**Value of a retirement annuity**  Personal Finance Problem   An insurance agent is trying to sell you an​ annuity, that will provide you with 

​$10 comma 30010,300 

at the end of each year for the next 

3535 

years. If you​ don't purchase this​ annuity, you can invest your money and earn a return of 

44​%. 

 What is the present value of the​ annuity?

Question content area bottom

Part 1

Ignoring​ taxes, the present value of the annuity is 

​$enter your response here. 

 ​(Round to the nearest​ cent.)


To calculate the present value (PV) of an annuity, we use the following formula for the present value of an ordinary annuity:

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

Where:
- $P$ is the payment per period (in this case, $10,300).
- $r$ is the interest rate per period (4% or 0.04 in decimal).
- $n$ is the number of periods (35 years).

### Substituting the values into the formula:

\[
PV = 10,300 \times \left(1 - (1 + 0.04)^{-35}\right) \div 0.04
\]

Now, let's calculate step-by-step:

1. First, compute $1 + r = 1 + 0.04 = 1.04$.
2. Then, compute $(1.04)^{-35}$.
3. Subtract this value from 1.
4. Multiply by the payment $P = 10,300$.
5. Finally, divide by the interest rate $r = 0.04$.

Let me calculate that for you.The present value of the annuity, rounded to the nearest cent, is \$192,245.52.

Would you like further details or have any other questions?

Here are 5 related questions to expand on this concept:
1. How would the present value change if the interest rate was higher?
2. What is the future value of this annuity at the end of 35 years?
3. How does inflation affect the real value of the annuity payments over time?
4. How would the calculation change if the payments were made monthly instead of annually?
5. What is the impact of taxes on the present value of the annuity?

**Tip:** When comparing investment options, always consider both the interest rate and the time period to get an accurate present value.

An insurance agent is trying to sell you an annuity that will provide you with $10,300 at the end of each year for the next 35 years. If you don't purchase this annuity, you can invest your money and earn a return of 4%. What is the present value of the annuity? (Round to the nearest cent.)

Learn how to calculate the present value of a 35-year annuity paying $10,300 annually, using a 4% interest rate. This step-by-step solution covers key financial concepts such as annuities, the time value of money, and the present value formula. Perfect for students in Grades 10-12 or finance courses.

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