Question

3. You would like to retire at the end of 40 years with an annual pension of $1 million per year for 30 years.

a) How much would you have to deposit every year for the next 40 years to meet your goal? Assume you invest in the stock market at an average return of 12 percent per year (for the entire 70 years).

b) Suppose your annual deposits calculated in part (a) actually earned only 6 percent per year for 40 years, how much would you be able to withdraw every year for 30 years following retirement? Assume the 6 percent return is earned over the entire 70 years.

Answer 1

Future value at the end of 40 years = Present value of stream of annual pension for 30 years

Annual pension (PMT) = $ 1 Million

Number of years (nper) = 30

Rate per year (rate) = 12%

Present value of stream of annual pension for 30 years(PV) = = $ 8,055,183.97

a)

Future value of deposit = $ 8,055,183.97

Number of years(nper) = 40

Rate = 12%

Annual Deposit (PMT) = = $ 10,500.94

b)

Annual Deposit (PMT) = $ 10,500.94

Rate = 6%

Number of years(nper) = 40

Future value at the end of 40 years(FV) = = $ 1,625,146.72

This is the Present value for the stream of payments every year for 30 years

PV = $ 1,625,146.72

rate = 6%

Nper = 30

Withdrawal every year for 30 years following retirement (PMT) = = $ 118,065.14