(a) What is the value of the CD when it matures?

To calculate the value of the CD at maturity, we use the formula for simple interest:

$A = P \left(1 + rt\right)$

Where:

• $A$ is the amount (the value of the CD at maturity),
• $P$ is the principal amount (initial deposit),
• $r$ is the annual interest rate (as a decimal),
• $t$ is the time the money is invested or borrowed for, in years.

Given:

• $P = 6000$ dollars,
• $r = 0.08$ (8% annual interest),
• $t = \frac{9}{12} = 0.75$ years (since the CD matures in 9 months).

Now, plug the values into the formula:

$A = 6000 \left(1 + 0.08 \times 0.75\right)$

$A = 6000 \left(1 + 0.06\right)$

$A = 6000 \times 1.06 = 6360$

So, the value of the CD when it matures is $6360.

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(b) How much did Bill receive from his friend?

The agreement with his friend specifies that the friend earns a 10% annual simple interest return on the loan, but the total amount Bill will pay back will be the future value of the CD at maturity ($6360).

Let $P_f$ be the amount Bill receives from his friend. The simple interest formula for the loan is:

$A_f = P_f \left(1 + rt\right)$

Where:

• $A_f = 6360$ (the amount Bill will pay back),
• $r = 0.10$ (10% annual interest),
• $t = \frac{3}{12} = 0.25$ years (since Bill borrowed money for 3 months).

Substitute into the formula:

$6360 = P_f \left(1 + 0.10 \times 0.25\right)$

$6360 = P_f \left(1 + 0.025\right)$

$6360 = P_f \times 1.025$

Now, solve for $P_f$:

$P_f = \frac{6360}{1.025} \approx 6200.00$

Thus, Bill received $6200.00 from his friend.

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Would you like further clarification on any part of the calculations?

Here are 5 related questions:

1. How would the total value of the CD change if the interest rate was 10% instead of 8%?
2. How would the loan agreement change if Bill borrowed for a longer or shorter period?
3. How do you calculate compound interest and how does it differ from simple interest?
4. What happens if the loan interest rate is lower than the interest rate on the CD?
5. If Bill had invested his money in a different type of investment with compound interest, how would the outcome change?

Tip: When dealing with simple interest, always remember that the interest amount is calculated only on the initial principal, not on the accumulated interest.