Break-Even Year
—
80% confidence range
Buy Net Cost
—
at horizon (median)
Rent Net Cost
—
at horizon (median)
Monthly Mortgage
—
principal + interest only
Home Value (FV)
—
at horizon (median)
Verdict
—
median scenario
Calculating…
PV · NPV · FV Analysis
| Metric | 5 Yrs | 10 Yrs | 20 Yrs | 30 Yrs |
|---|---|---|---|---|
| Calculating… | ||||
Monte Carlo — Buying Advantage Over Time
90th %ile
50th %ile (median)
10th %ile
Break-even
Positive = buying is cheaper; negative = renting is cheaper. Shaded band shows P10–P90 uncertainty.
Cumulative Net Cost Over Time
Net cost of buying (after equity)
Net cost of renting (after investment)
Monthly Cost Comparison Over Time
Total monthly ownership cost
Monthly rent
Formula Reference
Monthly Mortgage Payment (PMT)
PMT = P × [r(1+r)ⁿ] / [(1+r)ⁿ − 1]
- P = loan principal (home price − down payment)
- r = monthly interest rate (annual rate ÷ 12 ÷ 100)
- n = total number of monthly payments (years × 12)
Future Value (FV)
FV = PV × (1 + r)ⁿ
- PV = present value (home price or down payment)
- r = annual growth rate ÷ 100
- n = number of years
Present Value (PV)
PV = FV / (1 + r)ⁿ
- FV = future cash value
- r = discount rate per period
- n = number of years
Present Value of Annuity
PV = PMT × [1 − (1+r)⁻ⁿ] / r
- PMT = periodic payment
- r = monthly discount rate
- n = total number of periods
Net Present Value (NPV)
NPV = Σ [ CFₜ / (1 + r)ᵗ ] for t = 1 to n
- CFₜ = net cash flow in year t
- r = discount rate per year
Remaining Loan Balance
B = P × [(1+r)ⁿ − (1+r)ᵏ] / [(1+r)ⁿ − 1]
- k = payments made so far
Monte Carlo Simulation
X = μ + σ × Z where Z ~ N(0,1)
- μ = user-specified base rate
- σ = standard deviation (appreciation 2%, rent 1.5%, inv return 2.5%, maint 1%)
- 1,000 scenarios; P10/P50/P90 reported
Opportunity Cost of Down Payment
OC = DP × (1 + r_inv)ⁿ − DP
- DP = down payment amount
- r_inv = annual investment return ÷ 100