{
  "address": "926c6ab87d040d83a7d12c1188184800",
  "category": "other",
  "question": "What is the future value of a $1000 ordinary annuity (payments at the end of each period) paid 10 times at 5% interest per period?",
  "answer": "$12,577.89",
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  "madeAt": "2026-09-30T22:39:30.722Z",
  "validUntil": null,
  "validityClass": "forever",
  "sources": [
    {
      "label": "Principles of Corporate Finance",
      "url": null
    }
  ],
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  "source": {
    "kind": "edition_page",
    "value": "Brealey, Myers, Allen, Principles of Corporate Finance, 13th ed., Chapter 3, section 3-2 (Future Value of an Annuity)",
    "retrieved_utc": "2026-09-30T19:31:29Z"
  },
  "qsha256": "91316f2a904dae6c4ba38d0b73d6a962dbbc3ed7909331e924541ee06b6e71f2",
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  "cardContractVersion": "card_contract/1",
  "deck_id": "method-deck",
  "deck_title": "Method Deck",
  "method": {
    "name": "Future value of an annuity",
    "version": "1",
    "source_url_or_file": "methods/future-value-of-annuity.cjs",
    "sha256_of_method_file": "95e8308bf9a2cd1bc0b3eb0e711570a405e97ee4414b519dd99513dc5f3190d3"
  },
  "receipt": {
    "inSubstrate": false,
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  },
  "method_deck": {
    "inputs": [
      {
        "name": "payment",
        "type": "number",
        "unit": "currency units",
        "required": true,
        "description": "Equal payment made each period",
        "min": 0
      },
      {
        "name": "annual_rate_percent",
        "type": "number",
        "unit": "%",
        "required": true,
        "description": "Nominal annual rate, compounded once per payment period",
        "min": 0
      },
      {
        "name": "periods",
        "type": "integer",
        "required": true,
        "description": "Number of payment periods",
        "min": 1
      },
      {
        "name": "is_annuity_due",
        "type": "boolean",
        "required": true,
        "description": "True if payments occur at the start of each period (annuity due); false for the end (ordinary annuity)"
      }
    ],
    "outputs": [
      {
        "name": "future_value",
        "unit": "currency units",
        "description": "Value of the annuity at the end of the last period"
      }
    ],
    "steps": [
      "Convert the annual rate to a decimal per period: i = annual_rate_percent / 100 (one compounding per payment period).",
      "Ordinary annuity future value: FV_ordinary = payment * (((1 + i)^periods - 1) / i), or payment * periods if i = 0.",
      "If is_annuity_due is true, future_value = FV_ordinary * (1 + i); otherwise future_value = FV_ordinary.",
      "Round future_value to 2 decimals (money to cents)."
    ],
    "constants": [],
    "examples": [
      {
        "name": "worked example",
        "inputs": {
          "payment": 1000,
          "annual_rate_percent": 5,
          "periods": 10,
          "is_annuity_due": false
        },
        "expected": {
          "answer": "$12,577.89"
        },
        "check": "hand computation: FV = 1000*((1.05^10 - 1)/0.05) = 1000*(1.628894.../0.05) = 1000*12.577893... = 12577.89"
      },
      {
        "name": "test vector: annuity due",
        "inputs": {
          "payment": 1000,
          "annual_rate_percent": 5,
          "periods": 10,
          "is_annuity_due": true
        },
        "expected": {
          "answer": "$13,206.79"
        },
        "check": "hand computation: ordinary FV = 12577.8925..., due FV = 12577.8925*1.05 = 13206.7871..., rounds to 13206.79"
      }
    ],
    "disclaimer": null,
    "deck_category": "finance"
  },
  "status": "minted",
  "kind": "method",
  "provenanceClass": "own_question",
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        "source": {
          "kind": "edition_page",
          "value": "Brealey, Myers, Allen, Principles of Corporate Finance, 13th ed., Chapter 3, section 3-2 (Future Value of an Annuity)",
          "retrieved_utc": "2026-09-30T19:31:29Z"
        },
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        "supersedes": null,
        "added_utc": "2026-09-30T22:39:30.722Z",
        "added_by": "method:Future value of an annuity",
        "why": "the method that computed this answer",
        "check": null,
        "status_label": "pending",
        "signature": null
      }
    ]
  }
}