# The difference between the premium paid and the expected claim

A married couple purchases two insurance policies with single premium for each policies and the benefit is 12,000 if death occurs within policy years which will end after ten years. If the probabilities of

• Only the wife to live at least within policy years is 2.5%
• Only the husband to live at least within policy years is 3.6%
• Both of them are alive at least within policy years is 86.4%

Calculate the difference between the premium paid and the expected claim if it's known the husband is still alive at least within policy years.

a) 480$\qquad$ b) -11,000$\qquad$ c) 360$\qquad$ d) 520$\qquad$ e) None is correct

Here we know the premium paid will be $2\times500=1,000$ and the expected claim if it's known the husband is still alive at least within policy years is $3.6\%\times12,000=432$. So, the difference will be $1,000-432=568$ and the answer should be e) None is correct, but the key answer of this problem is 520. Where did I make mistake?

• How do you calculate the premium paid? – Jimmy R. Nov 10 '15 at 13:12