Question

Today is your 40th birthday. You expect to retire at age 65, and actuarial tables suggest that you will live to be 100. You want to move to Hawaii when you retire. You estimate that it will cost you $200,000 to make the move (on your 65th birthday). Starting on your 65th birthday and ending on your 99th birthday, your annual living expenses will be $25,000 a year. You expect to earn an annual return of 7% on your savings.  

A) How much will you need to have saved by your retirement date?

B)For this part, assume that you already have $50,000 in savings today. How much would you need to save today and at ages 41 to 64 to be able to afford this retirement plan?

Answer 1

Amount required on retirement date = Cost of moving + Present value of future withdrawals

= 200,000 + 25000*PVAD(7%, 35 years)

= 200,000 + 25000*13.8540

= $546,350

B. Value of 50,000 at age of 65 = 50,000*(1.07)^25

= $271,371.63

Additional amount required = $274,978.37

Let annual savings be x

Future value of annuity due = x*(1+r)*[{(1+r)^n - 1}/r]

274,978.37 = (1.07)*x*[{(1.07)^25 - 1}/0.07]

274.978.37 = 67.67647x

x = $4,063.13

Hence, amount required to be saved each year = $4,063.13