Interest Rate Calculator

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Solve the interest rate from a loan amount, loan term, and monthly payment. Optionally subtract taxes, insurance, or other non-loan costs.

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This uses standard monthly payments (principal + interest [the part that pays down the loan plus the cost of borrowing]).
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If your payment includes taxes or insurance, put those in Advanced so the math uses the payment that actually hits the loan.
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Example: escrow for taxes/insurance, HOA, or any fixed monthly add-on. This calculator subtracts it before solving the interest rate.
Used only to show an estimated payoff month.
How to use interest rate calculator
  1. Enter the loan amount: This is the principal you borrowed.
  2. Enter the term: Fill in years and months (months must be 0 to 11). The calculator converts this to a total number of monthly payments.
  3. Enter your monthly payment: Use the full monthly payment amount you pay each month.
  4. Open Advanced options (optional): If your payment includes non-loan items (taxes, insurance, HOA, fixed add-ons), enter that amount as “Other monthly costs” so the calculator solves the rate using the part that actually pays the loan.
  5. Optional first payment month: Add a start month to display an estimated payoff month (based on the term you entered).
  6. Click Calculate: Review the implied interest rate (APR nominal), the monthly rate, total interest paid, and the charts. Use “More details” for totals and assumptions.
Tip: If the calculator says the payment is too low, increase the payment or choose a longer term. Even at 0% interest, the minimum monthly payment is loan amount divided by number of months.

Methodology and sources

This calculator solves the interest rate that makes a standard fixed-payment loan match your inputs. It assumes monthly payments and monthly compounding.

Inputs used

– Loan amount (principal) is the starting balance.
– Term is years and months converted to total months (n).
– Monthly payment is the total you enter.
– If you enter “Other monthly costs”, the calculator subtracts that amount first. The remaining payment is the part that actually pays principal and interest.

Loan model

The loan is treated as a level-payment amortized loan (same payment each month). For a given monthly rate r and term n, the payment that exactly amortizes principal P is:
payment(r) = P * r / (1 – (1 + r)^(-n)) (for r > 0)
payment(0) = P / n
Each month, interest is balance * r. The rest of the payment reduces principal.

How the interest rate is solved

The calculator does not use a closed-form formula for r. It solves for r numerically by finding the rate where payment(r) equals your loan-payment amount.
  • If your loan-payment amount is below P/n, there is no solution (even 0% interest would not pay off the loan on time).
  • Otherwise, it uses a bisection (binary search) method to find r to a high precision.

Rates shown in results

– Monthly rate: r (the solved monthly rate).
– “APR (nominal)” here is shown as 12 * r. This is the common nominal annualisation of a monthly periodic rate.
– Effective annual rate is (1 + r)^12 – 1. This accounts for monthly compounding.

Totals and charts

After solving r, the calculator steps through each month of the schedule: interest = balance * r, principal = payment – interest, then balance decreases by the principal amount. It sums interest across all months to show “total interest paid”. The balance chart uses yearly checkpoints (plus the final point).
Limitations: This model assumes a fixed rate, fixed payment, and no balloon payment. Real lenders can use daily interest, different rounding rules, or fees that change the true APR.

Sources

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