​(Annuity interest​ rate)  ​You've been offered a loan of ​$25 comma 000​, which you will have to repay in 12 equal annual payments of ​$5 comma 000​, with the first payment due one year from now.  What interest rate would you pay on that​ loan?
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Part 1
The interest rate you would pay on the loan is 
  
enter your response here​%. ​ (Round to two decimal​ places.)

To solve this problem, we need to find the interest rate for an annuity. The problem can be solved using the formula for the present value of an ordinary annuity.

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

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

Where:
- $ PV $ is the present value of the loan (\$25,000)
- $ PMT $ is the annual payment (\$5,000)
- $ r $ is the interest rate
- $ n $ is the number of payments (12 years)

Given:
- $ PV = 25,000 $
- $ PMT = 5,000 $
- $ n = 12 $

We need to find $ r $. This equation cannot be solved algebraically in a simple manner, so we will use numerical methods to determine $ r $. Let’s proceed to calculate the interest rate.It seems like I can’t do more advanced data analysis right now. Please try again later. 

If you'd like, I can guide you through the manual steps to estimate the interest rate or assist with another question.

Would you like me to explain the manual process, or is there anything else you'd like to know? Here are some related questions you might consider:

1. How is the present value of an annuity calculated in general?
2. What is the difference between ordinary annuities and annuities due?
3. How does compound interest differ from simple interest in annuity problems?
4. What are some common methods for calculating interest rates when formulas get complicated?
5. How do changing interest rates affect loan repayments over time?

**Tip:** When dealing with annuity problems, understanding the relationship between the present value, payment, interest rate, and number of periods is crucial for solving these types of financial problems.

You've been offered a loan of $25,000, which you will have to repay in 12 equal annual payments of $5,000, with the first payment due one year from now. What interest rate would you pay on that loan? (Round to two decimal places.)

Learn how to calculate the interest rate for a $25,000 loan repaid in 12 equal annual payments of $5,000 using the present value of an ordinary annuity formula. This guide explains key financial concepts such as annuities, interest rate calculation, and loan repayment. Ideal for advanced high school math or college finance students.

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