A 10-year loan of 2000 is to be repaid with payments at the end of each year. It can be repaid under the following two options

• Equal annual payments at an annual effective interest rate of 8.07%
• Installments of 200 each year plus interest on the unpaid balance at an annual effective interest rate of i.

The sum of the payments under option (i) equals the sum of the payments under option (ii).

Calculate i.

• 8.75%
• 9.00%
• 9.25%
• 9.50%
• 9.75%

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

Solution: B

Option 1: [math]2000 = P a_{\overline{10}|0.0807}[/math]

Option 2: Interest needs to be 2990-2000=990

[[math]] \begin{array}{l}{{990=i[2000+1800+1600+\dots+200]}}\\ {{=11,000i}}\\ {{i=0.09=9.00\%}}\end{array} [[/math]]

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