You borrow $870 from your brother and agree to pay back $920 in 3 months. What simple interest rate will you pay?

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

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

where:
- $I$ is the interest paid,
- $P$ is the principal (initial amount borrowed),
- $r$ is the interest rate per time period (which we need to find),
- $t$ is the time in years.

First, calculate the interest paid:
\[
I = 920 - 870 = 50
\]

Now, convert the time to years, since simple interest rates are typically annual. Since 3 months is $ \frac{3}{12} = 0.25 $ years, we can substitute into the simple interest formula:

\[
50 = 870 \times r \times 0.25
\]

Solve for $r$:

\[
r = \frac{50}{870 \times 0.25} = \frac{50}{217.5} \approx 0.23
\]

Thus, the simple interest rate is approximately $23\%$ per year.

### Would you like more details or have any questions?

Here are 5 related questions:
1. How does compound interest differ from simple interest?
2. If the loan term were extended to 6 months, how would the interest rate change?
3. What would be the total amount paid if the interest rate were reduced to 18%?
4. How would you calculate interest if payments were made monthly instead of after 3 months?
5. What is the formula for compound interest, and how does it apply to loans?

**Tip:** Always convert time into the same units (usually years) when calculating interest rates.

Learn how to calculate the simple interest rate on a $870 loan repaid as $920 in 3 months. Using the formula I = P × r × t, this detailed solution shows how to find the interest rate as approximately 23% per year. Ideal for Grades 9-10 students.

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