A warranty pays 2000 at the end of the year of the first failure if a washing machine fails within three years of purchase. The warranty is purchased with a single premium, [math]G[/math], paid at the time of purchase of the washing machine.
You are given:
(i) [math]10 \%[/math] of the washing machines that are working at the start of each year fail by the end of that year
(ii) [math]\quad i=0.08[/math]
(iii) The sales commission is [math]35 \%[/math] of [math]G[/math]
(iv) [math]G[/math] is calculated using the equivalence principle
Calculate [math]G[/math].
Copyright 2024. The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.
Answer: D
[math]G=0.35 G+2000\left(\frac{0.1}{1.08}+\frac{0.9 \times 0.1}{1.08^{2}}+\frac{0.9 \times 0.9 \times 0.1}{1.08^{3}}\right)[/math]
[math]0.65 G=468.107[/math]
[math]G=720.16[/math]
Copyright 2024. The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.