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].

• 630
• 660
• 690
• 720
• 750

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.