Revision as of 21:52, 18 November 2023 by Admin (Created page with "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. <ul class="mw-excansopts"><li>8.75%</li><li>9.00%</li><li>9.2...")
ABy Admin
Nov 18'23
Exercise
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.
ABy Admin
Nov 18'23
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.