(Annuity interest​ rate)  Your folks just called and would like some advice from you.  An insurance agent just called them and offered them the opportunity to purchase an annuity for ​$18 comma 036.66 that will pay them ​$3 comma 000 per year for 10 years.  They​ don't have the slightest idea what return they would be making on their investment of ​$18 comma 036.66.  What rate of return would they be​ earning?
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Part 1
The annual rate of return your folks would be earning on their investment is

enter your response here​%. ​ (Round to two decimal​ places.)

To determine the rate of return (interest rate) for this annuity, we can use the formula for the present value of an ordinary annuity:

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

Where:
- $PV$ = Present value of the annuity = \$18,036.66
- $P$ = Annual payment = \$3,000
- $r$ = Interest rate (what we need to find)
- $n$ = Number of periods (years) = 10

We need to solve this equation for $r$, which typically requires an iterative approach since $r$ is not isolated in the formula. We can use a numerical method like trial and error or a financial calculator to determine the interest rate. Let me calculate that for you.The annual rate of return your folks would be earning on their investment is approximately **10.51%**.

Would you like further details on how this was calculated or any clarifications?

Here are some related questions you might find useful:
1. How is the present value of an annuity calculated?
2. What factors affect the rate of return in an annuity?
3. How does changing the number of periods affect the interest rate?
4. What is the difference between an ordinary annuity and an annuity due?
5. Can this formula be used for other types of financial investments?

**Tip:** Always ensure to consider inflation and fees when evaluating the actual return of an annuity or any long-term investment.

Your folks just called and would like some advice from you. An insurance agent just called them and offered them the opportunity to purchase an annuity for $18,036.66 that will pay them $3,000 per year for 10 years. They don't have the slightest idea what return they would be making on their investment of $18,036.66. What rate of return would they be earning?

Learn how to calculate the rate of return for an annuity worth $18,036.66 that pays $3,000 annually for 10 years. This solution covers the present value of an annuity, interest rate calculation using numerical methods, and financial concepts suitable for finance students or advanced high school learners.

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