To calculate PMT manually, you need three numbers from your loan — the principal, the periodic interest rate, and the total number of payments — and you plug them into the amortization formula PMT = P × [r(1 + r)n] / [(1 + r)n − 1]. The math involves one exponent step that requires a scientific calculator, but the whole process takes about five minutes once you know the sequence.
The Three Inputs
Every PMT calculation uses exactly three numbers. Get any of them wrong and your answer will be off, sometimes by hundreds of dollars a month.
Principal (P) is the total amount borrowed. For a home purchase, that’s the sale price minus your down payment, plus any closing costs you roll into the loan. Financing closing costs raises the principal above the purchase price.
Periodic interest rate (r) is your annual rate divided by the number of payments per year. For a monthly payment, divide by 12. A 6% annual rate becomes 0.06 ÷ 12 = 0.005 per month. Use the note rate from your loan documents, not the APR.
Total number of payments (n) is the loan term in years times payments per year. A 30-year mortgage with monthly payments has 360. A 15-year mortgage has 180.
Federal law requires the lender to disclose the principal and interest rate on your loan documents, so both figures should appear on your promissory note or closing disclosure.
Use the Note Rate, Not the APR
This is the single most common mistake in a hand calculation. Loan documents show two rates that look similar but mean different things. The interest rate — the note rate — is what the lender charges each year for borrowing the money. The APR is a broader figure that folds in points, broker fees, and other loan costs to reflect the total cost of credit over its life.1Consumer Financial Protection Bureau. What Is the Difference Between a Mortgage Interest Rate and an APR
The PMT formula uses the note rate. The APR exists for comparing offers between lenders and does not determine your actual monthly payment. Plug the APR in and your calculated payment will come out higher than what the lender charges, because you’d be double-counting fees already reflected elsewhere in the loan structure.
The Formula
The standard amortization formula has only three moving parts:
PMT = P × [r(1 + r)n] / [(1 + r)n − 1]
- P = loan principal
- r = periodic interest rate (annual rate ÷ 12 for monthly payments)
- n = total number of payments (years × 12 for monthly payments)
The fraction on the right is sometimes called the payment factor. Calculate it once, multiply by your principal, and you have the fixed monthly payment. On a fixed-rate loan that payment stays constant for the life of the loan, even though the interest and principal proportions shift each month.
Worked Example: $250,000 at 6% for 30 Years
Step 1: Convert the Rate and Count the Payments
Divide the annual rate by 12 and convert to decimal form:
r = 6% ÷ 12 = 0.5% per month = 0.005
Multiply the term by 12:
n = 30 × 12 = 360
Step 2: Calculate the Growth Factor
The expression (1 + r)n appears in both the numerator and denominator, so calculate it once and reuse it. Add 1 to the monthly rate and raise it to the 360th power:
(1.005)360 ≈ 6.02258
You need a scientific calculator or a phone calculator with an exponent function here. Raising 1.005 to the 360th power by hand isn’t realistic. Most phone calculators have an xy button that handles it. Carry at least five decimal places; rounding too early throws off the final answer.
Step 3: Calculate the Numerator
Multiply the monthly rate by the growth factor:
r × (1 + r)n = 0.005 × 6.02258 = 0.030113
Step 4: Calculate the Denominator
Subtract 1 from the growth factor:
(1 + r)n − 1 = 6.02258 − 1 = 5.02258
Step 5: Divide, Then Multiply by the Principal
Divide the numerator by the denominator:
0.030113 ÷ 5.02258 = 0.005996
Multiply that payment factor by the principal:
PMT = $250,000 × 0.005996 = $1,498.88 per month
That figure covers principal and interest only. Across 360 payments the total comes to $539,597, meaning $289,597 of it is interest.
Rounding and Precision
Rounding too aggressively at intermediate steps is where most hand calculations go wrong. The monthly rate on a 6% loan is 0.005, which is clean. A rate like 6.375% gives you 0.0053125 per month, and dropping decimals early creates errors that multiply through the exponent step. Carry at least five decimal places through every intermediate calculation and only round your final answer to the nearest cent.
Federal regulations don’t require lenders to calculate the periodic rate to a specific number of decimal places. The requirement is that the annualized equivalent stays within disclosure tolerances.2Consumer Financial Protection Bureau. Comment for 1026.14 – Determination of Annual Percentage Rate For your own math, more precision is always better than less. If your answer is off by a penny or two from the lender’s figure, rounding is the likely explanation.
What the Formula Doesn’t Cover
PMT calculates principal and interest only. If you’re buying a home, your actual monthly obligation almost always includes property taxes and homeowners insurance as well. The industry calls the four-part total PITI: principal, interest, taxes, and insurance.3Consumer Financial Protection Bureau. What Is PITI
Most lenders collect the tax and insurance portions monthly through an escrow account. Your servicer holds the funds and pays your property tax bill and insurance premium when they come due. To estimate the escrow portion, add your expected annual property taxes and annual insurance premium and divide by 12. Federal rules also allow the servicer to hold a cushion equal to up to one-sixth of the total annual escrow payments.4Consumer Financial Protection Bureau. 1024.17 Escrow Accounts
On a home assessed at $300,000 with a 1.2% effective property tax rate, you’d owe about $3,600 per year in property taxes, or $300 per month in escrow. Homeowners insurance runs roughly $1,500 to $4,000 annually for standard coverage. Adding both to the $1,498.88 principal-and-interest figure above can easily push the real monthly obligation past $2,000.
When Your Answer Doesn’t Match the Lender’s
If you run the formula carefully and your answer differs from the payment on your loan documents by more than a few cents, the discrepancy usually traces to one of three causes. You used the APR instead of the note rate. Closing costs were financed into the loan, so the true principal is higher than the purchase price minus your down payment. Or the lender uses a slightly different day-count method for the first partial month of interest.
A small mismatch is almost always a rounding difference. The formula above and the lender’s software rely on the same underlying math, so if the inputs match, the outputs should agree within a cent or two.