A loan company charges $74 interest for a 4 month loan of $800. Find the annual interest rate they are charging. Enter the rate in decimal form, rounded to 3 decimal places.


To find the annual interest rate in decimal form, we'll follow these steps:

1. **Calculate the monthly interest rate:**

   The interest charged for 4 months is $74 on a loan of $800.
   \[
   \text{Monthly Interest Rate} = \frac{\text{Interest}}{\text{Principal} \times \text{Number of Months}}
   \]
   \[
   \text{Monthly Interest Rate} = \frac{74}{800 \times 4} = \frac{74}{3200} = 0.023125
   \]

2. **Calculate the annual interest rate:**

   Since the loan period is 4 months, we need to annualize the monthly interest rate by multiplying by 12.
   \[
   \text{Annual Interest Rate} = 0.023125 \times 12 = 0.2775
   \]

Thus, the annual interest rate in decimal form, rounded to three decimal places, is **0.278**.

Would you like more details or have any questions?

Here are 5 related questions to expand your understanding:

1. How would the interest rate change if the loan period were 6 months instead of 4?
2. What would the monthly payment be if the loan was amortized over 12 months at the calculated annual interest rate?
3. How can you calculate the annual interest rate if only the total interest and principal are given without the loan period?
4. How does compound interest differ from simple interest in loan calculations?
5. How would the interest amount change if the loan amount was doubled?

**Tip:** Always double-check your calculations when dealing with percentages and decimal forms, especially when rounding.

A loan company charges $74 interest for a 4 month loan of $800. Find the annual interest rate they are charging. Enter the rate in decimal form, rounded to 3 decimal places.

Learn how to calculate the annual interest rate for a 4-month loan of $800 with $74 interest. This problem covers simple interest calculations and the process of annualizing monthly interest rates. Suitable for students in Grades 9-11.

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