You lend a friend ​$10,000​, for which your friend will repay you ​$27,027 at the end of 5 years.  What interest rate are you charging your​ "friend"? 

To find the interest rate your friend is being charged, we can use the formula for compound interest. In this case, we are calculating the interest rate (r) based on the future value (FV), present value (PV), and the time period (t).

The formula for compound interest is:

\[
FV = PV \times (1 + r)^t
\]

Where:
- $FV = 27,027$ (the amount repaid at the end of 5 years),
- $PV = 10,000$ (the initial amount lent),
- $t = 5$ years,
- $r$ is the annual interest rate (what we want to find).

We can rearrange this formula to solve for $r$:

\[
r = \left( \frac{FV}{PV} \right)^{\frac{1}{t}} - 1
\]

Let me calculate this for you.

The interest rate you are charging your friend is approximately **22% per year**.

Would you like any additional details or have any questions about the calculation?

Here are 5 related questions you might find interesting:
1. What would happen if the loan was repaid in 3 years instead of 5 years?
2. How does the interest rate change if your friend repays only $20,000 instead of $27,027?
3. How does simple interest differ from compound interest in this scenario?
4. What if you wanted to charge a fixed interest rate of 15%? How much would the repayment be?
5. How does the compounding frequency (annually, quarterly, etc.) affect the interest rate?

**Tip:** Always clarify whether interest is compounded annually, quarterly, or monthly, as this can greatly affect the total repayment amount.

You lend a friend $10,000, for which your friend will repay you $27,027 at the end of 5 years. What interest rate are you charging your friend?

Learn how to calculate the interest rate for a $10,000 loan repaid as $27,027 over 5 years using the compound interest formula. This example demonstrates algebraic concepts of exponential growth, making it suitable for Grades 10-12 students.

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