Final answer:
To determine the initial deposit needed to fulfill the requirement of withdrawing $40,000 annually for 25 years at an 8% interest rate, we use the present value of an annuity formula. By calculating the present value with the given annual payment, interest rate, and number of periods, we can arrive at the sum required to be deposited at the beginning.
Step-by-step explanation:
The question asks how much money needs to be deposited at the beginning to be able to withdraw $40,000 each year for 25 years from an account that earns 8% interest. To solve this, we use the formula for the present value of an annuity because the withdrawals represent a series of payments at regular intervals. The formula is: PVA = PMT * [(1 - (1 + r)^-n) / r], where PVA is the present value of an annuity, PMT is the annual payment, r is the interest rate per period, and n is the number of periods.
Using this formula, we want to find PVA when PMT is $40,000, r is 0.08 (8% interest), and n is 25 (years). Therefore:
PVA = $40,000 * [(1 - (1 + 0.08)^-25) / 0.08]
After calculating the above expression, we will know the amount that needs to be deposited initially to satisfy the conditions presented.