Final answer:
The centurion commands 100 soldiers with an expected death rate of 5% annually. To cover the costs of burials and lost income for the deceased soldiers, each of the 100 soldiers would need to contribute 11 denarii per year to the fund. If the legion were assigned to the front lines, the increased risk would necessitate higher contributions.
Step-by-step explanation:
Calculating the Risk Pooling Fund for a Roman Legion
The centurion commands 100 soldiers (10 units each composed of 10 men). With an annual death rate of 5%, we expect 5 soldiers to die each year. Of these, 2% are from battle wounds, which means 2 soldiers will be covered by the fund (since the 3% dying from illnesses unrelated to battle are not covered).
For the burials and two years of lost income of each soldier who died in battle, considering that the annual salary is 225 denarii and the burial costs 50 denarii, the fund must collect a total of (2 soldiers * (50 denarii + 2 * 225 denarii)) = 1,100 denarii every year.
Since there are 100 soldiers contributing to this fund, each soldier must contribute 11 denarii annually to cover this cost (1,100 denarii total fund requirement divided by 100 soldiers).
If the legion was called to the front lines, we could expect a higher rate of deaths due to increased battle activities, which would increase the required contributions to the fund, thereby increasing the risk for each soldier in the risk pool.