finance
Why Your First Mortgage Payment Is Mostly Interest
On a $375,000 loan at 7%, payment one is $2,187.50 interest and $307.38 principal. The two-line formula behind it, the crossover month, extra payments, and PMI.
Your first mortgage statement arrives, you pay $2,494.88, and the balance drops by about $300. It’s easy to assume the bank has loaded the fees up front. It hasn’t. Each month’s interest is just the rate times whatever you still owe, and in month one you owe nearly everything. The payment stays level, so interest takes almost all of it at the start and principal takes almost all of it at the end. The rest of this post derives the formula, finds the month where the split flips, and uses the same schedule to show what extra payments, bi-weekly plans and PMI rules actually do.
Every number below comes from running our mortgage calculator’s code, not from a spreadsheet we typed by hand. The running example is a $375,000 loan at 7% for 30 years, first payment November 2026. These are estimates for planning, not financial advice.
The formula in two lines
Call the loan amount P, the monthly rate r (the annual rate ÷ 12, so 7% → 0.0058333…) and the number of payments n. Each month, the balance grows by interest and shrinks by your payment M:
B(k) = B(k−1) · (1 + r) − MUnroll that recurrence k times and you get the balance after k payments:
B(k) = P(1 + r)^k − M · ((1 + r)^k − 1) / rThat’s the first line. For the second, a fully amortizing loan ends with B(n) = 0, so solve for M:
M = P · r(1 + r)^n / ((1 + r)^n − 1)This is the formula our calculators use (written in the equivalent form M = P·r / (1 − (1 + r)^−n) in src/lib/finance/amortization.ts). For our loan, n = 360:
| Quantity | Value |
|---|---|
| Exact formula payment | $2,494.884356… |
| Payment, rounded to the cent | $2,494.88 |
| Total of 360 payments | $898,161.84 |
| Total interest | $523,161.84 |
Total interest comes to about 139.5% of the amount borrowed. If you want to check that kind of ratio yourself, the percentage calculator does it in one step.
Month one: $2,187.50 interest, $307.38 principal
The split isn’t a policy. It comes straight out of the recurrence. Month-one interest is the full balance times the monthly rate:
$375,000 × 0.07 / 12 = $2,187.50Whatever is left of the $2,494.88 payment goes to principal: $307.38. So 87.7% of your first payment is interest. The CFPB puts it plainly: “At the beginning of your loan term, more of your payment is generally applied toward the interest rather than the principal.”
Here is the part people rarely see spelled out. Principal paid in month k + 1 is exactly (1 + r) times the principal paid in month k, because the principal you paid last month stops accruing interest and that saving gets added to this month’s principal. So the principal share grows by a constant factor of about 0.58% a month, which is exponential:
principal(k) = (M − rP) · (1 + r)^(k−1)Our schedule shows it: $307.38, then $309.17, then $310.98. Here’s how it plays out over the life of the loan:
| Payment # | Interest | Principal | Balance after |
|---|---|---|---|
| 1 | $2,187.50 | $307.38 | $374,692.62 |
| 12 | $2,167.19 | $327.69 | $371,190.76 |
| 60 (year 5) | $2,061.66 | $433.22 | $352,993.74 |
| 120 (year 10) | $1,880.73 | $614.15 | $321,797.15 |
| 180 (year 15) | $1,624.25 | $870.63 | $277,572.05 |
| 242 | $1,246.21 | $1,248.67 | $212,387.34 |
| 300 (year 25) | $745.21 | $1,749.67 | $125,999.97 |
| 360 | $14.50 | $2,485.42 | $0.00 |
In the first year you pay $26,129.32 in interest and $3,809.24 in principal. After ten years of payments you have paid off about $53,000 of a $375,000 loan.
The crossover month
The crossover is the first payment where principal beats interest, which means principal(k) > M/2. Using the growth formula above:
k − 1 > ln(M / (2(M − rP))) / ln(1 + r)
= ln(2494.88 / 614.76) / ln(1.0058333) ≈ 240.8So k = 242, the December 2046 payment, just over 20 years into a 30-year loan. Our schedule agrees: payment 241 still tips toward interest, and payment 242 is the first with more principal ($1,248.67 vs $1,246.21). You don’t reach half the original balance until payment 261.
What an extra $200 a month does
Extra principal skips the queue. It lowers the balance right away, so every later month’s interest is computed on a smaller number, and the whole exponential curve moves forward. Adding $200 to every payment:
| Standard | +$200/month | |
|---|---|---|
| Payments | 360 | 288 |
| Payoff | Oct 2056 | Oct 2050 |
| Total interest | $523,161.84 | $398,684.33 |
| Interest saved | — | $124,477.51 |
Six years sooner and about $124,500 less interest, for $57,400 of extra principal. (The final payment is only $253.77.)
In the calculator, enter the amount under Extra payments as “extra every month”, “extra once a year” (applied with payments 12, 24, 36…) or “one-time extra” at a payment number you choose. It then shows the result next to the same loan without extras. Before you prepay, confirm with your servicer that the extra money goes to principal and that your loan has no prepayment penalty.
Why bi-weekly means 13 payments
A bi-weekly plan has you pay half your monthly payment every two weeks. A year has 52 weeks, so that’s 26 half-payments, which equals 13 full payments instead of 12. The plan works because of that extra payment, not because paying more often is special.
Our calculator has no bi-weekly mode, but you can model the 13th payment by entering one full payment ($2,494.88) as “extra once a year”. On our loan that pays off in 288 payments and saves $123,182.77 in interest, almost exactly what $200 a month does. Spreading the same yearly amount across months ($207.91 extra each month) does slightly better: 285 payments and $128,033.36 saved, since each extra dollar starts reducing interest sooner. Real bi-weekly results depend on when your servicer actually credits the half-payments. Some hold them until a full payment has built up. Paying one-twelfth extra each month gets the same effect with no enrollment fee.
Why the last payment isn’t $2,494.88
The formula payment is $2,494.884356…, and a lender can’t charge a fraction of a cent. Our schedule works the way a servicer does. It keeps everything in integer cents, rounds each month’s interest to the cent, rounds the scheduled payment to the cent, and adjusts the final payment so the balance comes out to exactly zero. Those roundings leave a few dollars of difference over 360 months. On our loan the final payment is $2,499.92 ($2,485.42 principal + $14.50 interest), which is $5.04 more than the regular payment.
PMI: 78% happens on its own, 80% you have to ask for
Put down less than 20% and a conventional lender will usually charge private mortgage insurance. The rules for ending it are in the Homeowners Protection Act, and there are two thresholds that are easy to mix up:
- 78%, automatic. PMI must terminate on the “termination date”: the date the principal balance, “based solely on the initial amortization schedule,” is first scheduled to reach 78% of the original value (12 U.S.C. §4901(18), §4902(b)). You must be current on payments.
- 80%, on request. You can ask to cancel PMI on the “cancellation date,” which is based either on the initial schedule or on actual payments (§4901(2)). You need a good payment history, you must be current, you may have to show the property hasn’t lost value, and there can’t be a second lien (§4902(a)).
- Midpoint backstop. If neither of those has happened, PMI must end the month after the midpoint of the amortization period (§4902(c)).
“Original value” is the lower of the contract sales price and the appraised value. The CFPB’s summary adds the practical point: “You can ask to cancel PMI ahead of the scheduled date, if you have made additional payments that reduce the principal balance.”
For our example, suppose a $400,000 house with $25,000 down (93.75% LTV) and PMI at our calculator’s default of 0.75% of the loan per year, which is $234.38 a month:
| Milestone | Balance threshold | Reached at |
|---|---|---|
| 80%, scheduled | $320,000 | payment 123 (Jan 2037) |
| 78%, scheduled: automatic end | $312,000 | payment 136 (Feb 2038) |
| 80% with +$200/month: you can ask | $320,000 | payment 85 (Nov 2033) |
| Midpoint backstop | — | after payment 180 |
Our calculator follows the statute on both dates. It charges PMI while the balance on the original schedule is above 78% of the price you enter: 136 payments and $31,875.68 in total, and that stays 136 payments even with +$200 a month, because the law’s automatic termination ignores extra payments. What extra payments really speed up is your right to request cancellation at 80%, so the calculator separately reports the payment after which your actual balance is at 80%: payment 85 (November 2033) in this example, against payment 123 without extras. From that point you have to ask, and the lender can require that you be current and, in some cases, an appraisal. FHA loans have their own mortgage insurance rules that the HPA doesn’t cover.
Interest rate vs APR
Use the interest rate in the mortgage calculator, not the APR. The CFPB’s explanation is that the interest rate “does not reflect fees or any other charges,” while the APR also includes “any points, mortgage broker fees, and other charges that you pay to get the loan.” On a Loan Estimate, the rate is on page 1 under Loan Terms and the APR is on page 3 under Comparisons. Regulation Z defines APR as “a measure of the cost of credit, expressed as a yearly rate” and allows a disclosed APR to be off by up to 1/8 of a percentage point for regular transactions (12 CFR 1026.22). If you enter the APR as the rate, you add the fees to every month’s interest and overstate the payment. The APR is for comparing offers. Our loan calculator works the same way: fixed rate, monthly payments, no fees or APR adjustments. It can also solve for whichever of amount, rate, term or payment you leave blank.
Car loans: same formula, messier principal
An auto loan amortizes the same way. The difference is in the amount financed, and our auto loan calculator computes it as:
price + sales tax + fees − down payment − (trade-in value − trade-in payoff)When you owe more on your trade-in than it’s worth, the part in parentheses is negative, and that negative equity is added to the new loan. You end up paying interest on a car you no longer own.
Sales tax depends on your state. Texas lets you deduct the trade-in’s value (the vehicle’s value, “not the equity”) from the taxable price (Texas Comptroller). California doesn’t: dealers “cannot deduct the allowance for the trade-in” (CDTFA). Our calculator uses price minus trade-in by default, and you can switch it to full price.
Here’s an example: a $35,000 car, $3,000 down, a trade-in worth $10,000 with $14,000 still owed, a 7.25% tax rate, $500 in fees, and 7% for 60 months:
| Tax on price − trade-in | Tax on full price | No negative equity* | |
|---|---|---|---|
| Sales tax | $1,812.50 | $2,537.50 | $1,812.50 |
| Amount financed | $38,312.50 | $39,037.50 | $34,312.50 |
| Monthly payment | $758.63 | $772.99 | $679.43 |
| Total interest | $7,205.53 | $7,341.84 | $6,453.19 |
*Same deal, but the trade-in is paid off in full ($10,000 owed).
The $4,000 of negative equity adds $79.20 a month and $752.34 of interest. The calculator also shows 36 to 84-month terms side by side for the same amount financed.
Compound interest is the same formula run forward
The balance equation at the top works for savings too. Flip the sign of the payment, so each contribution adds to the balance instead of subtracting from it, and you get the future value of regular deposits:
FV = P(1 + i)^N + PMT · ((1 + i)^N − 1) / iWith a loan, interest works against you. With savings, it’s the same growth working for you. Our compound interest calculator has a “Roth IRA max, 25 yrs” preset: $7,500 a year, which is the IRS limit for 2026 across all your traditional and Roth IRAs ($8,600 if you’re 50 or older, or your taxable compensation if that’s lower), at an assumed 7% compounded annually. With contributions at the end of each year, which is the calculator’s default, it grows to $474,367.78 on $187,500 of contributions. Switch the timing to start of year and it’s $507,573.53. The preset keeps the contribution flat for all 25 years, and 7% is an assumption, not a promise. For the difference between a rate going from 6% to 7% and a 1% change, see percentage points vs percent change.
Try it on your own loan
Open the mortgage calculator, enter your price, down payment and the note rate from your Loan Estimate, and scroll the amortization schedule to your current payment number. You’ll see this month’s split, your crossover month and your PMI date. Then try an extra monthly amount and see how much interest and time it saves. Everything runs in your browser, and you can download the full schedule as CSV. These are estimates. Your servicer’s statement is the final word.
Comparing offers? APR vs APY, and why compounding frequency matters less than you think explains why the APR on a Loan Estimate isn’t the note rate. And the same amortization math is why a longer car loan costs more even when the payment looks better.