Consider an amortization schedule for a loan at interest rate i per period, i > 0, being repaid with payments of 1 at the end of each period for n periods.

Determine which of the following statements about this schedule is true.

• The total interest paid equals [math]n-a_n[/math].
• The total interest paid equals [math]i a_n[/math].
• The total principal repaid equals [math]n-i a_n[/math].
• The principal repaid in payment [math]t[/math] equals [math]v^{n-t}[/math].
• The total payment amount equals [math]a_n[/math].

Copyright 2023 . The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.

Solution: A

The total amount paid is n. The initial loan amount is [math]a_{\overline{n} |t } [/math]. The total interest paid equals [math] n - a_{\overline{n} | t}[/math]

Copyright 2023 . The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.