Toni is 67 years old, has just retired and will receive her first pension check
ID: 2613575 • Letter: T
Question
Toni is 67 years old, has just retired and will receive her first pension check of $32,000 in exactly one year. The pension payments will thereafter grow with inflation, which she believes will be 2% per year, for the remaining years of her life. The effective rate she could earn on CDs across various maturities from at her bank is 3% per year. (Label your answers in either dollars or millions of dollars.)
a) If Toni expects to live forever, how much would you estimate is the current value of these pension payments to Toni?
b) Toni’s financial advisor points out that realistically she is not likely to live beyond 30 years. Given that, how much would you estimate is the current value of these pension payments to Toni?
c) Tom has the same pension plan as Toni except that Tom is 61 years old and will not retire for another 6 years: One year after retirement he will receive his first pension check of $32,000 which will grow thereafter at 2% for 30 years. Given that, how much would you estimate is the current value of these pension payments to Tom?
Please explain step by step as I already have the answers but I'm unsure about procedure. Thanks
Explanation / Answer
a) If Toni expects to live forever, how much would you estimate is the current value of these pension payments to Toni?
current value of these pension payments = Expected Pension/(Rate of Return - growth rate)
current value of these pension payments = 32000/(3%-2%)
current value of these pension payments = $ 3,200,000
b) Toni’s financial advisor points out that realistically she is not likely to live beyond 30 years. Given that, how much would you estimate is the current value of these pension payments to Toni?
current value of these pension payments = Expected Pension/(Return - growth rate) * (1- (1+g)^n/(1+r)^n)
current value of these pension payments = 32000/(3%-2%) * (1-(1+2%)^30/(1+3%)^30)
current value of these pension payments = $ 811,977.63
c) Tom has the same pension plan as Toni except that Tom is 61 years old and will not retire for another 6 years: One year after retirement he will receive his first pension check of $32,000 which will grow thereafter at 2% for 30 years. Given that, how much would you estimate is the current value of these pension payments to Tom?
Value of Pension in year 67 = Expected Pension/(Return - growth rate) * (1- (1+g)^n/(1+r)^n)
Value of Pension in year 67 = 32000/(3%-2%) * (1-(1+2%)^30/(1+3%)^30)
Value of Pension in year 67 = $ 811,977.63
current value of these pension payments to Tom = Value of Pension in year 67/(1+rate)^6
current value of these pension payments to Tom = 811977.63/(1+3%)^6
current value of these pension payments to Tom = $ 680,018.48