Kathleen works for an insurance company. One of the company's clients just turned 67 years old, and according to the insurance company, his life expectancy is 86 years. The client has just invested $925,000 with the company in a lifetime annuity with an APR of 3.12%, compounded monthly. As part of her job, Kathleen has to do some calculations related to this client. Provide Kathleen with some assistance by doing the calculations yourself. 

Part I: How many more months does the insurance company Kathleen works for expect the client to live?

Part II: What is the periodic interest rate of the annuity?

Part III: What will the client's monthly payment be?

Part IV: Suppose the client lives until his 99th birthday. How much in total will he have received in payments from the lifetime annuity?

Part V: How much more will the client have received in payments than the insurance company Kathleen works for expected to pay out?