please do the work by hand instead of Excel, and use the formula from the formula sheet.

Professor Sanders will retire 6 years from today on his 70th birthday. He currently has retirement savings of $1,000,000 invested to earn a 10% annual rate (compounded weekly). If he were to retire today, he would receive immediately his annual Social Security payment of $34,800. As long as he does not retire before attaining the age of 70, his annual Social Security payment will increase at a rate of 7.7208% per year (compounded monthly). Once he retires, his social security payment is expected to increase at a rate of 2% per year (compounded annually) Professor Sanders will receive his first Social Security payment on his retirement date. a. What will be the amount of his first Social Security payment? You must show your work. b. Professor Sanders has it on good authority that he will die with certainty on the day before his 90th birthday (and will not receive the Social Security payment due on his 90th birthday). The appropriate discount rate for Social Security Payments is 3%. What is the value today of the Social Security payments Professor Sanders will receive before his death? You must show your work Professor Sanders wants to leave $400,000 of his retirement savings to his heirs upon his death Beginning on his 70th birthday and continuing on every birthday thereafter until his death, he also wants to make annual withdrawals from his retirement account that increase by 4% per year (compounded annually). What is the amount of the first annual withdrawal he can make from his retirement savings starting on his 70th birthday and achieve his withdrawal and estate goals? Again, Professor Sanders will die the day before his 90th birthday (i.e., no 90th birthday withdrawal). You must show your work. C. Formula Sheet Periodic compounding: Price of a dollar at time t DF0,t + 1 PVo FVt X DFo,t Present value of future amount Present value of a perpetuity (in arrears) C PV0,Perpetuity Present value of a growing perpetuity (in arrears) PV0,Growing Perpetuity = Present value of a T-period annuity (in arrears) X 1+r. 1 PV0,Annuity r Present value of a T-period growing annuity (in arrears) 1 + g X PV0,Growing Annuity r-g r-g Effective annual rate (EAR) (1 EAR -1 Continuous compounding: DF0,t = e-rt Price of a dollar at time t PVo FV X DFo, Present value of future amount Present value of a perpetuity (in arrears) PV0,Perpetuity er - 1 Present value of a growing PV0,Growing Perpetuity e(r-g) 1 perpetuity (in arrears) C C Present value of a T-period annuity (in arrears) PV0,Annuity -r er - 1 er - 1 C C Present value of a T-period growing annuity (in arrears) xe-(r-g)r PVo, Growing Annuity e(r-g) - 1 e(r-g) - 1 Other: Expected Value of 8 E(R) Probi x Xi i=1 NPV Ct NPV = (1k)t t 0 Professor Sanders will retire 6 years from today on his 70th birthday. He currently has retirement savings of $1,000,000 invested to earn a 10% annual rate (compounded weekly). If he were to retire today, he would receive immediately his annual Social Security payment of $34,800. As long as he does not retire before attaining the age of 70, his annual Social Security payment will increase at a rate of 7.7208% per year (compounded monthly). Once he retires, his social security payment is expected to increase at a rate of 2% per year (compounded annually) Professor Sanders will receive his first Social Security payment on his retirement date. a. What will be the amount of his first Social Security payment? You must show your work. b. Professor Sanders has it on good authority that he will die with certainty on the day before his 90th birthday (and will not receive the Social Security payment due on his 90th birthday). The appropriate discount rate for Social Security Payments is 3%. What is the value today of the Social Security payments Professor Sanders will receive before his death? You must show your work Professor Sanders wants to leave $400,000 of his retirement savings to his heirs upon his death Beginning on his 70th birthday and continuing on every birthday thereafter until his death, he also wants to make annual withdrawals from his retirement account that increase by 4% per year (compounded annually). What is the amount of the first annual withdrawal he can make from his retirement savings starting on his 70th birthday and achieve his withdrawal and estate goals? Again, Professor Sanders will die the day before his 90th birthday (i.e., no 90th birthday withdrawal). You must show your work. C. Formula Sheet Periodic compounding: Price of a dollar at time t DF0,t + 1 PVo FVt X DFo,t Present value of future amount Present value of a perpetuity (in arrears) C PV0,Perpetuity Present value of a growing perpetuity (in arrears) PV0,Growing Perpetuity = Present value of a T-period annuity (in arrears) X 1+r. 1 PV0,Annuity r Present value of a T-period growing annuity (in arrears) 1 + g X PV0,Growing Annuity r-g r-g Effective annual rate (EAR) (1 EAR -1 Continuous compounding: DF0,t = e-rt Price of a dollar at time t PVo FV X DFo, Present value of future amount Present value of a perpetuity (in arrears) PV0,Perpetuity er - 1 Present value of a growing PV0,Growing Perpetuity e(r-g) 1 perpetuity (in arrears) C C Present value of a T-period annuity (in arrears) PV0,Annuity -r er - 1 er - 1 C C Present value of a T-period growing annuity (in arrears) xe-(r-g)r PVo, Growing Annuity e(r-g) - 1 e(r-g) - 1 Other: Expected Value of 8 E(R) Probi x Xi i=1 NPV Ct NPV = (1k)t t 0