Your friend needs a loan of $4,000 for 5 months. You tell him for the simple interest loan service he needs to pay you back $4,100.00. What is the simple interest rate on your friendly loan?

To calculate the simple interest rate for the loan, we can use the simple interest formula:

\[
A = P(1 + rt)
\]

Where:
- $ A $ is the total amount to be paid back ($4,100),
- $ P $ is the principal loan amount ($4,000),
- $ r $ is the simple interest rate (what we're trying to find),
- $ t $ is the time in years (since it's 5 months, we convert this to years as $ \frac{5}{12} $).

First, rearrange the formula to solve for $ r $:

\[
r = \frac{A - P}{P \times t}
\]

Now, let's plug in the values:

\[
r = \frac{4100 - 4000}{4000 \times \frac{5}{12}}
\]

Now I'll calculate this.The simple interest rate on your loan is 6%.

Would you like more details or have any other questions? Here are some related questions to consider:

1. How does compound interest differ from simple interest?
2. What would the total amount be for different loan periods with the same interest rate?
3. How would the interest change if the loan was extended to 12 months?
4. What if the principal amount was $5,000 instead of $4,000?
5. How does the annual percentage rate (APR) compare to the simple interest rate?

**Tip:** When calculating simple interest, ensure the time period is in years to match the standard formula.

Learn how to calculate the simple interest rate on a loan of $4,000 over 5 months with a final repayment of $4,100. This problem involves key algebraic concepts, including the simple interest formula, and is suitable for students in Grades 9-12.

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