Aarón already knows that he will have $500,000 when he retires. If he sets up a payout annuity for 20 years in an account paying 2.05% interest, how much could the annuity provide each week? Round your answer to the nearest dollar.

To determine how much Aarón's annuity could provide each week, we will use the formula for the present value of an annuity, which is:

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

Where:
- $ PV $ is the present value of the annuity (which is $500,000 in this case),
- $ P $ is the weekly payment (the unknown we are solving for),
- $ r $ is the weekly interest rate,
- $ n $ is the number of payments per year (52 weeks in a year),
- $ t $ is the number of years (20 years).

### Step 1: Convert the annual interest rate to a weekly interest rate.
The annual interest rate is 2.05%, or 0.0205. The weekly interest rate, $ r $, is:

\[
r = \frac{0.0205}{52}
\]

### Step 2: Calculate the total number of weeks in 20 years.
Since there are 52 weeks in a year and the annuity lasts for 20 years:

\[
nt = 52 \times 20 = 1040 \text{ weeks}
\]

### Step 3: Rearrange the formula to solve for $ P $ (weekly payment).
Rearranging the annuity formula to solve for $ P $:

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

Now, let's calculate the weekly payment.Aarón's annuity could provide approximately $586 per week for 20 years, assuming the account pays 2.05% interest.

Would you like further details or have any questions?

Here are 5 related questions you could explore:
1. How would the weekly payment change if the interest rate were higher or lower?
2. What would happen if the annuity lasted for 30 years instead of 20 years?
3. How is the weekly payment affected if Aarón received payments monthly instead of weekly?
4. What is the total amount Aarón will have received after 20 years?
5. What portion of the $500,000 is made up of interest over the 20 years?

**Tip:** The longer the payout period of an annuity, the smaller the regular payments become, as the same principal is spread out over more time.

Discover how to calculate weekly annuity payments based on a $500,000 retirement fund for 20 years at 2.05% interest. This financial mathematics problem covers the present value of annuities, interest rates, and the time value of money. Ideal for college-level students or financial planners.

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