Instructions: There is only one problem To solve it, use the sample life table from your textbook introduced in section 3.7, namely e-0.00005 (1.09); x = 0,1,2,... 118 9x= 1; x = 119 Take all ages to be integers. Interest is 5% during the first 10 years, and 4% thereafter. Use Excel to carry out your calculations, but write down on your paper the foundation/ justification/ explanation of the steps and calculations you make. In particular, make sure you explicitly present the cash flow vectors corresponding to any benefits, and the cash flow vector for the premiums. Use appropriate notation. You have a client who is your own age. (This means you will have to disclose your age, sorry!). This client wishes to purchase an insurance policy with the following characteristics: a) The contract is a deferred endowment policy that provides coverage for death with a benefit of $500,000, payable at the end of the year of death, extended over the period from t=0 and up until just before your client turns 65. (That is, if the last period where your client is covered for death is the year between when they turn 64 and when they turn 65.) During that deferred period (with coverage for death), your client will pay annual, level premiums. Once they turn 65, they are to receive annual benefits of $50,000, for life. Find the annual premium. b) Suppose your client wants to modify the contract so that, upon survival to age 65, they receive the $50,000 benefit for at least 10 years, or until their death. (That is, there are 10 payments guaranteed.) Recalculate the premium.