Question

Bilbo plans to retire in 25 years (t=25) from today and to save $4,000 per month until his retirement with the first saving starting from today (t=0). He expects to have $2,000 monthly expense starting from the first month after year 25 (t=25) through year 50 (t=50). He also wants to leave an amount of inheritance to his son Frodo at year 50 (t=50). The discount rate for Bilbo’s entire life is 6% (APR). Suppose Bilbo strictly follows his financial plan,

a) how much savings would Bilbo have in year 25 (t=25)? [10 marks]

b) how much at most would Bilbo’s inheritance be in year 50 (t=50)? [15 marks]

Answer 1

a) how much savings would Bilbo have in year 25 (t=25)? [10 marks]
=4000/(6%/12)*((1+6%/12)^(12*25)-1)*(1+6%/12)
=2785835.729

b) how much at most would Bilbo’s inheritance be in year 50 (t=50)? [15 marks]

=(2785835.729-2000/(6%/12)*(1-1/(1+6%/12)^(12*25)))*(1+6%/12)^(12*25)=11052684.51