{
  "id": "simple-interest",
  "version": "ff70b4873acd",
  "status": "published",
  "name": "Simple Interest Calculator",
  "question": "What is my simple interest?",
  "summary": "Computes simple interest, I = P × r × t, and the total amount, or solves for the principal, rate, or time from the others.",
  "category": "finance",
  "subcategory": "investing",
  "url": "https://www.acalculator.org/finance/simple-interest-calculator",
  "markdown": "https://www.acalculator.org/finance/simple-interest-calculator.md",
  "kind": "formulas",
  "method": "I = P × r × t, with r per year and t in years (months ÷ 12, days ÷ 365); A = P + I.",
  "assumptions": [
    "Interest is charged on the principal only; it never earns interest itself.",
    "A time in months is months ÷ 12 years; a time in days is days ÷ 365 years.",
    "The rate is a yearly rate and does not change."
  ],
  "inputs": {
    "$schema": "https://json-schema.org/draft/2020-12/schema",
    "type": "object",
    "properties": {
      "principal": {
        "title": "Principal",
        "description": "The amount borrowed or invested.",
        "type": "number",
        "x-unit": "USD",
        "exclusiveMinimum": 0,
        "maximum": 1000000000000
      },
      "rate": {
        "title": "Interest rate (per year)",
        "description": "The simple interest rate per year.",
        "type": "number",
        "x-unit": "percent",
        "minimum": 0,
        "maximum": 100
      },
      "years": {
        "title": "Time",
        "description": "How long the money is borrowed or invested, in the chosen unit.",
        "type": "number",
        "exclusiveMinimum": 0,
        "maximum": 12000
      },
      "interest": {
        "title": "Interest",
        "description": "The interest earned or paid: principal × rate × time.",
        "type": "number",
        "x-unit": "USD",
        "minimum": 0
      },
      "timeUnit": {
        "title": "Time in",
        "description": "The unit of the time: years, months, or days (a 365-day year).",
        "type": "string",
        "enum": [
          "years",
          "months",
          "days"
        ]
      }
    }
  },
  "solve": {
    "fillAny": 3,
    "variables": [
      "principal",
      "rate",
      "years",
      "interest"
    ],
    "inputsOnly": []
  },
  "outputs": {
    "principal": {
      "label": "Principal",
      "description": "The amount borrowed or invested.",
      "format": "money"
    },
    "rate": {
      "label": "Interest rate (per year)",
      "description": "The simple interest rate per year.",
      "format": "percent"
    },
    "time": {
      "label": "Time",
      "description": "How long the money is borrowed or invested, in the unit chosen under “Time in”.",
      "format": "number"
    },
    "interest": {
      "label": "Interest",
      "description": "The interest earned or paid: principal × rate × time.",
      "format": "money"
    },
    "total": {
      "label": "Total amount",
      "description": "The principal plus the interest.",
      "format": "money"
    }
  },
  "defaultAnswer": {
    "inputs": {
      "timeUnit": "years",
      "principal": 10000,
      "rate": 5,
      "years": 10
    },
    "outputs": {
      "interest": 5000,
      "total": 15000
    },
    "text": "Simple interest on $10,000.00 at 5% a year for 10 years is $5,000.00, for a total of $15,000.00."
  },
  "examples": [
    {
      "given": {
        "principal": 5000,
        "rate": 3.5,
        "years": 18,
        "timeUnit": "months"
      },
      "expect": {
        "interest": 262.5
      },
      "source": "hand calculation in content.mdx: 5,000 × 0.035 × 18 ÷ 12; OpenStax, Prealgebra 2e, §6.4 Solve Simple Interest Applications (I = Prt). https://openstax.org/books/prealgebra-2e/pages/6-4-solve-simple-interest-applications"
    },
    {
      "given": {
        "principal": 10000,
        "rate": 5,
        "years": 3,
        "timeUnit": "years"
      },
      "expect": {
        "interest": 1500,
        "total": 11500
      },
      "source": "I = P × r × t (the textbook simple interest formula); hand calculation in content.mdx; OpenStax, Prealgebra 2e, §6.4 Solve Simple Interest Applications (I = Prt). https://openstax.org/books/prealgebra-2e/pages/6-4-solve-simple-interest-applications"
    },
    {
      "given": {
        "principal": 10000,
        "rate": 6,
        "years": 90,
        "timeUnit": "days"
      },
      "expect": {
        "interest": 147.94520547945206,
        "total": 10147.945205479453
      },
      "source": "hand calculation in content.mdx: 10,000 × 0.06 × 90 ÷ 365; OpenStax, Prealgebra 2e, §6.4 Solve Simple Interest Applications (I = Prt). https://openstax.org/books/prealgebra-2e/pages/6-4-solve-simple-interest-applications"
    },
    {
      "given": {
        "interest": 500,
        "rate": 5,
        "years": 2,
        "timeUnit": "years"
      },
      "expect": {
        "principal": 5000,
        "total": 5500
      },
      "source": "the old page FAQ: P = I ÷ (r × t) = 500 ÷ (0.05 × 2); OpenStax, Prealgebra 2e, §6.4 Solve Simple Interest Applications (I = Prt). https://openstax.org/books/prealgebra-2e/pages/6-4-solve-simple-interest-applications"
    },
    {
      "given": {
        "principal": 10000,
        "interest": 1000,
        "years": 2,
        "timeUnit": "years"
      },
      "expect": {
        "rate": 5
      },
      "source": "the old page FAQ: r = I ÷ (P × t) = 1,000 ÷ (10,000 × 2); OpenStax, Prealgebra 2e, §6.4 Solve Simple Interest Applications (I = Prt). https://openstax.org/books/prealgebra-2e/pages/6-4-solve-simple-interest-applications"
    },
    {
      "given": {
        "principal": 10000,
        "rate": 5,
        "interest": 1500,
        "timeUnit": "years"
      },
      "expect": {
        "years": 3,
        "total": 11500
      },
      "source": "hand calculation in content.mdx: t = I ÷ (P × r) = 1,500 ÷ (10,000 × 0.05); OpenStax, Prealgebra 2e, §6.4 Solve Simple Interest Applications (I = Prt). https://openstax.org/books/prealgebra-2e/pages/6-4-solve-simple-interest-applications"
    }
  ],
  "sources": [
    "Simple interest I = P × r × t: S. A. Broverman, Mathematics of Investment and Credit, section 1.3.",
    "Consumer Financial Protection Bureau, What is the difference between a simple interest loan and a precomputed interest loan? https://www.consumerfinance.gov/ask-cfpb/",
    "OpenStax, Prealgebra 2e, §6.4 Solve Simple Interest Applications (I = Prt). https://openstax.org/books/prealgebra-2e/pages/6-4-solve-simple-interest-applications"
  ],
  "related": [
    "compound-interest",
    "cd"
  ],
  "changelog": [
    {
      "date": "2026-09-29",
      "note": "Worked examples name a published reference for their rule."
    },
    {
      "date": "2026-10-01",
      "note": "The time unit reads in lower case in the answer (“for 10 years”), the Time box says the switch keeps the number, and a solved time shows 2 decimals."
    }
  ]
}