Compare · Property desk · 2 minutes
You have the price of the house. The question is whether the bank's money is cheaper than yours. This instrument runs both paths month by month — the mortgage's coupon, the invested lump, the tax shield if your jurisdiction grants one — and prints the wealth each leaves at the end of the term, plus the exact return where they cross.
Arithmetic under your assumptions — not advice. A mortgage is leverage; the simulation shows expected paths, not bad sequences.
You have this in cash — that's the premise.
Sets the payment-load gauge.
The comparison horizon — both paths are read at this date.
What the un-spent lump earns. The whole decision is this against the rate.
Varies by jurisdiction and use. If yes, the shield is invested as it arrives.
Only used if interest is deductible.
Nothing you type leaves this page. The instrument runs entirely in your browser; there is no account and no record.
Mortgage, and invest the rest.
+$157,035
end-of-term wealth, mortgage path against cash path
| Monthly payment | — |
| Total interest paid over the term | — |
| End wealth — cash path | — |
| End wealth — mortgage path | — |
| Break-even return | — |
| The difference | — |
| If invested money returns | Better path | By |
|---|---|---|
| — | — | — |
| — | — | — |
| — | — | — |
Sequence risk is invisible to an average return. If the invested lump halves in year two, the mortgage path feels very different from the smooth line simulated here.
A paid-off house is a position too — a bond paying the mortgage rate, tax-free, uncallable. Some people are paid in basis points; others are paid in sleep.
Rates move. A mortgage can usually be refinanced when they fall; the cash decision cannot be unmade nearly as cheaply.
Both paths buy the same house on day one and enjoy the same income thereafter, so the house itself cancels out and only the money paths differ. The simulation runs month by month — no closed-form shortcuts.
Cash path: pay P. Invest the mortgage-sized payment
each month at i = r/12.
Mortgage path: pay down·P. Invest (P − down·P) at i.
Pay pmt from income (symmetric with the
cash buyer's investing). If deductible,
invest interest_t × bracket monthly.
pmt = L·j / (1 − (1+j)^−m), j = rate/12, m = months
End wealth is compared at the final month; the break-even return is found by bisection — the r at which the two paths tie. The gauge reads annual payments against net income with the line at the classic 28% housing convention.
Limitations. Constant rates and returns; no refinancing, prepayment, or investment taxes; the tax shield uses your flat marginal bracket. Sequence-of-returns risk — the real argument for caution with leverage — cannot appear in an expected-value table.