If you paid $ 59 to a loan company for the use of $ 1 comma 064 for 127 ​days, what annual rate of interest did they​ charge? (Assume a​ 360-day year.)

To find the annual rate of interest charged, we can use the **simple interest formula**:

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

Where:
- $ I $ is the interest paid,
- $ P $ is the principal (the amount borrowed),
- $ r $ is the annual interest rate (what we need to find),
- $ t $ is the time in years.

### Step 1: Organize the information given:
- $ I = 59 $ (the amount paid to the loan company),
- $ P = 1064 $ (the amount borrowed),
- $ t = \frac{127}{360} $ (since 127 days is a fraction of the 360-day year).

### Step 2: Rearrange the simple interest formula to solve for $ r $:
\[
r = \frac{I}{P \times t}
\]

### Step 3: Plug in the known values:
\[
r = \frac{59}{1064 \times \frac{127}{360}}
\]

Let me calculate that for you.The annual interest rate charged by the loan company is approximately **15.72%**.

Would you like further clarification or details on this process?

Here are five related questions for further practice:
1. How would the interest change if the loan term was 180 days instead of 127 days?
2. What would the interest rate be if only $45 was paid in interest for the same loan amount and period?
3. How much interest would be paid if the loan was $2,000 over 200 days with the same interest rate?
4. What happens to the interest rate if the principal amount borrowed is doubled?
5. How does using a 365-day year instead of a 360-day year affect the interest calculation?

**Tip:** When calculating simple interest, always ensure the time period $t$ is in years, especially when working with daily or monthly periods.

If you paid $59 to a loan company for the use of $1,064 for 127 days, what annual rate of interest did they charge? (Assume a 360-day year.)

Learn how to calculate the annual interest rate for a loan of $1,064 over a period of 127 days with a payment of $59 in interest. This problem involves the simple interest formula and proportional time conversion using a 360-day year. Ideal for high school students in Grades 10-12.

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