{
    "name": "Interest Rate Calculator",
    "url": "https://calculators.geekmidst.com/calculators/interest-rate-calculator",
    "markdown": "https://calculators.geekmidst.com/calculators/interest-rate-calculator.md",
    "category": "Finance",
    "description": "Work out the interest rate on a loan from the amount borrowed, the monthly payment and the number of payments, as an annual rate and an effective rate.",
    "summary": "If you know what you borrow, what you repay each month and for how long, the interest rate is fixed by the maths. This calculator finds it, so you can check an offer or compare loans.",
    "also_called": [
        "Loan rate calculator"
    ],
    "applies_to": "Worldwide",
    "last_updated": "2026-10-29",
    "computation": "Results are computed in the visitor’s browser on the HTML page. This API describes the calculator; it does not compute results.",
    "inputs": [
        {
            "name": "principal",
            "label": "Amount borrowed",
            "type": "number",
            "default": "25000"
        },
        {
            "name": "payment",
            "label": "Monthly payment",
            "type": "number",
            "default": "483.32"
        },
        {
            "name": "months",
            "label": "Number of monthly payments",
            "type": "number",
            "default": "60",
            "unit": "months"
        },
        {
            "name": "currency",
            "label": "Currency",
            "type": "currency",
            "default": "USD"
        }
    ],
    "outputs": [
        {
            "key": "apr",
            "label": "Annual interest rate",
            "format": "percent"
        },
        {
            "key": "effective_rate",
            "label": "Effective annual rate",
            "format": "percent"
        },
        {
            "key": "monthly_rate",
            "label": "Monthly rate",
            "format": "percent"
        },
        {
            "key": "total_interest",
            "label": "Total interest",
            "format": "currency"
        },
        {
            "key": "total_paid",
            "label": "Total of all payments",
            "format": "currency"
        }
    ],
    "formula": {
        "text": "Find i such that Payment = L × i(1+i)^n ÷ ((1+i)^n − 1) (solved numerically by bisection);  Annual rate = 12 × i;  Effective rate = (1 + i)^12 − 1",
        "variables": {
            "L": "amount borrowed",
            "n": "number of monthly payments",
            "i": "monthly interest rate"
        }
    },
    "worked_example": {
        "inputs": {
            "principal": "25000",
            "payment": "483.32",
            "months": "60",
            "currency": "USD"
        },
        "steps": [
            "Total repaid = 483.32 × 60 = $28,999.20, so interest = $3,999.20.",
            "At i = 0.5% a month, 25,000 × 0.005 × 1.005^60 ÷ (1.005^60 − 1) = 483.32, matching the payment.",
            "Annual rate = 12 × 0.5% = 6%; effective rate = 1.005^12 − 1 = 6.1678%."
        ],
        "result": "Borrowing $25,000 and repaying $483.32 a month for 60 months means a 6% annual interest rate."
    },
    "interpretation": "If a lender quotes a lower rate than this calculator finds for the same payment, fees or add-ons have been folded into the payment. The effective rate is useful when comparing with savings rates.",
    "assumptions": [
        "Payments are equal, monthly and start one month after the loan is made.",
        "The amount borrowed is what you actually receive; fees deducted upfront raise the true rate."
    ],
    "limitations": [
        "This is the rate implied by the payments, not a regulatory APR, which may include specific fees under local rules."
    ],
    "rules": null,
    "faqs": [
        {
            "question": "Why is there no simple formula for the rate?",
            "answer": "The payment formula cannot be rearranged for the rate, so it is found by trying rates until the payment matches, as financial calculators do."
        },
        {
            "question": "What if the payments add up to exactly what I borrowed?",
            "answer": "Then the rate is 0%. If they add up to less, no positive rate fits."
        }
    ],
    "sources": [],
    "related": [
        {
            "name": "Loan Calculator",
            "url": "https://calculators.geekmidst.com/calculators/loan-calculator"
        },
        {
            "name": "Finance Calculator",
            "url": "https://calculators.geekmidst.com/calculators/finance-calculator"
        },
        {
            "name": "Auto Loan Calculator",
            "url": "https://calculators.geekmidst.com/calculators/auto-loan-calculator"
        },
        {
            "name": "EMI Calculator",
            "url": "https://calculators.geekmidst.com/calculators/emi-calculator"
        }
    ],
    "disclaimer": "This calculator gives estimates for planning. It is not financial advice, and lenders’ actual terms, fees and rounding may differ.",
    "publisher": "GM¹X CalcVerse"
}