Today is Dec. 31, 2020. David is planning to retire in 40 years from today and wants to save some money to support his living for at least 20 years, i.e., 2061 through 2080, after his retirement. David estimates that he will need $50,000 each year from Jan. 1, 2061 to Dec. 31, 2080. Assume that the interest rate is 10% and will be constant over time. Answer questions a) and b) below.

a. Determine how much he needs to save by the end of 2060.

Answer (show the steps/calculation toward your results):

Need $50K at the end of each year from 2061-2080, i.e., an annuity with C =50K; T =20; r =10%. Find the PV, as of t=2060, of the annuity:

b. Suppose that David will start saving money from one year from today by making 40 annual installment deposits. How much per year, at the end of each year from 20212060, does he need to save? (*Hint: To work in the present value as of today (t=2020), discount the funds needed by t=2060 back to the PV as of t=2020 and then solve for the annual payment for next 40 years.)