On January 1, Bob just reached age 40. He has already saved $50,000 in 401(k) plans for his retirement. He earned $100,000 at the end of last year. It is assumed that his salary will remain constant and is paid at the end of each year. Bob would like to retire when he reaches 65 (25 years from today) and expects to live 22 years after retirement. After some basic analysis, you estimate that wage replacement ratio will be 80%. After retirement, the retirement need will grow at 2% each year (i.e. inflation rate is 2%) and is paid at the beginning of each year. The investment return (discount rate) is 8%.

Keep four decimals if applicable. Please show all your work and inputs for full/partial credits. Points will be deducted if you fail to show how you derive the final answers even the answers are correct.

(a). What's the amount of first year retirement need?

(b). Whats the present value of all future retirement needs after retirement at age 65, assuming that he needs the retirement funding at the beginning of each year in retirement? (please show your inputs such as N, PMT, and etc.)

(c). How much is the present value of all retirement needs as of today ?

(d). How much does he need to save in the next 25 years after considering the available retirement funding today? Show the present value as of today.

(e).What is the present value of all his future earnings as of today? Assuming all salaries are paid at the end of each year (please show your inputs such as N, PMT, and etc.)

(f). What should be his annual saving rate to meet the retirement needs?