You are completing a retirement plan and you expect to work for an additional 25 years until retirement. You plan for a retirement horizon of 20 years. During retirement, you would like to withdraw an annual income equal that affords purchasing power equal to $150,000 today (so your withdrawals must adjust for inflation). Assume you will make 20 annual withdrawals during retirement with the first occurring one year following your retirement date. You would like to also have $1,000,000 in your account as a bequest (or to fund additional expenses should you live longer than expected) at the end of the 20-year retirement horizon. You currently have $150,000 in a savings account. You will make additional monthly deposits to this account as described below in order to meet your retirement goals. Assume a constant 7% interest rate per year (EAR) and a constant 2% inflation rate per year (also treat this as an EAR). Answer the following in your uploaded response. Label the separate parts clearly and show your work.

Determine the value at retirement date of your retirement goals including the desired annual withdrawals and the bequest amount.

a) Suppose you will deposit $3,500 per month during your working life (first deposit one month from now). Given your current savings and these deposits, will you meet your retirement goals? Determine the excess or shortfall in your account, relative to your goal, as of your retirement date.

b) Now suppose that you make a deposit of $3,500 one month from now, but then increase subsequent deposits at the rate of inflation. Determine the updated excess or shortfall in your account as of your retirement date.

c) Finally, suppose you instead decide to make deposits of $4,000 per month (first deposit in one month) for a certain number of months (call this "N"). Thereafter you will cut down your work hours and reduce your remaining deposits by one-half (to $2,000/month) until full retirement 25 years from now. Determine, to the closest integer, the number of months N you will need to contribute $4,000 so that you exactly meet your retirement goal.