Please draw the cash flow diagrams and explain the steps that you are going to approach to solve the problems then solve the problem. Show the details in solving the problems.

1) What amount will be required to purchase, on mans 40th birthday, an annuity to provide him with thirty equal semi-annual of $1000 each, the first to be received on his 50th birthday, if nominal interest rate is 12% compounded semi-annually?

2) An engineer is thinking of starting a part-time consulting business next September 5,on his 40^th birthday. He expects the business will require an initial cash outlay of $5000, to come from his savings, and will cost $500 per year to operate; the business ought to generate $2000 per year in cash receipts. During the 20 years that he expects to operate the business, he plans to deposit the annual net proceeds in a bank each year, at an interest rateof8% per year, compounded annually. When he retires, on his 60th birthday, the engineer expects to invest whatever proceeds plus interest he then has from the business in a long-term savings plan that pays 10% per year, compounded annually. What is the maximum amount he could withdraw from the savings plan each year during his retirement and still have the funds last 15 years.