How Loan Payments Are Calculated, and Where the Money Goes

Every fixed-rate loan payment comes out of the same formula: M = P × r / (1 − (1 + r)−n). P is the amount borrowed, n is the number of monthly payments, and r is the monthly interest rate — the annual rate divided by 12 and then by 100, so 6% a year is 0.005 a month. Borrow $250,000 over 30 years at 6% and the arithmetic gives 250,000 × 0.005 ÷ (1 − 1.005⁻³⁶⁰), which is $1,498.88 a month for 360 payments. Mortgage, car loan, student loan, personal loan: if the rate is fixed and the payments are equal, it is this formula.

What the formula is doing

An amortizing loan has to satisfy two conditions at the same time. Every payment is identical, and the balance lands on exactly zero at the end of the term. Inside each month the rule is simple — interest is the outstanding balance times the monthly rate, and whatever is left of your payment comes off the balance. Because the balance falls, next month's interest is slightly smaller and slightly more of the payment reaches the debt.

The formula is just the answer to "what single payment size makes that sequence hit zero on payment n". The denominator, 1 − (1 + r)−n, is what a stream of n payments of one unit is worth today. Nothing more exotic than compound interest run backwards, pointed at you instead of at your savings.

One special case: if the rate is genuinely 0%, both halves of the fraction collapse to zero and the formula tells you nothing. The payment is just the amount divided by the number of months.

Why almost all of the first payment is interest

Interest is charged on what you still owe, and you never owe more than you do on day one. On the $250,000 example, the first month's interest is 250,000 × 0.005 = $1,250. Your payment is $1,498.88. That leaves $248.88 — about a sixth of it — actually reducing the debt.

Stretch that over a year and it is worse than it sounds. You hand over $17,986 in the first twelve months and the balance drops by roughly $3,070. Five years in, having paid $89,933, you have cut a $250,000 balance down to $232,636. About $72,600 of that money was rent on the loan.

This is not a trick. It falls straight out of charging interest on a balance that starts high. But it is invisible unless you look at the schedule, which is why the loan calculator here breaks the split down year by year — what you paid, how much of it was interest, and what is left. Put your own figures in, open the schedule, and read year one before you read the monthly payment.

When does principal finally overtake interest?

On a 30-year loan at 6%, at payment 223 — a little past the 18-year mark. The crossover happens when the balance drops below the payment divided by twice the monthly rate, which on these numbers is $149,888. Before that point, most of each payment is interest. After it, most of it is yours.

Two things follow. Refinancing into a fresh 30-year term puts you back at the start of that curve even if the rate is better, so compare total interest, not just the payment. And selling early is expensive in a way the monthly figure hides: five years of payments retired 7% of the debt.

Which number moves the payment most

The amount borrowed is linear — halve it and the payment halves. The other two inputs are not, and that is where the money is.

• Term. Cutting the same $250,000 loan from 30 years to 15 raises the payment from $1,498.88 to $2,109.65. That is 41% more, not double, and it takes total interest from about $289,600 down to about $129,700. Halving the term saves roughly $160,000.
• Rate. Going from 6% to 7% adds only $164 to the monthly payment — an 11% increase you might shrug at. Over 30 years it adds about $59,000 in interest, a 20% increase. One percentage point is not a small difference, it just looks like one on a monthly statement.

The general shape: the term controls how long interest has to accumulate, the rate controls how fast. Both compound, which is why they punch above what the monthly figure suggests. If percentage-point arithmetic is where you lose the thread, the difference between a percent and a percentage point is worth five minutes.

What paying extra actually buys

An extra payment has no interest attached to it yet, so it comes off the principal in full — and takes with it every month of future interest that principal would have earned. That is why the savings look out of proportion to the money.

On the $250,000 loan at 6%, an extra $100 a month clears it in 25 years and 6 months instead of 30, and saves about $51,600 in interest. The common biweekly trick — half the payment every two weeks, which is 26 half-payments and therefore 13 monthly payments a year — takes about five and a half years off the same loan. It is the same mechanism dressed up as a payment schedule.

Timing matters more than size. An extra payment in year two cancels 28 years of interest on that money. The same payment in year 25 cancels five. The same money is worth several times as much early in the schedule as late in it.

Two things get in the way. Some lenders apply anything above the scheduled amount to your next payment rather than to the balance, which achieves almost nothing unless you tell them in writing that overpayments go to principal. And early repayment charges are real, more common outside the United States, and can swallow the benefit entirely. The agreement says which applies; the marketing does not.

Why your lender's number will not match exactly

Compare the formula against your paperwork and the figures will differ. Usually for one of these reasons:

• Escrow. The amount that leaves your account may include property tax, home insurance, mortgage insurance and HOA dues. On a US mortgage those routinely add hundreds a month on top. The formula covers principal and interest only.
• Rate versus APR. The APR folds origination fees and points into one annualised number, so it is normally higher than the interest rate and never lower unless the lender is crediting you money. Use the interest rate in the formula. Use the APR to compare two offers, because comparing by rate alone is how you pick the more expensive loan.
• Compounding convention. Dividing the annual rate by 12 is the US convention. Canadian fixed-rate mortgages are quoted with semi-annual compounding, and most UK mortgages charge interest daily on the balance. Expect a gap of a few units of currency, not a few hundred.
• Rounding. The scheduled payment is rounded to the cent. Rounding up is what makes the balance clear inside the term, and it leaves the final payment slightly smaller than all the others — the calculator here rounds up for that reason. It is why your last statement never matches the rest.

When this formula does not apply

It assumes a fixed rate and equal amortizing payments. Three common loans break that assumption:

• Flat-rate or add-on interest. Common in car and consumer finance in parts of Asia, Africa and Latin America. A "10% flat" rate over three years means total interest of 30% of the original amount, charged as if you never paid any of it back. Quoted the way a mortgage rate is quoted, that deal is about 18% a year. The two numbers are not comparable until you convert one.
• Interest-only and balloon loans. The balance does not fall during the interest-only period, so none of the schedule above happens until it ends.
• Variable and adjustable rates. The formula still works, but only for as long as the rate holds. Running it twice — once at today's rate and once at a rate that would be uncomfortable — gives you the range the payment can move inside.

The mirror image is worth knowing too, because it is the same arithmetic with the sign flipped: money you owe compounds against you exactly the way money you save compounds for you. A 6% loan and a 6% investment are the same curve seen from opposite sides, and a compound interest calculator draws the side facing the other way — which is the comparison sitting underneath the question of whether to overpay a mortgage or invest the difference.

Last updated September 19, 2026