Question

Suppose you plan to retire at age 70, and you want to be able to withdraw an amount of $83,000 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% 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

We can use formula of the present value (PV) of annuity due where the amount is due at the starting of the period to calculate the present value of your annual withdrawals for 31 years after retirement.

Formula of the present value (PV) of annuity due

PV of annuity due= A * [1- (1+i) ^-n / i] * (1+i)

Where,

Present value PV =?

Annual withdrawals after retirement A =$83,000

Interest rate i = 6% per annum or 0.06

Time period of annuity n = 31 years

Therefore,

PV = $83,000 * [1- (1+0.06) ^-31 / 0.06] * (1+0.06)

Or PV= $1,225,480.99 or $1,225,481 (the nearest dollar.)

The money needs to be in the account by the time you reach your 70th birthday is $1,225,481