Final answer:
To calculate Mrs. Sonilana's annual withdrawal, the present value annuity formula is used with her investment's present value, her desired future value, the annual interest rate, and the number of periods. The PMT value derived will provide the correct annual withdrawal amount to achieve her financial retirement goal.
Step-by-step explanation:
Mrs. Sonilana can determine how much she can withdraw at the end of each year for 20 years while earning a 5.0% return on investment and still have $2,000,000 at the end of her retirement by using the annuity formula:
PV = PMT [((1 - (1 + r)^-n) / r)] + FV / (1+r)^n
Where:
- PV = Present Value of the investment $6,310,100
- PMT = Payment amount per period (what we're trying to find)
- r = Interest rate per period (5.0% or 0.05)
- n = Number of periods (20 years)
- FV = Future Value desired ($2,000,000)
Rearranging the formula to solve for PMT:
PMT = (PV - FV / (1+r)^n) / ((1 - (1 + r)^-n) / r)
Substituting the values into the formula:
PMT = ($6,310,100 - $2,000,000 / (1+0.05)^20) / ((1 - (1 + 0.05)^-20) / 0.05)
The calculations yield the annual withdrawal amount. After computing the value, you can compare it against the multiple choice options provided (a. $100,000 per year, b. $150,000 per year, c. $200,000 per year, d. $250,000 per year) to determine the correct answer.