A fixed-rate mortgage has one monthly payment that stays the same for decades, which hides what is going on inside it. In the first years almost all of the payment is interest. Near the end, almost all of it is principal. Understanding that shift explains why paying a little extra early on saves so much, and why the total cost of a loan is far higher than the amount you borrowed. This guide shows the formula, a worked 30-year example and what extra payments do.
The payment formula
For a fixed-rate loan paid monthly, the payment is M = P × i × (1 + i)^n / ((1 + i)^n − 1).
P is the amount borrowed. i is the monthly interest rate, which is the annual rate divided by 12, so 6% a year is 0.5% a month or 0.005. n is the total number of monthly payments: 360 for a 30-year loan and 180 for a 15-year loan.
The formula chooses the one payment that leaves the balance at exactly zero after the last month, given that interest is charged each month on whatever balance remains.
Worked example: 300,000 at 6% for 30 years
Here P = 300,000, i = 0.005 and n = 360. The growth factor (1.005)^360 is about 6.0226.
M = 300,000 × 0.005 × 6.0226 / (6.0226 − 1) = 9,033.9 / 5.0226 = about 1,798.65 per month.
Over 360 payments you will pay 1,798.65 × 360 = about 647,515. That is 300,000 of principal and about 347,515 of interest, more than the amount you borrowed. This is not a trick; it is what charging interest on a balance for thirty years does.
What the first payment is made of
In month one, interest is the monthly rate times the full balance: 0.005 × 300,000 = 1,500. The payment is 1,798.65, so only 298.65 goes to principal. The balance after the first payment is 299,701.35.
In month two, interest is 0.005 × 299,701.35 = 1,498.51, and the principal part is 300.14. Each month the interest part shrinks a little and the principal part grows by a little, while the total payment stays the same. This table of the split, month by month, is called an amortization schedule.
After 15 years of this 30-year loan, you have paid half of the payments but you still owe about 213,000, which is roughly 71% of the original amount. The balance falls slowly at first and quickly at the end.
How the term changes the cost
The same 300,000 at the same 6% over 15 years has n = 180. The growth factor is about 2.4541, so M = 1,500 × 2.4541 / 1.4541 = about 2,531.57 per month.
The monthly payment is about 733 higher, but total payments are 2,531.57 × 180 = about 455,683, so total interest falls to about 155,683, less than half of the 30-year interest. A shorter term costs more per month and much less overall. The interest rate on short loans is often a little lower as well, which widens the gap.
What extra payments do
Suppose you add 200 a month to the 30-year loan, so you pay 1,998.65. All of the extra goes straight to principal. The loan is repaid in about 23 years and 2 months instead of 30 years, and total interest drops by roughly 91,000.
The effect is large because each extra payment lowers the balance on which all later interest is charged, so it saves the interest for every remaining month. The earlier you make it, the more it saves. Check that your lender applies extra money to principal and does not charge a penalty for early repayment.
Things the formula does not include
The payment above covers principal and interest only. Most mortgages also collect property tax and homeowners insurance, often through an escrow account, and they may include mortgage insurance if the deposit is small. These can add several hundred a month, so your real payment is higher than the formula result.
Adjustable-rate mortgages change the rate after an initial period, so the payment is recalculated using the remaining balance and remaining term. Fees at closing, such as arrangement and valuation fees, are paid separately and affect the true cost of the loan.
Frequently asked questions
Why is so much of my early payment interest? Because interest is charged on the whole balance, and the balance is largest at the start.
Is a 15-year loan better than a 30-year loan? It costs less in total interest but needs a higher payment. It depends on what payment you can sustain comfortably and what you would do with the difference.
Do bi-weekly payments help? Paying half the monthly amount every two weeks gives 26 half-payments, which equals 13 full payments a year instead of 12. The extra payment goes to principal and shortens the loan.
What is APR? The annual percentage rate includes some fees in addition to the interest rate, so it lets you compare loans more fairly than the headline rate does.
Run your own numbers
Use our loan and mortgage calculators to enter your own amount, rate and term, view the amortization schedule and test the effect of extra payments. The numbers in this article are examples, not offers or financial advice; your lender's terms will differ.