Sam is exactly 35 years old. At the end of this year, Sam will begin
making regular deposits into a tax-sheltered account at a Bank. Sam plans to make annual payments until he retires on his birthday at age 55 (the last deposit occurs on Sam’s birthday). The bank anticipates that the account will earn 6% APR compounded semi-annually until Sam retires at age 55. At retirement, Sam will begin withdrawing a fixed amount of $50,000 semi-annually
(the first withdrawal will be six months after retirement). Sam is in excellent physical condition and for financial planning purposes wishes to ensure that he can withdraw funds to age 90. Assume that Sam’s money will also earn 6% APR compounded semi-annually after retirement.
Rych,

You're right. I misread the original information

Three step approach still needed. The order changes a bit.

1. Find out how much Sam will need at age 55 to guarantee a semi-annual payment of $50k for 35 years.

2. Calculate the effective annualized rate of 6% compounded semi-annually

3. Find out the monthly amount Sam must fund the account beginning now, to have the amount calculated in step 1 by his 55th birthday.

The answers are:

1. Compute the Present Value (PV) of a semi-annual payment of $50,000 for 35 years using a discount rate of 3.00% per period. I used Excel (but any financial calculator will give you the same answer) entering $50,000 as the Payment, 3.00% as the Rate, and 70 as the Number of Periods. The answer came back as $1,456,171.07.

2. 1.03 X 1.03 = 1.0609, so the annualized earning rate is 6.09%

3. Now calculate the annual payment needed to accumulate $1,456,171.07. in 20 years. Again I used Excel using the PMT (Payment) function - setting $1,456,171.07. as the Future Value, 20 as the number of Periods and 6.09% as the rate. That answer came back as $39,203.95.

So the answer is $39,203.95 per year