Harry borrows 10,000 from Sally and agrees to repay the five-year loan with equal payments at the end of each quarter. Interest on the loan is charged at an annual nominal rate of 6% convertible quarterly. Immediately after the fourth payment, Harry and Sally get married and Sally forgives the remaining debt.

Calculate the total interest payments that Sally forgoes receiving by having forgiven the remaining debt.

• 582
• 951
• 1,088
• 1,270
• 1,769

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

Solution: C

[[math]] \begin{aligned} & 10,000=P a_{\overline{20} \mid 0.015} \\ & P=582.46 \\ & O B_4=582.46 a_{\overline{16} \mid 0.015} \\ & O B_4=8230.86 \end{aligned} [[/math]]

Remaining payments total:

[[math]] \begin{aligned} & 16(582.46)=9319.32 \\ & 9319.32-8230.86=1088.46 \end{aligned} [[/math]]

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