net worth

A positive value means the buyer is ahead in the modeled month; a negative value means the renter is ahead.

How the monthly simulation works

  1. The model calculates the purchase price, down payment, closing costs, loan amount, and monthly principal-and-interest payment.
  2. For each month, it grows the home value, rent, insurance, property tax, HOA dues, and maintenance allowance using the rates you provide.
  3. It calculates mortgage interest, principal paid, remaining balance, and PMI when the loan has not reached the modeled equity threshold.
  4. It compares the buyer's and renter's housing cash outflows. The option with the lower outflow receives the difference as a contribution to its investment balance.
  5. It grows both investment balances at the after-tax return assumption, then calculates each path's net worth.

How break-even is defined

HomeMath calls break-even the first month when buyer net worth reaches or exceeds renter net worth and remains essentially ahead for the following modeled months. This is intentionally stricter than comparing one isolated month. A result that crosses back and forth is a signal that the assumptions are sensitive, not a clean recommendation.

Important limitations

Home prices and rents do not grow in a straight line. Local taxes, insurance premiums, repairs, vacancies, moving expenses, financing fees, refinancing, capital improvements, and selling timelines can all differ from a simplified estimate. The model also does not price lifestyle flexibility, commute changes, the value of a private yard, or the risk of being unable to sell when you need to move.

The optional tax section is deliberately limited. It uses a simplified estimate only when you enable it, choose an estimated marginal rate, and indicate itemization. Tax law, filing status, income, limits, and deductions are more complicated than this model. Review current IRS mortgage-interest guidance and consult a qualified professional.

Best practice: run a range

Start with a baseline that you can defend, then test a lower appreciation rate, slower rent growth, higher maintenance, a shorter stay, and a different investment return. If the conclusion stays similar across reasonable ranges, the result is more robust. If it flips quickly, the honest conclusion is that the decision depends on assumptions that deserve more research.