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Prepaying a loan: Shouldn't the interest be recalculated like a shorter loan?
The key to understanding a mortgage is to look at an amortization schedule.  Put in 100k, 4.5% interest, 30 years, 360 monthly payments and look at the results.  You should get roughly 507 monthly P&I payment.  Amortization is only the loan portion, escrow for taxes and insurance and additional payments for PMI are extra. You'll get a list of all the payments to match the numbers you enter.  These won't exactly match what you really get in a mortgage, but they're close enough to demonstrate the way amortization works, and to plan a budget.  For those terms, with equal monthly payments, you'll start paying 74% interest from the first payment.  Each payment thereafter, that percentage drops. The way this is all calculated is through the time value of money equations.  https://en.wikipedia.org/wiki/Time_value_of_money.  Read slowly, understand how the equations work, then look at the formula for Repeating Payment and Present Value.  That is used to find the monthly payment.   You can validate that the formula works by using their answer and making a spreadsheet that has these columns:  Previous balance, payment, interest, new balance.  Each line represents a month.  Calculate interest as previous balance * APR/12.  Calculate new balance as previous balance minus payment plus interest. Work through all this for a 1 year loan and you will understand a lot better.