A 45-year-old woman decides to put funds into a retirement plan. She can save $2,000 a year and earn 9 percent on this savings. How much will she have accumulated if she retires at age 65. At retirement how much can she withdraw each year for 20 years from the accumulated savings if the savings continue to earn 9%?

To determine the amount accumulated by the time the woman retires and the amount she can withdraw each year, we can use the future value of an annuity formula.

First, let's calculate the amount accumulated by the time the woman retires at age 65.

We know that she can save $2,000 per year and earn a 9% return on this savings. The formula to calculate the future value of an annuity is:

FV = P * ((1 + r)^n - 1) / r

Where:
FV = future value (the accumulated amount)
P = payment per period ($2,000 per year)
r = interest rate per period (9% or 0.09)
n = number of periods (years until retirement, which is 65 - 45 = 20)

Plugging in the numbers, the formula becomes:

FV = $2,000 * ((1 + 0.09)^20 - 1) / 0.09

Using a scientific calculator or spreadsheet, we can calculate the result:

FV = $2,000 * (1.09^20 - 1) / 0.09
= $2,000 * (4.968147 - 1) / 0.09
= $2,000 * 3.968147 / 0.09
= $2,000 * 44.09052
= $88,181.04

Therefore, the woman will have accumulated approximately $88,181.04 by the time she retires at age 65.

Now, let's calculate how much she can withdraw each year for 20 years from the accumulated savings if the savings continue to earn 9%.

We can use the annuity payment formula:

P = FV * r / ((1 + r)^n - 1)

Where:
P = payment per period (amount she can withdraw each year)
FV = future value ($88,181.04)
r = interest rate per period (9% or 0.09)
n = number of periods (20 years)

Plugging in the numbers, the formula becomes:

P = $88,181.04 * 0.09 / ((1 + 0.09)^20 - 1)

Again, using a calculator or spreadsheet, we can calculate the result:

P = $88,181.04 * 0.09 / (1.09^20 - 1)
= $88,181.04 * 0.09 / 2.367206
= $7,963.29

Therefore, the woman can withdraw approximately $7,963.29 each year for 20 years from the accumulated savings if the savings continue to earn 9%.