To figure a loan payment on a fixed-rate loan, you need three numbers from your loan documents and one formula. The numbers are the amount borrowed (principal), the interest rate on the note, and the term in months. The formula is M = P × [i(1 + i)^n] / [(1 + i)^n – 1], where i is the monthly interest rate expressed as a decimal and n is the total number of payments. On a $200,000 mortgage at 6% over 30 years, that formula produces a monthly payment of about $1,199.10, and running it yourself lets you check lender quotes and compare offers.
The Three Numbers You Need
Pull these straight from your promissory note or loan estimate. Federal law requires lenders to lay the terms out clearly.1eCFR. 12 CFR Part 226 – Truth in Lending (Regulation Z)
- Principal: the total amount you’re borrowing. On a home purchase, it’s the price minus your down payment. On a car loan, it’s the financed amount after any trade-in credit.
- Interest rate: the annual rate your lender charges, as shown on your promissory note (sometimes called the “note rate”). This is not the same as the APR.
- Loan term: the length of the loan in months. A 30-year mortgage has 360 monthly payments; a 5-year car loan has 60.
Use the Note Rate, Not the APR
Your monthly payment is calculated from the interest rate on your note. The annual percentage rate rolls in extra costs like origination fees, discount points, and mortgage insurance to show the total annual cost of the loan. APR is useful when you’re comparing offers from different lenders, but if you plug it into the payment formula, your result will be too high. Use the note rate.
To prepare the note rate, divide it by 12 to get a monthly rate, then express it as a decimal. A 6% annual rate becomes 0.06 ÷ 12 = 0.005 per month.
The Fixed-Rate Payment Formula
The standard amortization formula looks dense, but it’s one fraction multiplied by the loan amount:
M = P × [i(1 + i)^n] / [(1 + i)^n – 1]
- M = monthly payment
- P = principal (loan amount)
- i = monthly interest rate (annual rate ÷ 12, as a decimal)
- n = total number of monthly payments
Worked Example: $200,000 at 6% for 30 Years
Start with the three inputs. Principal is $200,000. Monthly rate is 0.06 ÷ 12 = 0.005. Payment count is 30 × 12 = 360.
Now work the formula in pieces. Add 1 to the monthly rate: 1 + 0.005 = 1.005. Raise that to the 360th power: 1.005^360 ≈ 6.023. Any phone calculator with an exponent button or any spreadsheet will do this step. Multiply the exponential result by the monthly rate for the numerator: 0.005 × 6.023 = 0.03011. Subtract 1 from the exponential result for the denominator: 6.023 – 1 = 5.023. Divide: 0.03011 ÷ 5.023 = 0.005996. Multiply by the principal: $200,000 × 0.005996 = $1,199.10 per month.
That $1,199.10 stays the same for all 360 payments if you never refinance or make extra payments. What changes each month is how the payment splits between interest and principal. In the first month, interest takes $1,000 of the $1,199.10 ($200,000 × 0.005), and only $199.10 reduces your balance. By the final year, nearly the whole payment goes to principal because the balance left to charge interest on is tiny.
Figuring Total Interest Over the Life of the Loan
Once you have the monthly payment, total interest is easy. Multiply the payment by the number of payments, then subtract the original principal.
For the example above: $1,199.10 × 360 = $431,676. Subtract the $200,000 principal, and you’ve paid $231,676 in interest. That is more than the purchase price of the house.
This is the calculation that makes shorter terms look attractive. The same $200,000 at 6% over 15 years produces a higher monthly payment of about $1,688, but total interest drops to roughly $103,800. Cutting the term in half saves almost $128,000.
Run this on every loan offer you receive. Two loans with the same monthly payment can carry very different total costs when one has a longer term. Lenders sometimes stretch terms to make a payment look affordable while doubling the interest you’ll pay.
Simple Interest Loans
Not every loan uses the standard amortization formula. Some personal loans and auto financing agreements calculate interest daily using simple interest. Instead of dividing the annual rate by 12, you divide by 365 for a daily rate, then multiply that by your current principal balance to get one day’s interest.
For a $15,000 car loan at 7%, the daily charge is ($15,000 × 0.07) ÷ 365 = $2.88. If 30 days pass between payments, you owe $86.30 in interest for that period, and the rest of your payment cuts the balance.
Simple interest rewards early and on-time payments. Because interest accrues daily on whatever your current balance happens to be, paying a few days early means a few fewer days of interest. Paying late lets interest pile up for extra days. Over the life of the loan, consistently late payments on a simple interest product can add hundreds of dollars that wouldn’t show up under standard amortization.
Interest-Only Payments
Some loans begin with an interest-only period, usually five to ten years, before switching to full amortizing payments. The math during that period is as simple as it gets: multiply the loan amount by the annual rate, then divide by 12.
On a $300,000 loan at 7%, the monthly interest-only payment is ($300,000 × 0.07) ÷ 12 = $1,750. That covers the cost of borrowing without touching the balance. When the interest-only period ends, the loan recalculates using the standard amortization formula over the remaining term, and the new payment jumps because you have fewer years to pay down the full principal.
What Escrow Adds to a Mortgage Payment
The number from the amortization formula is only principal and interest. Most mortgage borrowers also pay an escrow amount each month for property taxes, homeowners insurance, and sometimes private mortgage insurance. The lender holds that money and pays the bills when they come due. The industry shorthand for the full payment is PITI: principal, interest, taxes, and insurance.
Calculating the escrow portion is straightforward. Add your annual property tax bill and your annual insurance premiums, then divide by 12. If property taxes are $4,800 per year and homeowners insurance runs $1,500, escrow adds ($4,800 + $1,500) ÷ 12 = $525 per month on top of principal and interest. Lenders may hold a cushion of up to two months’ worth of escrow payments to cover unexpected increases.2Consumer Financial Protection Bureau. 12 CFR 1024.17 – Escrow Accounts
Private Mortgage Insurance
If your down payment is less than 20% of the home’s value, the lender will almost certainly require private mortgage insurance, which protects the lender if you default. PMI typically costs 0.5% to 1% of the original loan amount per year, added to monthly escrow. On a $250,000 loan, that’s roughly $104 to $208 per month.
You can request cancellation once your balance drops to 80% of the home’s original value. The servicer must automatically cancel PMI when your balance reaches 78% of the original value based on the amortization schedule, as long as you’re current on payments.3Office of the Law Revision Counsel. 12 USC 4902 – Termination of Private Mortgage Insurance On a standard 30-year loan, that automatic point can take over a decade to reach without extra payments.
How Extra Payments Change the Numbers
Every dollar you pay above the required monthly amount goes directly to principal, and that reduction compounds. Because next month’s interest is calculated on a smaller balance, each extra payment shrinks the interest portion of every future payment.
On the $200,000 loan at 6%, adding $100 per month to every payment saves roughly $40,000 in total interest and takes about five years off the loan. The savings grow disproportionately when the extra payments come early, because interest charges are highest when the balance is largest. Occasional lump-sum payments make a noticeable difference as long as they are applied to principal.
Recasting After a Lump Sum
Some lenders offer a formal recast after you make a large principal payment. A recast keeps your original interest rate and remaining term, but recalculates your monthly payment based on the lower balance. There’s no credit check, no appraisal, no closing costs. The lender plugs the reduced balance into the same amortization formula. Recasting is useful if you want a lower required payment rather than a shorter payoff timeline.
Recalculating After a Rate Change
Adjustable-rate loans begin with a fixed rate for an initial period, commonly five, seven, or ten years, then reset periodically based on a market index plus a margin set by the lender. When the rate adjusts, your monthly payment changes because you’re plugging a new interest rate into the amortization formula along with the remaining balance and the remaining months.
Say your 5/1 ARM started at 5% on a $300,000 balance with 25 years left after the fixed period ends. If the rate adjusts to 6%, you’d recalculate using P equal to the current balance, i = 0.06 ÷ 12 = 0.005, and n = 300 (25 years × 12). Same formula, new inputs.
Rate caps limit how much the rate can move. The subsequent adjustment cap on most ARMs is one or two percentage points per adjustment period, and a lifetime cap limits the total increase over the life of the loan.4Consumer Financial Protection Bureau. What Are Rate Caps With an Adjustable-Rate Mortgage (ARM), and How Do They Work Your servicer must send a notice estimating the new rate and payment before each adjustment, giving you time to refinance or prepare.
Check for a Prepayment Penalty Before You Pay Ahead
Before making extra payments or paying off a loan early, check whether your contract carries a prepayment penalty. These penalties exist to compensate the lender for interest income lost when you pay ahead of schedule. Common structures include a flat percentage of the remaining balance, a charge equal to several months of interest, or a sliding scale that decreases over the first few years.
Federal law limits prepayment penalties on qualified mortgages to a phased schedule: no more than 2% of the outstanding balance during the first two years, no more than 1% during the third year, and no penalty at all after three years.5Office of the Law Revision Counsel. 15 USC 1639c – Minimum Standards for Residential Mortgage Loans Adjustable-rate mortgages that qualify as qualified mortgages cannot carry prepayment penalties at all. For non-mortgage consumer loans, state law governs whether prepayment penalties are allowed, and the rules vary widely.
Any penalty large enough to offset your interest savings defeats the purpose of paying early. When you’re comparing payoff strategies, subtract the penalty from the projected interest savings and see whether early repayment still comes out ahead.