Revision as of 23:34, 18 November 2023 by Admin (Created page with "Tim takes out an n-year loan with equal annual payments at the end of each year. The interest portion of the payment at time (n − 1) is equal to 0.5250 of the interest portion of the payment at time (n − 3) and is also equal to 0.1427 of the interest portion of the first payment. Calculate n. <ul class="mw-excansopts"><li>18</li><li>20</li><li>22</li><li>24</li><li>26</li></ul> {{soacopyright | 2023 }}")
ABy Admin
Nov 18'23
Exercise
Tim takes out an n-year loan with equal annual payments at the end of each year. The interest portion of the payment at time (n − 1) is equal to 0.5250 of the interest portion of the payment at time (n − 3) and is also equal to 0.1427 of the interest portion of the first payment.
Calculate n.
- 18
- 20
- 22
- 24
- 26
Copyright 2023 . The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.
ABy Admin
Nov 18'23
Solution: C
[[math]]
\begin{array}{l}{{1- v^{2}=0.52{\bar{s}}(1- v^{4})\Rightarrow1=0.52{\bar{s}}(1+ v^{2})\Rightarrow v^{2}=0.90476\Rightarrow v=0.95119}}\\ {{1- v^{2}=0.1427(1- v^{n})\Rightarrow1- v^n=(1-0.90476)/0.1427=0.667414\Rightarrow v^{n}=0.3325966}}\\ {{n=\ln(0.32596)/\ln(0.95119)=22}}\end{array}
[[/math]]
Copyright 2023 . The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.