1. Suppose the force of interest is a constant 0.06 and that μ(t) = 0.04 for all t. An insurer sells 100 contracts, each of which pays 1000 upon failure. Assuming a normal approximation, how much should be charged as a single premium on each contract, so that there is a 95% chance that premiums will be sufficient to cover the aggregate claims for this group of 100 contracts.
2. Suppose the contract in above question is sold with premiums paid continuously for life at a level rate, where the security loading θ = 0.10. Assuming a normal approximation, how many contracts must be sold, so there is a 95% chance that total premiums will cover total benefits?