American General offers a 

1919​-year 

annuity with a guaranteed rate of 

8.758.75​% 

compounded annually. How much should you pay for one of these annuities if you want to receive payments of 

​$900900 

annually over the 

1919 

year​ period?

Question content area bottom

Part 1

How much should a customer pay for this​ annuity?

​$enter your response here 

​(Round to the nearest​ cent.)

To calculate how much a customer should pay for this annuity, we can use the formula for the present value of an ordinary annuity:

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

Where:
- $ PV $ is the present value (the amount the customer should pay).
- $ P $ is the annual payment (in this case, $900).
- $ r $ is the annual interest rate (in decimal form, so $ r = 8.75\% = 0.0875 $).
- $ n $ is the number of periods (19 years).

### Step-by-Step Calculation:

1. **Identify the known variables**:
   - $ P = 900 $
   - $ r = 0.0875 $
   - $ n = 19 $

2. **Substitute the values into the formula**:

\[
PV = 900 \times \left( 1 - (1 + 0.0875)^{-19} \right) \div 0.0875
\]

Now, let's calculate this value.The customer should pay approximately **$8,196.04** for the annuity. 

Would you like any further details or clarification?

Here are 5 related questions to expand on this topic:
1. How does the present value of an annuity change if the interest rate decreases?
2. What is the impact of extending the number of years in an annuity?
3. How does compound interest affect the future value of an annuity?
4. Can annuities be structured with payments at different intervals, such as monthly or quarterly?
5. What is the difference between an ordinary annuity and an annuity due?

**Tip**: Always ensure to convert interest rates from percentage to decimal form in financial calculations.

American General offers a 19-year annuity with a guaranteed rate of 8.75% compounded annually. How much should you pay for one of these annuities if you want to receive payments of $900 annually over the 19-year period? (Round to the nearest cent.)

Learn how to calculate the present value of a 19-year annuity with an 8.75% interest rate and annual payments of $900. This step-by-step guide explains the key formulas and mathematical concepts, such as the present value of an ordinary annuity, and is ideal for high school students (Grades 10-12).

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