Amortization Calculator

A fixed-rate loan is paid back in equal monthly payments. The payment comes from the level-payment formula, the same one a spreadsheet PMT function uses:

• $M$ is the monthly payment of principal and interest.
• $P$ is the amount you borrowed.
• $i$ is the monthly rate: the yearly rate divided by 12. At 6.5% that is $i = \dfrac{0.065}{12}$.
• $n$ is the number of payments: 30 years is 360.

The schedule then goes one payment at a time. Each month, interest is the balance you still owe times $i$. The rest of the payment is principal, and it comes off the balance:

Here $B_k$ is the balance after payment $k$, $I_k$ its interest and $R_k$ its principal. Extra principal is taken off the balance too, so the next interest charge is smaller. The last payment is cut down to what is left, so the balance ends at exactly zero.

Because the balance is biggest at the start, early payments are mostly interest. On a $300,000 loan at 6.5%, the first payment of $1,896.20 is $1,625.00 of interest and only $271.20 of principal.

Dana reads her mortgage schedule

Dana borrows $300,000 at 6.5% for 30 years, with the first payment in January 2027. Her payment is $1,896.20. Over the full term she pays $382,633 in interest, more than the loan itself.

Principal first beats interest at payment 233, in May 2046. Half the loan is repaid at payment 257, in May 2048. After ten years she still owes $254,328. Open this example in the tool

Dana pays 200 more a month

Dana adds $200 of extra principal to every payment. The loan now ends after 277 payments, in Jan 2050, instead of 360. That is 6 years 11 months sooner, and she saves $103,449 in interest. Open this example in the tool

Marco takes a personal loan

Marco borrows $15,000 at 11% for 36 months. His payment is $491.08 and the loan costs $2,678.91 in interest. On a short loan the balance is small next to the payment, so principal is larger than interest from the very first payment: $353.58 against $137.50. Open this example in the tool

The big number is principal and interest only. A mortgage bill is often higher, because the lender also collects property tax, insurance and sometimes mortgage insurance in an escrow account. The CFPB explains how this payoff pattern works on a loan.

Watch the date where principal passes interest. On Dana's 30-year loan it comes in year 20, so the balance falls slowly at first. On a 5-year car loan it is usually the first payment. If you plan to sell or refinance early, check the schedule for what you will still owe that year.

The rate changes the total far more than the payment suggests. At 7.5% instead of 6.5%, Dana's payment rises by $201.44, but total interest grows by $72,518 over 30 years.

Extra principal saves the most when it starts early. A dollar paid in year one stops interest on that dollar for the rest of the loan. The same dollar paid in year 25 saves only a few years of interest.

• Using the APR as the rate. The APR adds fees to the rate, so it is higher than the rate on your note. Use the note rate, or the payment and interest will come out too high.
• Expecting the payment to drop after paying extra. Extra principal makes the loan end sooner. The required payment stays the same unless the lender agrees to recast the loan.
• Letting the servicer hold the extra money. Some servicers apply an extra amount to next month's payment instead of the balance. Ask for it to go to principal, and check your next statement.
• Comparing the wrong months. Your statement counts from the first payment date, not the closing date. Set the first payment month and year so the dates line up.
• Forgetting rounding. Lenders round each payment to the cent, and some charge interest by the day. Their figures can differ from these by a few cents a month.