Buying a home: the five mortgage decisions
The housing journey is five distinct decisions — whether
(/v1/mortgage/rent-vs-buy), how much
(/v1/mortgage/affordability), points or not
(/v1/mortgage/points), 15 or 30 years
(/v1/mortgage/term-comparison), and later, refinance?
(/v1/mortgage/refinance). Each is one deterministic call.
1 · Whether: rent vs buy
A $500k home with 20% down at 7%, against $2,500 rent, over a 7-year holding period — with the down payment's opportunity cost (5% invested) and the sale costs counted.
curl -X POST https://api.numeratica.com/v1/mortgage/rent-vs-buy \
-H "Authorization: Bearer nmr_sk_test_xxx" \
-H "Content-Type: application/json" \
-d '{
"home_price": 500000, "down_payment": 100000,
"mortgage_rate": 0.07, "loan_term_months": 360,
"monthly_rent": 2500, "rent_growth": 0.03,
"holding_period_months": 84,
"investment_return": 0.05, "home_appreciation": 0.03
}'{
"result_id": "rentvsbuy_1353004012303ff4",
"engine_version": "rent-vs-buy-1.0.0",
"result": {
"monthly_mortgage_payment": 2661.21,
"upfront_cost": 115000, /* down payment + closing */
"home_value_at_sale": 614936.93, /* 3%/yr appreciation, 7 yrs */
"sale_proceeds": 213451.06, /* after loan payoff + selling costs */
"buy_net_present_cost": 237359.18,
"rent_net_present_cost": 196321.05, /* incl. investing the down payment */
"cost_difference": -41038.13,
"recommendation": "rent"
},
"disclaimer": "Calculation engine output for informational purposes only; not lending, tax, or financial advice."
}At these numbers renting wins by $41,038 over 7 years — the invested down payment and avoided selling costs beat the equity built at a 7% mortgage rate. The engine has no thumb on the scale: stretch the holding period or drop the rate and the recommendation flips. That honesty is the point.
2 · The other four calls
How much house: $120k income, $300/mo debts, $60k down →
$403,774 max price, bound by the front-end DTI, with the payment split
into P&I/tax/insurance/PMI (result_id afford_3801f3bdf277d1f0).
Points: 2 points for 25bps costs $8,000 and breaks even at
month 120 — "worthwhile" only if you'll hold the loan ten years
(points_e6dba079e99b366c). 15 vs 30: at a 5%
investment return the 15-year path ends $281,665 wealthier — investing the
payment difference doesn't beat a 7% mortgage (termcmp_4e65f54b0bf2421e).
Refinance later: 7% → 5.5% with $6,000 closing costs pays back in
15 months (refi_742520945aa94e35).
3 · Render it
The verdict card for the featured call.
<div style="font-family:-apple-system,Segoe UI,Roboto,Helvetica,Arial,sans-serif;color:#1a2230;max-width:600px">
<div style="font-size:14px;color:#5b6675;margin-bottom:8px">$500k home, 20% down @ 7% vs $2,500 rent · 7-year horizon</div>
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<div style="font-size:12px;color:#16a34a;font-weight:600">Rent (and invest the down payment)</div>
<div style="font-size:22px;font-weight:700">$196,321<span style="font-size:12px;font-weight:400;color:#5b6675"> net cost</span></div>
</div>
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<div style="font-size:12px;color:#5b6675">Buy (equity net of all costs)</div>
<div style="font-size:22px;font-weight:700">$237,359<span style="font-size:12px;font-weight:400;color:#5b6675"> net cost</span></div>
</div>
</div>
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<div><strong>Renting wins at these inputs</strong><span style="color:#5b6675;font-size:13px"> · longer stay or lower rate flips it</span></div>
<div style="font-size:22px;font-weight:700;color:#16a34a">−$41,038</div>
</div>
<div style="color:#5b6675;font-size:12px;margin-top:6px">result_id rentvsbuy_1353004012303ff4 · not lending advice</div>
</div>
Before the house: where the next
saved dollar goes (the down-payment-vs-401k question) and the generic
/v1/loan/amortization schedule for any fixed-rate loan.