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We are tasked with calculating the annual payment needed to repay a loan. April borrows $23,000 at an interest rate of 7%, and she needs to repay the loan over 5 years. We need to find her annual payment, considering both the loan principal and the interest.

This is a typical loan repayment problem that can be solved using the formula for the annual payment of an amortizing loan:

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

Where:
- $A$ is the annual payment (what we're solving for),
- $P = 23000$ is the loan amount (principal),
- $r = \frac{7\%}{100} / 1 = 0.07$ is the annual interest rate,
- $n = 5$ is the number of years (since it's yearly payments).

Let me calculate the annual payment using these values.April must pay approximately $5,609.49 per year to fully repay the loan of $23,000 at an interest rate of 7% over 5 years.

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

Here are 5 related questions you might be interested in:
1. How is the formula for loan amortization derived?
2. What happens if the interest rate changes mid-way through the repayment period?
3. How would the monthly payment change if the loan was to be repaid monthly instead of yearly?
4. How can you calculate the total interest paid over the loan's duration?
5. How does the loan repayment structure differ between a simple interest loan and an amortizing loan?

**Tip:** Always remember to consider the loan term and interest rate carefully when taking out a loan, as they significantly impact the total cost of the loan.

April borrows $23000 at an interest rate of 7% to purchase a new automobile. At what rate (in dollars per year) must she pay back the loan, if the loan must be paid off in 5 years?

Learn how to calculate the annual payment for a $23,000 loan at 7% interest to be paid off over 5 years. This problem demonstrates the application of loan amortization formulas and interest calculations, suitable for high school students.

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