Use the formula for the present value of an ordinary annuity or the amortization formula to solve the following problem.
PV equals=​$9,000​
PMT=​$600
n=30
i=​?

To solve for the interest rate ($i$) in an ordinary annuity problem, we can use the Present Value of an Ordinary Annuity formula:

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

Where:
- $PV$ is the present value of the annuity (here $PV = 9,000$),
- $PMT$ is the periodic payment (here $PMT = 600$),
- $n$ is the total number of payments (here $n = 30$),
- $i$ is the periodic interest rate, which we are solving for.

Plugging in the known values:

\[
9,000 = 600 \times \left( \frac{1 - (1 + i)^{-30}}{i} \right)
\]

This equation cannot be solved algebraically in a simple form because the interest rate $i$ appears both inside and outside the exponent. Therefore, numerical methods (such as trial and error, interpolation, or using a financial calculator) are typically used to solve for $i$.

Let me compute it for you using numerical methods to find the interest rate.The interest rate ($i$) that satisfies the present value of the annuity is approximately **5.22%**.

Would you like further details on how this was calculated or how to interpret this result? Here are some related questions you might find helpful:

1. How is the present value of an annuity different from the future value of an annuity?
2. What are the steps for solving annuity problems manually without using numerical methods?
3. How does changing the payment amount affect the interest rate in an annuity?
4. How can you use financial calculators to solve for unknown variables in annuities?
5. What is the relationship between compounding frequency and the interest rate in annuity calculations?

**Tip:** When solving for interest rates in annuity problems, trial and error methods like Newton's method or specialized financial calculators are often the best approach due to the complexity of the equation.

Use the formula for the present value of an ordinary annuity or the amortization formula to solve the following problem. PV equals=$9,000, PMT=$600, n=30, i=?

Solve for the interest rate (i) in an annuity problem with PV=$9,000, PMT=$600, and n=30 using the present value of an ordinary annuity formula. Learn the step-by-step process and understand the numerical methods involved. Suitable for advanced high school or college students.

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