Mortgage Calculator Methodology

This page documents exactly how the FriendlyCalc Mortgage Calculator computes your monthly payment, total interest, and amortization schedule — the formula, the assumptions, the rounding rules, and the authority sources behind each step.

1. The formula

The calculator uses the industry-standard fully-amortizing fixed-rate mortgage formula with monthly compounding. This is the same identity used by every major U.S. lender and referenced by the Consumer Financial Protection Bureau in disclosure examples.

M = P × ( r(1+r)ⁿ ) ÷ ( (1+r)ⁿ − 1 )

M — the fixed monthly principal-and-interest payment
P — the loan amount (home price minus down payment)
r — the monthly interest rate (annual rate ÷ 12)
n — the total number of monthly payments (years × 12)

When the interest rate is zero, the formula collapses to M = P ÷ n, and the calculator switches to that branch to avoid a divide-by-zero.

2. Inputs and how they're handled

Home price

Treated as a positive dollar amount. No cap — you can model any price.

Down payment

Accepted as either a dollar amount or a percentage. The two fields stay synchronized: editing one updates the other based on the current home price. Changing the home price preserves the percentage and recomputes the dollar value.

Loan term

Entered in years and converted to months (years × 12). The 1–50 year range covers every mainstream U.S. product, from a 5-year jumbo payoff through the 40-year extended term some servicers now offer as a modification.

Interest rate

Entered as an annual percentage rate (APR-equivalent, not APY). The calculator converts to a monthly rate by dividing by 12. This matches U.S. mortgage industry convention where nominal rates are compounded monthly rather than continuously.

3. Amortization schedule

After computing M, the calculator walks the loan forward one month at a time:

interest_i = balance_i−1 × r
principal_i = M − interest_i
balance_i = balance_i−1 − principal_i

The yearly view aggregates twelve months at a time, summing principal and interest and reporting the year-end balance. The final balance is floored at zero to absorb floating-point drift on the last payment.

4. What is NOT included

Property taxes. Vary by county and assessed value. Typical range is 0.5%–2.5% of home value per year.
Homeowners insurance. Depends on property, location, and coverage. Typical range is $1,200–$2,500 per year nationally.
Private mortgage insurance (PMI). Applies to conventional loans with less than 20% down. Typically 0.3%–1.5% of the loan amount per year.
HOA dues, flood insurance, and other escrow items. These vary too much to include in a general-purpose calculator.
Closing costs and points. Not financed in this model — treat the stated loan amount as the balance after closing.
Prepayments. The schedule assumes the stated monthly payment for the full term with no extra principal applied.

The result you see is principal and interest only — what lenders call "P&I" on a loan estimate. Your actual monthly bill from the servicer will normally be higher.

5. Rounding and display

All internal math runs at full floating-point precision. Values are rounded to whole dollars only at the display layer. Aggregate totals (total paid, total interest) are derived from the unrounded monthly payment, so they may differ by a few dollars from what you'd get by multiplying the rounded display values — this is expected and matches how lenders present the same numbers.

6. Assumptions in plain English

The calculator assumes a fully-amortizing, fixed-rate loan with monthly compounding, no prepayments, no points, no refinancing, and no change to the principal schedule over the life of the loan. It does not model adjustable-rate loans, interest-only loans, balloon payments, or reverse mortgages.

7. Authority and sources

Consumer Financial Protection Bureau — Owning a Home — disclosure standards, PMI rules, and borrower protections.
Federal Reserve H.15 Selected Interest Rates — benchmark rates for context and calibration.
HUD / FHA Mortgage Limits — FHA down payment and loan limit thresholds.
IRS Publication 936 — Home Mortgage Interest Deduction — deductibility rules referenced in supporting content.

8. Known limitations

Because this is a fixed-rate model, it cannot correctly value an ARM past its first reset, an interest-only period, or any loan whose principal schedule is negotiable. It also cannot model prepayment penalties, recasts, or loan modifications. For any of those scenarios, treat the output as a baseline and adjust manually.

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Reviewed by the FriendlyCalc Math & Editorial Team. Last methodology update: 2026-04 · Next review due: 2027-04

Estimate only. Methodology describes the math this page performs — it is not financial, tax, legal, or investment advice. Verify important decisions with a licensed mortgage professional.