There can be an infinite number of arrangements made for loan repayments, just as long as the borrower and lender agree on them. Generally payments are made periodically to cover the interest on the remaining principal for the immediate period, with any remainder's being applied to the reduce that principal. The unique characteristic and the seemingly complex formulas traditionally involved in modern mortgages, merely serve to make the payments a constant over the entire term.
The tables whose links appear below show the annual summary repayment schedule for a loan with a Principal of $100,000 at 10% for 30 years and for 25 years. Note that the payment for 30 years is $878 and for 25 years is $909 --- which is only a little more. The latter case requires an increased payment of just over $30, but it reduces the total time by 5 years, and reduces the total cost by over $43,000.!.!.! The same savings can be realized by merely raising the monthly payment on an original 30 year arrangement by that same $30, PROVIDED that the lender is willing to accept it. Prudent monitoring of the account balance should be done to see that proper credit is being made and that things are progressing as expected.The Table for 30 years -- rather standard    
In the graph whose link appears below, for any point in the term of the mortgage, the distance below the graphline represents the portion paid to interest, the distance above the graphline represents the portion paid to principal; hence for the area up to any point in the term of the mortage, the area under the graphline represents the total paid to interest, the area over the graphline represents the total paid to principal. Thus it can be readily seen that longer term mortgages significantly increase the total paid to interest -- even though the individual payments will be lower.Comparison of Term Lengths