{
  "tool": "Annual Percentage Yield Calculator",
  "author": "Aisha Henry",
  "location": "Union County, NC",
  "version": "1.0.0",
  "date": "2026-07-18",
  
  "formula": {
    "id": "Q4118506",
    "wikidata_slug": "annual-percentage-yield",
    "equation": "APY = (1 + i_nom/N)^N - 1",
    "description": "True annual yield accounting for compounding frequency",
    "variables": {
      "APY": {
        "type": "output",
        "unit": "decimal ratio",
        "description": "Annual Percentage Yield (effective annual rate)"
      },
      "i_nom": {
        "type": "input",
        "unit": "decimal ratio",
        "description": "Nominal annual interest rate (e.g., 0.0675 for 6.75%)"
      },
      "N": {
        "type": "input",
        "unit": "count per year",
        "description": "Number of compounding periods per year",
        "common_values": {
          "annually": 1,
          "quarterly": 4,
          "monthly": 12,
          "weekly": 52,
          "daily": 365
        }
      }
    }
  },
  
  "secondary_formula": {
    "name": "Monthly Mortgage Payment",
    "equation": "M = P × [r(1+r)^n] / [(1+r)^n − 1]",
    "variables": {
      "M": "monthly payment",
      "P": "principal loan amount",
      "r": "monthly interest rate (annual rate / 12)",
      "n": "total number of payments (years × 12)"
    }
  },
  
  "union_county_context": {
    "median_home_price_usd": 312000,
    "typical_down_payment_percent": 20,
    "first_time_buyer_rate_percent": 3.25,
    "credit_union_partners": ["Union Credit Union", "Fayetteville FCU", "Southeastern FCU"],
    "data_source": "Union County Housing Authority Q2 2026 Report"
  },
  
  "work_example": {
    "scenario": "Union County first-time buyer, median home",
    "inputs": {
      "nominal_rate_percent": 6.75,
      "compounds_per_year": 12,
      "loan_amount_usd": 249600,
      "term_years": 30
    },
    "outputs": {
      "apy_percent": 6.976,
      "difference_percent": 0.226,
      "total_interest_usd": 331847,
      "total_paid_usd": 581447,
      "monthly_payment_usd": 1615.13
    }
  },
  
  "license": "CC0-1.0",
  "human_page_url": "https://aisha-henry.4ort.net/apr-calculator.html"
}