To determine how much you should pay for the annuity, we can use the present value of annuity formula since you will be receiving payments over a fixed period with a fixed interest rate.

The formula for the present value of an annuity is:

$PV = P \times \left( \frac{1 - (1 + r)^{-n}}{r} \right)$

Where:

• $PV$ is the present value (the amount you need to pay today).
• $P$ is the annual payment (in this case, $1100).
• $r$ is the annual interest rate (in decimal form, so 8.81% = 0.0881).
• $n$ is the number of periods (in this case, 16 years).

Plugging the values into the formula:

$PV = 1100 \times \left( \frac{1 - (1 + 0.0881)^{-16}}{0.0881} \right)$

Let's calculate that step-by-step:

1. Calculate $(1 + r)^{-n}$: $(1 + 0.0881)^{-16} = 1.0881^{-16} \approx 0.25457$

2. Subtract this from 1: $1 - 0.25457 = 0.74543$

3. Divide by $r$: $\frac{0.74543}{0.0881} \approx 8.46$

4. Multiply by the annual payment: $1100 \times 8.46 = 9306.00$

So, you would need to pay approximately $9306 today for this annuity.

Summary:

To receive $1100 annually for 16 years at a guaranteed rate of 8.81% compounded annually, you would pay about $9306 for the annuity.

Would you like further clarification or details on how this formula works? Here are some related questions you might find useful:

1. How would the present value change if the interest rate were higher or lower?
2. What happens to the present value if the annuity payment amount is increased or decreased?
3. How can I calculate the present value of a different type of annuity, such as one that is not guaranteed?
4. How does the compounding frequency affect the present value of an annuity?
5. Can I use this same formula for annuities with different payment periods (e.g., monthly or quarterly)?

Tip: Always make sure to convert the percentage interest rate to a decimal before plugging it into the formula (e.g., 8.81% becomes 0.0881).