To borrow​ money, you pawn your guitar. Based on the value of the​ guitar, the pawnbroker loans you

​$600600.

One month​ later, you get the guitar back by paying the pawnbroker

​$11721172.

What annual interest rate did you​ pay?

Question content area bottom

Part 1

You will pay a simple interest rate of

enter your response here​%

​(Round to the nearest whole number as​ needed.)

We can calculate the annual interest rate using the formula for simple interest:

\[
I = P \times r \times t
\]

Where:
- $ I $ is the interest paid,
- $ P $ is the principal amount (loan),
- $ r $ is the annual interest rate (expressed as a decimal),
- $ t $ is the time period in years.

First, let's calculate the interest paid:
\[
I = 1172 - 600 = 572
\]

So the interest paid is $572.

Next, since the loan duration was one month, the time $ t $ in years is:
\[
t = \frac{1}{12}
\]

Now, we can plug in the values into the simple interest formula and solve for $ r $:

\[
572 = 600 \times r \times \frac{1}{12}
\]

Solve for $ r $:

\[
r = \frac{572 \times 12}{600} = \frac{6864}{600} = 11.44
\]

Thus, the annual interest rate is approximately 11.44, which rounds to **11%**.

### Answer:
You paid a simple interest rate of **11%**.

---

Would you like more details or explanations on any part of the process? Here are some related questions:

1. How is simple interest different from compound interest?
2. What if the loan duration was 6 months? How would the interest change?
3. What does it mean for interest to be "annualized"?
4. Can you apply the same formula if the loan duration is in days?
5. How do you calculate interest on a compounded loan?

**Tip:** Always double-check if interest is simple or compounded, as the method to calculate changes accordingly!

To borrow money, you pawn your guitar. Based on the value of the guitar, the pawnbroker loans you $600. One month later, you get the guitar back by paying the pawnbroker $1172. What annual interest rate did you pay?

Learn how to calculate the annual interest rate for a loan using simple interest. In this example, a $600 loan is repaid with $1172 after one month. Find out how to apply the simple interest formula to determine the interest rate, perfect for high school students (Grades 9-12).

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