The cumulative probability of default for a security for 4 years is 11.47%. The marginal probability of default for the security for year 5 is 5%…

The cumulative probability of default for the security for the 5 years is [1 - (1 - probability of default

upto year 4)*(1 - probability of default in year 5)]. An easier way to think about this is that the

Probability of survival till year 5 = (Probability of survival till year 4 * Probability of survival during

year 5). Using the relationship that probability of default = 1 - probability of survival, we can calculate

the required probability in all cases.

In this case, the cumulative probability of default for the security for 5 years = 1 - (1 - 11.47%)*(1 -

5%) = 15.8695%, therefore Choice 'c' is the correct answer.