Case: Your 21 years old client just graduated from college and started a job with monthly salary of $3,500 per month. He wants to retire when he is 60 years old and wants to start saving for retirement right away. We cannot be sure of how long we live after retirement, but the client wants to be extra careful and save for 30 years of after retirement life. Market expectation for average annual inflation for the future is 1.5% (Let's assume inflation to be 0 after retirement period). Because of inflation, he will need substantially higher retirement monthly income to maintain the same purchasing power. He plans to purchase a lifetime annuity from an insurance company one month before he retires, where the retirement annuity will begin in exactly 39 years (468 months). The insurance company will add a 3.00 percent premium to the pure premium cost of the purchase price of the annuity. The pure premium is actuarial cost of his anticipated lifetime annuity. He has just learned the concept of time value of money and never saved anything earlier. He will make the first payment in a month from now and the last payment one month before he retires (a total of 467 monthly payments). 1) Given a rate of return of 4.5% for the foreseeable future, how much does he need to save each month until the month before he retires? 2) He also wants to take big vacation as soon as he retires. He is anticipating that he will need $50,000 for that (at the end of 467 months of saving). How much should he save every month? 3) Starting from 1) again, if he decides to save $200 more every month (compared to the answer in number 1), how much can he receive as the first month retirement income? 4) What are the non-quantifiable factors (list 4) that he should be aware of? Please write full sentences, how will it affect the savings plan