you lend a friend

​$10,000​

for which your friend will repay you

​$27027

at the end of

5

years.  What interest rate are you charging your​ "friend"?

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.

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?

Discover how to calculate the interest rate for a loan of $10,000 repaid at $27,027 after 5 years using the compound interest formula. This step-by-step guide explains the necessary calculations and concepts involved, making it suitable for students in Grades 10-12.

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