How is the total payment calculated for an amortized loan, and how does it change over time according to the example provided in the chapter?

The total payment for an amortized loan is calculated by determining a fixed payment amount that includes both principal and interest, which remains constant throughout the loan term. Over time, as the loan balance decreases, the interest portion of each payment declines while the principal portion increases, resulting in a fixed total payment that covers both components.

In an amortized loan, the total payment is calculated using the formula for an ordinary annuity, which ensures that the borrower pays a consistent amount each period. For example, a $5,000 loan at 9 percent interest amortized over five years results in fixed payments of $1,285.46. As the loan is paid down, the interest charged each year decreases because it is based on the remaining balance. Consequently, while the total payment remains the same, the distribution between interest and principal changes, with more of each payment going towards the principal as time progresses.