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.