Final answer:
Using the present value formula for an annuity, Ms. Walters needs to put down approximately $2,054,137.50 today to have an annual income of $225,000 every year for the next 20 years at a 9% return rate. The closest option provided is (d) none of the answers is correct.
Step-by-step explanation:
To determine how much Ms. Walters need to put down today to ensure she has a $225,000 annual income every year for the next 20 years, we use the formula for the present value of an annuity. Given a 9 percent average rate of return, we can calculate the present value (PV) which is the initial amount needed to achieve the desired future cash flows.
The formula for PV of an annuity is:
PV = Pmt × ((1 - (1 + r)^-n) / r)
Where:
- Pmt is the annual payment ($225,000)
- r is the annual interest rate (9% or 0.09)
- n is the number of periods (20 years)
Let's calculate the present value:
PV = $225,000 × ((1 - (1 + 0.09)^-20) / 0.09)
Now, let's solve for PV:
PV = $225,000 × ((1 - (1 + 0.09)^-20) / 0.09) = $225,000 × 9.1295 = $2,054,137.50
Since none of the given options exactly match this number, and considering rounding differences, the correct answer would be (d) none of the answers is correct.