Question

Suppose you plan to retire at age 70, and you want to be able to withdraw an amount of $95,000 per year on each birthday from age 70 to age 100 (a total of 31 withdrawals). If the account which contains your savings earns 6.8% per year simple interest, how much money needs to be in the account by the time you reach your 70th birthday? (Answer to the nearest dollar.) Hint: This can be solved as a 30-year ordinary annuity plus one withdrawal at age 70, or as a 31-year annuity due.

Answer 1

PVA_due = Annuity + Annuity x [{1 - (1 + r)^-(n-1)} / r]

= $95,000 + $95,000 x [{1 - (1.068)^-(31-1)} / 0.068]

= $95,000 + $95,000 x [0.8610 / 0.068]

= $95,000 + [$95,000 x 12.6625]

= $95,000 + $1,202,935.77 = $1,297,935.77