To determine how much Bill received from his friend, we first need to calculate the total value of the CD when it matures and then find out how much Bill needs to pay his friend based on the agreement.

1. Calculate the maturity value of the CD:

   The formula for simple interest is: $\text{Interest} = P \times r \times t$ Where:

   • $P$ = principal amount ($2000)
   • $r$ = annual interest rate (8% or 0.08)
   • $t$ = time in years (9 months = 0.75 years)

   $\text{Interest} = 2000 \times 0.08 \times 0.75 = 120$

   Now, add the interest to the principal to get the maturity value: $\text{Maturity Value} = P + \text{Interest} = 2000 + 120 = 2120$

2. Determine how much the friend will lend Bill:

   Bill has 3 months left until the CD matures. We need to find out how much he can borrow from his friend with a 10% interest rate for those 3 months.

   The loan duration in years is: $t = \frac{3}{12} = 0.25$

   Let $L$ be the amount borrowed by Bill. The interest on the loan can be calculated as: $\text{Interest} = L \times r \times t = L \times 0.10 \times 0.25 = 0.025L$

   The total amount Bill needs to pay back to his friend is the sum of the loan amount and the interest: $\text{Total Amount to Pay Back} = L + 0.025L = 1.025L$

   Since this amount equals the maturity value of the CD, we set it equal to $2120: $1.025L = 2120$

   Now solve for $L$: $L = \frac{2120}{1.025} \approx 2073.17$

Thus, Bill received approximately $2073.17 from his friend.

Summary

• Bill received about $2073.17 from his friend.

Would you like more details or have any questions about this calculation? Here are some related questions you might consider:

1. How would the calculation change if the interest rate on the CD were different?
2. What would happen if the loan interest rate were lower than the CD's interest rate?
3. How does simple interest differ from compound interest in this scenario?
4. If Bill needed the money earlier, how would that affect his overall interest earnings?
5. What are some alternatives to borrowing against a CD?

Tip: Always consider the effective interest rate when comparing different investment or borrowing options.