RightFiguresA 15-year mortgage and a 30-year mortgage can use different interest rates. This comparison shows the regular principal-and-interest payment, the last payment, the interest, and the principal and interest paid through the month each balance reaches zero.
The terms are scheduled for 15 years and 30 years. Those lengths are not inputs. The payoff period is the number of months until that loan’s balance reaches zero. Cent rounding can finish a loan before the scheduled term. When that happens, the result says how many months the loan actually ran.
What is included
Each side uses only the loan amount and its own annual rate. Taxes, insurance, mortgage insurance, points, and lender fees are not included. The difference between the monthly payments is not invested, and no extra principal payments are applied.
The principal-and-interest total is the sum of the payments through payoff. When the balance ends at zero, that total equals the loan principal plus the interest charged. It is not the “total of payments” on a Closing Disclosure, which can also include mortgage insurance and loan costs.
How the payments are calculated
The regular payment is the standard monthly loan payment, rounded half-up to the cent, and at least one cent. A 0% rate divides the principal by 180 or 360 months. Each month, interest is the remaining balance times the annual rate divided by 12, rounded half-up to the cent. The payment is the regular amount until the remaining balance and that month’s interest are smaller. The last scheduled month pays whatever balance and interest remain.
A rate is rejected when a month before the last scheduled month would charge interest at least as large as the regular payment, because the balance would not fall. A rate is also rejected when the final payment would be more than twice the regular payment. Either rejection removes the whole comparison.
Worked example
A $320,000 loan at 6% on both terms has a 15-year payment of $2,700.34 and a 30-year payment of $1,918.56. The 15-year payment is $781.78 more each month. The 30-year loan charges $204,621.67 more interest. Both loans repay the same principal, so the extra amount paid is the same $204,621.67. A different rate on each term changes both the payment and the interest.
Sources & review
- Shopping for a mortgage — Consumer Financial Protection Bureau
- What does total of payments mean when getting a mortgage? — Consumer Financial Protection Bureau
- How does paying down a mortgage work? — Consumer Financial Protection Bureau
Last reviewed: . The formula is reproduced above so you can check the math independently.
Educational principal-and-interest comparison only. It is not a Closing Disclosure total of payments, and it does not invest the monthly difference.