Tammy took out a loan for 

11

 months and was charged simple interest at an annual rate of 

2.4%

.
The total interest she paid on the loan was 

$143

.

How much money did Tammy borrow?
Do not round any intermediate computations. If necessary, refer to the 

list of financial formulas

.

$

To find out how much money Tammy borrowed, we can use the formula for simple interest:

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

Where:
- $ I $ is the interest paid ($143)
- $ P $ is the principal amount (the amount Tammy borrowed, which we need to find)
- $ r $ is the annual interest rate (2.4% or 0.024)
- $ t $ is the time in years (11 months or $ \frac{11}{12} $ years)

Let's rearrange the formula to solve for $ P $:

\[
P = \frac{I}{r \times t}
\]

Now, substitute the known values into the equation:

\[
P = \frac{143}{0.024 \times \frac{11}{12}}
\]

Let's calculate this step by step.

1. First, calculate the time in years:
   \[
   t = \frac{11}{12} = 0.9167
   \]

2. Next, multiply the interest rate by the time:
   \[
   0.024 \times 0.9167 \approx 0.0220008
   \]

3. Finally, divide the total interest by this product to find $ P $:
   \[
   P = \frac{143}{0.0220008} \approx 6500
   \]

So, Tammy borrowed **$6,500**.

Would you like more details on the calculation, or do you have any other questions?

Here are five related questions for further exploration:
1. What would the principal be if the interest rate was 3.5% instead of 2.4%?
2. How much interest would Tammy pay if the loan duration was 18 months?
3. If the interest rate doubled, how would that affect the amount borrowed?
4. How would the total interest change if Tammy borrowed $7,000 instead?
5. What is the difference in interest if the loan was taken out for 1 year instead of 11 months?

**Tip:** Always double-check your calculations, especially when dealing with financial formulas, to ensure accuracy.

Learn how to calculate the principal loan amount using the simple interest formula. This problem involves determining the amount borrowed by Tammy based on the interest paid, annual interest rate, and loan duration. Suitable for high school students studying financial mathematics.

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