To find the interest rate being charged, we can use the Future Value formula of compound interest:

$A = P(1 + r)^t$

Where:

• $A$ is the amount to be repaid (the future value), which is $27,027.
• $P$ is the principal amount (the loan), which is $10,000.
• $r$ is the annual interest rate (which we need to find).
• $t$ is the number of years, which is 5.

Rearranging the formula to solve for $r$:

$r = \left( \frac{A}{P} \right)^{\frac{1}{t}} - 1$

Substitute the values into the equation:

$r = \left( \frac{27027}{10000} \right)^{\frac{1}{5}} - 1$

Now, let's calculate this.The interest rate you're charging your friend is approximately 22% per year.

Would you like further details or have any other questions?

Here are 5 related questions you might find interesting:

1. How would the interest rate change if the repayment time was shorter?
2. What is the total interest paid over the 5 years?
3. How would the repayment amount change with different interest rates?
4. How does compound interest differ from simple interest?
5. What would happen if your friend repaid you in installments?

Tip: Always compare interest rates when making loans to see the true cost or benefit over time.