American General offers a 10​-year annuity with a guaranteed rate of 5.11​% compounded annually. How much should you pay for one of these annuities if you want to receive payments of ​$2400 annually over the 10 year​ period?
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Part 1
How much should a customer pay for this​ annuity?

To find out how much a customer should pay for the annuity, we can calculate the present value (PV) of an annuity. The present value of an annuity represents the amount of money that must be invested today in order to receive a series of future payments.

The formula for the present value of an ordinary annuity is:

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

Where:
- $ P $ is the payment per period ($2400 in this case),
- $ r $ is the interest rate per period (5.11% annually, so $ r = 0.0511 $),
- $ n $ is the total number of periods (10 years).

Let's calculate the present value.

\[
PV = 2400 \times \left( \frac{1 - (1 + 0.0511)^{-10}}{0.0511} \right)
\]

I'll compute this now.The customer should pay approximately **$18,433.56** for the annuity to receive annual payments of $2,400 over a 10-year period at a guaranteed rate of 5.11% compounded annually.

Would you like more details on how this was calculated, or do you have any other questions?

Here are five related questions:
1. How does the interest rate affect the present value of an annuity?
2. What would happen to the present value if the payment period was extended to 15 years?
3. How do different compounding periods (monthly, quarterly) affect the annuity’s value?
4. What is the future value of this annuity after 10 years?
5. How would inflation impact the value of these payments over time?

**Tip:** When buying an annuity, understanding the impact of interest rates on the present value can help in making more informed decisions.

American General offers a 10​-year annuity with a guaranteed rate of 5.11​% compounded annually. How much should you pay for one of these annuities if you want to receive payments of ​$2400 annually over the 10 year​ period?

Discover how to calculate the present value of a 10-year annuity offered by American General, with a guaranteed annual interest rate of 5.11%. Learn how much to pay upfront to receive annual payments of $2400 using financial mathematics and the time value of money concept.

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