Question

Find the month k that you can retire given our bank account model:

y[k] = (1+r/12) y[k-1] + u[k] Assume that the annual percentage rate (APR) is 6% and that y[k-1]=0.

Also assume that: u[k] before retirement = $400 u[k] after retirement = -$4000

Your goal is for your money to last until k = 780, which corresponds to 65 years from now.

a) Solve this problem using a spreadsheet.

b) Solve this problem in closed form using the z-transform.

Answer 1

Yearly savings = $ 4000

future value of this saving = 4000*(1.05^40 - 1) / .05 = $ 483199.1

Future value of inheritance ( to be received in 15 years and invested for 25 years)= 50000*1.05^25 = $169317.75

So total amount at retirement = $ 483199.1+$169317.75 = $ 652516.85

for 30 years of use of the funds

652516.85 = annual withdrawal*(1-1/1.05^30) / .05

annual withdrawal = $ 42447.29