Jason already knows that he will have $800,000 when he retires. If he sets up a payout annuity for 30 years in an account paying 2.2% interest, how much could the annuity provide each week? Round your answer to the nearest dollar.

To determine how much Jason's annuity can provide each week, we need to use the formula for the present value of an annuity, which is:

\[
PV = P \times \frac{1 - (1 + r)^{-nt}}{r}
\]

Where:
- $PV$ is the present value (initial amount) = $800,000
- $P$ is the weekly payout (the amount we are solving for)
- $r$ is the weekly interest rate
- $t$ is the number of years = 30
- $n$ is the number of payouts per year = 52 (since payments are weekly)
  
### Step 1: Calculate the weekly interest rate.
The annual interest rate is 2.2%. To find the weekly rate:
\[
r = \frac{2.2\%}{52} = \frac{0.022}{52} \approx 0.0004231
\]

### Step 2: Plug values into the annuity formula and solve for $P$.

Rewriting the formula to solve for $P$:
\[
P = \frac{PV \times r}{1 - (1 + r)^{-nt}}
\]
\[
P = \frac{800,000 \times 0.0004231}{1 - (1 + 0.0004231)^{-52 \times 30}}
\]

Now, I will calculate the result.It seems like I can’t do more advanced data analysis right now. Please try again later. If you'd like, I can still guide you through the necessary steps to calculate the annuity yourself. 

Would you like some further explanation on how to proceed, or details about any specific part of the process?

Here are some related questions to consider:
1. How does changing the interest rate affect the weekly payout?
2. What if Jason wanted payouts for 40 years instead of 30 years?
3. How would the calculation change if payments were monthly instead of weekly?
4. What would happen if Jason increased his initial amount to $1 million?
5. How does inflation impact the value of future annuity payments?

**Tip:** When calculating payouts, remember that converting between periods (like annual to weekly) is crucial for accuracy.

Find out how much Jason's $800,000 retirement annuity can provide each week for 30 years with a 2.2% interest rate. This problem covers key financial concepts such as the present value of an annuity and calculating weekly payouts using the annuity formula. Suitable for high school students or those studying financial mathematics.

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