Final answer:
To find how much Sam needs in his retirement account now to withdraw $75,000 per year for 30 years at a 7% return, the present value of an annuity formula is used, taking into account the withdrawal amount, interest rate, and duration of the withdrawals.
Step-by-step explanation:
The task is to determine how much money Sam needs in his retirement account now to withdraw $75,000 per year for 30 years with an account compounding annually at 7%. This type of problem requires the use of the present value of an annuity formula, which is used in finance to calculate the amount needed today to fund a series of future withdrawals. The formula for the present value of an annuity is P = PMT × [(1 - (1 + r)^-n) / r], where P is the present value of the annuity, PMT is the annual withdrawal amount, r is the annual interest rate (as a decimal), and n is the number of years.
Using this formula, we will calculate the present value P by substituting PMT with $75,000, r with 0.07 (7%), and n with 30:
P = $75,000 × [(1 - (1 + 0.07)^-30) / 0.07]
Calculating with this formula will give us the amount Sam needs to have in his retirement savings to fulfill his plan.