A loan company charges $66 interest for a 6 month loan of $400. 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 can follow these steps:

1. **Calculate the interest rate for the 6-month period:**

   \[
   \text{Interest rate for 6 months} = \frac{\text{Interest}}{\text{Principal}} = \frac{66}{400} = 0.165
   \]

2. **Annualize the 6-month interest rate:**

   Since the loan period is 6 months, to annualize it, we multiply the 6-month rate by 2 (since there are two 6-month periods in a year):

   \[
   \text{Annual interest rate} = 0.165 \times 2 = 0.330
   \]

So, the annual interest rate in decimal form is **0.330** (rounded to 3 decimal places).

Would you like more details or have any questions?

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Here are 5 related questions you might find helpful:

1. How do you convert a percentage interest rate to a decimal interest rate?
2. What is the formula for calculating simple interest?
3. How does the compounding period affect the annual interest rate?
4. What is the difference between nominal and effective interest rates?
5. How can you calculate the interest rate if the loan term is given in months instead of years?

**Tip:** Always ensure that the time period of the interest rate matches the time period of the loan when making comparisons or calculations.

Find out how to calculate the annual interest rate for a $400 loan with a $66 interest over 6 months. This step-by-step solution explains the simple interest concept, includes key formulas, and shows how to annualize the interest rate. Ideal for high school students in Grades 9-12.

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