{
  "version": "2026.1",
  "generated_at": "2026-09-07",
  "generated_by": "scripts/gen_mortgage_study.mjs",
  "study": "pay-off-mortgage-or-invest-2026",
  "url": "https://quantcalc.app/research/pay-off-mortgage-or-invest-2026/",
  "license": "CC-BY-4.0",
  "method": {
    "engine": "QuantCalc C Monte Carlo engine (quantcalc-server 2.0.0), constant-real withdrawals with a scheduled nominal life event, over the public simulate contract",
    "capital_market_assumptions": {
      "source": "JPMorgan LTCMA 2026",
      "as_of": "2025-11-01",
      "asset_classes": [
        "US Equity",
        "International Equity",
        "Bonds",
        "Real Estate",
        "Cash"
      ],
      "expected_returns": [
        0.067,
        0.074,
        0.048,
        0.065,
        0.032
      ],
      "volatilities": [
        0.152,
        0.18,
        0.05,
        0.15,
        0.01
      ],
      "correlations": [
        [
          1,
          0.87,
          0.3,
          0.6,
          -0.01
        ],
        [
          0.87,
          1,
          0.34,
          0.55,
          -0.03
        ],
        [
          0.3,
          0.34,
          1,
          0.2,
          -0.24
        ],
        [
          0.6,
          0.55,
          0.2,
          1,
          0.05
        ],
        [
          -0.01,
          -0.03,
          -0.24,
          0.05,
          1
        ]
      ]
    },
    "plan": {
      "capital": 1000000,
      "retirement_age": 65,
      "end_age": 95,
      "horizon_years": 30,
      "base_spending_annual_real": [
        50000,
        40000,
        30000
      ],
      "plan_mix": {
        "key": "60/40",
        "allocation": [
          0.45,
          0.15,
          0.4,
          0,
          0
        ]
      },
      "inflation_rate": 0.025,
      "social_security": 0,
      "pension": 0,
      "taxes": "pre-tax, single pool"
    },
    "mortgage": {
      "balance": 200000,
      "term_years": 15,
      "rates": [
        0.04,
        0.055,
        0.065
      ],
      "payment": "level monthly payment from the amortisation formula P = L·r/(1 − (1 + r)^−n), r = rate/12, n = 180",
      "loans": {
        "r4p0": {
          "rate": 0.04,
          "monthly_payment": 1479.3758512185157,
          "annual_payment": 17752.510214622187,
          "final_balance": 7.725702744210139e-9,
          "total_interest": 66287.65321933957,
          "total_paid": 266287.6532193328,
          "balance_by_year": {
            "1": 190066.69216288225,
            "2": 179728.68603818305,
            "3": 168969.4935932494,
            "4": 157771.9550475382,
            "5": 146118.21150457097,
            "6": 133989.67646887165,
            "7": 121367.00620246114,
            "8": 108230.06887362925,
            "9": 94557.91244878015,
            "10": 80328.73127614197,
            "11": 65519.83130804531,
            "12": 50107.59390630356,
            "13": 34067.43817296876,
            "14": 17373.781746384204,
            "15": 7.725702744210139e-9
          }
        },
        "r5p5": {
          "rate": 0.055,
          "monthly_payment": 1634.1669092422671,
          "annual_payment": 19610.002910907206,
          "final_balance": 3.1466242944588885e-9,
          "total_interest": 94150.0436636113,
          "total_paid": 294150.0436636081,
          "balance_by_year": {
            "1": 191169.6028705908,
            "2": 181841.10193275707,
            "3": 171986.40021641564,
            "4": 161575.81586151774,
            "5": 150577.99271779688,
            "6": 138959.80590164027,
            "7": 126686.26202562479,
            "8": 113720.39380021532,
            "9": 100023.14869016965,
            "10": 85553.27129029008,
            "11": 70267.17906624232,
            "12": 54118.831086180035,
            "13": 37059.58934780137,
            "14": 19038.072283161142,
            "15": 3.1466242944588885e-9
          }
        },
        "r6p5": {
          "rate": 0.065,
          "monthly_payment": 1742.2147305947308,
          "annual_payment": 20906.57676713677,
          "final_balance": -4.031790012959391e-9,
          "total_interest": 113598.65150704834,
          "total_paid": 313598.65150705155,
          "balance_by_year": {
            "1": 191853.56786007012,
            "2": 183161.55407251607,
            "3": 173887.42002397787,
            "4": 163992.18004248926,
            "5": 153434.23751343068,
            "6": 142169.2100198646,
            "7": 130149.74277219483,
            "8": 117325.30954286492,
            "9": 103642.0002692838,
            "10": 89042.29443212738,
            "11": 73464.81925636425,
            "12": 56844.09171855661,
            "13": 39110.2432759123,
            "14": 20188.72615993167,
            "15": -4.031790012959391e-9
          }
        }
      }
    },
    "pay_off_arm": "Savings at 65 reduced by the balance (800000); spending is the base amount, constant in real terms.",
    "keep_arm": "Full 1000000 at 65; the level monthly payment is charged for 180 months as a nominal constant (engine life event, inflationCategory \"none\") and stops at 80; base spending is constant in real terms.",
    "paths_per_arm": 10000,
    "pairing": "seed s with n ≤ 30 paths reads Sobol cache rows s..s+n−1 (random.c generate_sobol_normal offset = seed mod (rows − n + 1)); the 334 windows tile rows 0..9999 exactly",
    "paired_statistic": "per path: keep-the-mortgage terminal real wealth − pay-it-off terminal real wealth on the same market path; reported as median, p10, p90, mean, the share of paths where each arm ends higher, and survival crossovers",
    "breakeven": "the whole grid re-run with every asset's expected return shifted in parallel by δ ∈ {-4, -3, -2, -1, 1, 2, 3} pp through the contract's customCme override (same volatilities and correlations); the δ at which a paired statistic crosses zero is interpolated linearly between adjacent grid points, and the sign-test crossing (share of paths keep ends higher = share pay-off ends higher) is refined by 2 regula-falsi steps of additional engine runs; reported as the portfolio's weighted expected nominal return (60/40 weights × the roster's published expected returns) at that δ, and its real equivalent at 2.5% inflation",
    "reference_breakeven": "closed form: without dispersion the two arms tie when the portfolio return equals the mortgage rate (nominal)",
    "dollars": "real (today's dollars); the engine deflates every reported value by its inflation path",
    "success": "a path counts as a success when the portfolio never reaches $0 during retirement; the terminal value of a ruined path is $0",
    "account_types": "single pre-tax pool; the contract used here does not distinguish taxable from tax-deferred money, so no payoff-source variant is run",
    "checks": {
      "amortisation": {
        "r4p0": {
          "monthly_payment": 1479.3758512185157,
          "final_balance": 7.725702744210139e-9
        },
        "r5p5": {
          "monthly_payment": 1634.1669092422671,
          "final_balance": 3.1466242944588885e-9
        },
        "r6p5": {
          "monthly_payment": 1742.2147305947308,
          "final_balance": -4.031790012959391e-9
        }
      },
      "nominal_payment_replica": {
        "max_abs_gap": 198.00776598558878,
        "ruin_year": 13,
        "inflating_alternative_max_gap": 28737.067863147622,
        "note": "0%-return, minimum-volatility custom roster: engine yearly real values for ARM B match an independent month-by-month replica of inflating base spending plus a level nominal payment for 180 months"
      },
      "override_identity": {
        "max_relative_gap": 0,
        "success_default": 0.3336,
        "success_override": 0.3336,
        "note": "the customCme override with the roster's own returns, volatilities and correlations reproduces the default run path by path, so shifted runs differ from the base only by the shift"
      },
      "determinism": {
        "arm": "B_s50000_r5p5_d0_0",
        "seed": 210,
        "n": 30,
        "identical": true
      },
      "engine_ruin_count_matches_terminal_gt_zero": true,
      "batched_equals_single_call": {
        "arms": 12,
        "max_gap": 0
      },
      "starting_wealth_identity": true
    }
  },
  "cells": [
    {
      "mortgage_rate": 0.04,
      "base_spending_annual_real": 50000,
      "loan": {
        "rate": 0.04,
        "monthly_payment": 1479.3758512185157,
        "annual_payment": 17752.510214622187,
        "final_balance": 7.725702744210139e-9,
        "total_interest": 66287.65321933957,
        "total_paid": 266287.6532193328,
        "balance_by_year": {
          "1": 190066.69216288225,
          "2": 179728.68603818305,
          "3": 168969.4935932494,
          "4": 157771.9550475382,
          "5": 146118.21150457097,
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        }
      },
      "withdrawal_rate_pay_off": 0.0625,
      "year1_withdrawal_rate_keep": 0.0677525102146222,
      "pay_off": {
        "savings_at_65": 800000,
        "success_rate": 0.2956,
        "success_ci95": [
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        ],
        "terminal_real": {
          "p5": 0,
          "p10": 0,
          "p25": 0,
          "p50": 0,
          "p75": 100447.92135383708,
          "p90": 690747.0449509806,
          "p95": 1195332.8478219935,
          "mean": 207951.60480071596
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      },
      "keep": {
        "savings_at_65": 1000000,
        "success_rate": 0.3579,
        "success_ci95": [
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        ],
        "terminal_real": {
          "p5": 0,
          "p10": 0,
          "p25": 0,
          "p50": 0,
          "p75": 270568.4322862486,
          "p90": 1001751.779392985,
          "p95": 1599679.1753066524,
          "mean": 302895.4809129649
        }
      },
      "paired": {
        "median_diff": 0,
        "p10_diff": 0,
        "p25_diff": 0,
        "p75_diff": 165264.84459540196,
        "p90_diff": 308471.0400042514,
        "mean_diff": 94943.87611224921,
        "share_b_higher": 0.3579,
        "share_a_higher": 0,
        "share_tied": 0.6421,
        "b_survives_a_fails": 623,
        "a_survives_b_fails": 0,
        "both_fail": 6421,
        "by_year": [
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      "breakeven": {
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        "spend": 50000,
        "rate": 0.04,
        "portfolio_expected_nominal_base": 0.060450000000000004,
        "portfolio_expected_real_base": 0.03458536585365857,
        "reference_shift": -0.020450000000000003,
        "reference_nominal": 0.04,
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        "mean_diff": null,
        "success": null,
        "refinements": [],
        "points": [
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            "shift": -0.04,
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            "success_a": 0.0108,
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            "median_a": 0,
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