What happens if I pay extra principal on my mortgage?

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Definitions

Annual interest rate (APR)
The yearly cost of a mortgage, including interest, mortgage insurance, and the origination fee (point(s)), expressed as a percentage. Maximum APR is 20%.
Mortgage length (years)
Total length, or term, of your original mortgage in years. Most common lengths are 30 years and 15 years.
Original mortgage amount
The original amount financed with your mortgage. Not to be confused with the remaining balance or principal balance.
Additional monthly payment
Your proposed extra payment per month. This payment will be used to reduce your principal balance.
Scheduled payment
Monthly principal and interest payment (PI) based on your original mortgage amount, term and interest rate.
Accelerated payment
Scheduled payment plus additional monthly payment.
Total savings
Total amount you would save in interest if you made the accelerated payment until your mortgage was paid in full.