Earl Watkins is ready to retire and has saved up $250,000 for that purpose. He places all of this money into an account which will pay him annual payments for 20 years. How large will these annual payments be if the account earns 17% compounded annually?

To calculate the annual payments, we can use the formula for the present value of an ordinary annuity:

PV = PMT * [1 - (1 + r)^-n] / r

Where:
PV = Present value (initial savings) = $250,000
PMT = Annual payment
r = Interest rate per period = 17% = 0.17
n = Number of periods = 20 years

Substituting the given values into the formula, we have:

$250,000 = PMT * [1 - (1 + 0.17)^-20] / 0.17

To solve for PMT, we need to simplify the equation and isolate PMT:

250,000 = PMT * (1 - (1.17)^-20) / 0.17
250,000 * 0.17 = PMT * (1 - 0.0328)
42,500 = PMT * 0.9672
PMT = 42,500 / 0.9672

Using a calculator, we find:

PMT ≈ $43,987.37

Therefore, Earl Watkins' annual payments will be approximately $43,987.37.

To find out the size of the annual payments, we need to use the formula for the present value of an annuity. The formula is:

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

Where:
P = Present value or initial amount invested ($250,000 in this case)
A = Annual payment
r = Interest rate per compounding period (17% or 0.17 in decimal form)
n = Number of years (20 in this case)

We can rearrange the formula to solve for A:

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

Now we can substitute the given values into the formula and calculate the annual payment:

A = $250,000 * 0.17 / (1 - (1 + 0.17)^(-20))

Using a calculator or a spreadsheet, we can plug in these values and calculate the result:

A = $250,000 * 0.17 / (1 - 1.17^(-20))
A ≈ $250,000 * 0.17 / (1 - 0.04244)
A ≈ $250,000 * 0.17 / 0.95756
A ≈ $250,000 * 0.177171
A ≈ $44,292.75

Therefore, the annual payments will be approximately $44,292.75.