Calculate a loan's monthly principal and interest

Mortgage payment questions become manageable once the units match. Use the amount borrowed, the interest rate per payment period, and the total number of payments. For a fixed-rate loan with monthly payments, that means converting the annual rate to a monthly rate and the term in years to months before using the amortization formula.

The fully amortizing payment formula

Let P be the original loan principal, r the monthly interest rate as a decimal, and n the total number of monthly payments. The scheduled monthly principal-and-interest payment M is: M = P × r ÷ [1 − (1 + r)^−n]. This payment is level each month when the rate and payment schedule are fixed. The shares going to interest and principal change over time.

Convert the inputs first

• Principal (P): use the amount financed, not the home price. If the price is $400,000 and the down payment is $80,000, the starting principal is $320,000 before any financed costs.
• Monthly rate (r): for a 6% annual nominal rate with monthly payments, divide 0.06 by 12. The formula needs 0.005, not 6 or 0.06.
• Number of payments (n): a 30-year monthly loan has 30 × 12 = 360 payments. A 15-year monthly loan has 180.

Worked example

For a $100,000, 30-year fixed-rate mortgage at 4% nominal annual interest, P = 100,000, r = 0.04 ÷ 12, and n = 30 × 12. Substituting these into the formula gives a monthly principal-and-interest payment of about $477.42, which rounds to $477 when stated to the nearest dollar. That is the same scale as the CFPB's example.

To check the first payment, multiply the opening balance by the monthly rate: $100,000 × (0.04 ÷ 12) = about $333.33 interest. Subtract that interest from the payment; about $144.09 reduces principal. The next month's interest is lower because the balance has fallen. Over time, the principal portion grows while the interest portion shrinks.

What this payment includes

The formula gives principal and interest only. A borrower's total monthly housing payment may also include property taxes, homeowners insurance, mortgage insurance, and other amounts collected through escrow. Those costs do not belong in the amortization formula unless the question explicitly asks for the total payment and gives the extra amounts.

The scheduled amount also assumes a fully amortizing loan. An interest-only period, adjustable rate, balloon feature, payment-option ARM, or other special term changes the payment analysis. For an ARM, the rate and payment may be recalculated at adjustment dates. For a balloon loan, regular payments may leave a large balance due at maturity.

Common calculation errors

• Using the annual rate as r instead of dividing it by 12.
• Entering 6 for a 6% rate rather than 0.06, or 0.5 instead of 0.005 for a 6% monthly rate.
• Using 30 as the number of payments instead of 360 for a 30-year monthly loan.
• Using the purchase price as principal without subtracting the down payment.
• Adding taxes and insurance to a question that asks for principal and interest only.
• Rounding the monthly rate or intermediate values too early. Keep precision through the calculation and round the final payment as directed.

Calculator setup and result check

On a financial calculator, enter the number of monthly payments as N, the annual rate divided by 12 as I/Y (or the calculator's per-period rate field), the amount financed as PV, and zero as FV for a fully paid-off loan. Set payments per year to 12 if the calculator has that setting. Solve for PMT. Confirm the sign convention: calculators often show the payment opposite in sign from the present value because cash flows in and out are treated as opposite directions.

A rough reasonableness check helps catch setup errors. A higher loan amount, higher rate, or shorter term raises the monthly principal-and-interest payment. A longer term lowers the payment but generally means more total interest over the full schedule. If your answer is only a few dollars on a six-figure mortgage, you likely mixed annual and monthly units or failed to convert the term.

Exam method

Write P, monthly r, and monthly n separately before calculating. Decide whether the question asks for principal and interest or the full housing payment. Then solve, sanity-check the direction of the answer, and round at the end. This order is faster than trying to remember numbers without tracking their units.