Let's go through this problem step by step.

We are given:

• Interest Rate = 7.0% compounded monthly.
• Duration = 6 months.
• Initial Principal = $1,000.

(a) Find the annual yield of one of these CDs.

To calculate the annual yield, we use the formula for compound interest:

$A = P \left(1 + \frac{r}{n}\right)^{nt}$

Where:

• $A$ is the amount of money accumulated after $t$ years, including interest.
• $P$ is the principal amount (initial investment).
• $r$ is the annual interest rate (decimal).
• $n$ is the number of times the interest is compounded per year.
• $t$ is the time the money is invested or borrowed for, in years.

Since we need the annual yield, we will solve this for one year ($t = 1$).

Given:

• $r = 0.07$
• $n = 12$ (compounded monthly)
• $t = 1$ year

Now, let's compute the annual yield.

(b) How much would a $1,000 CD be worth at maturity?

Since the CD is held for 6 months, we use the same compound interest formula but with $t = 0.5$ (for 6 months).

(c) How much interest would you earn?

The interest earned is the final amount minus the initial principal:

$\text{Interest} = A - P$

(d) What percent of the original $1,000 is this interest?

We calculate the percentage by dividing the interest by the original principal and multiplying by 100:

$\text{Percent} = \frac{\text{Interest}}{1000} \times 100$

(e) Explanation

Here, we need to compare part (a) and part (d). Part (a) is for a full year, while part (d) is for 6 months. Therefore, they aren't directly comparable in terms of time.

(f) Explanation

The answer to part (d) is not exactly half of part (a) because compound interest takes into account the interest on interest, which is why it grows faster.

Let me calculate the answers for parts (a) to (d).Here are the calculated answers:

(a) The annual yield of the CD:

1072.29 \, (\text{or a 7.23% increase from the original amount of $1,000})

(b) The value of a $1,000 CD at maturity (after 6 months):

$1035.51$

(c) The interest earned after 6 months:

$35.51$

(d) The interest as a percentage of the original $1,000:

$3.55\%$

If you need further details or have any questions, feel free to ask.

Here are some related questions for further exploration:

1. How does increasing the compounding frequency affect the yield?
2. How would the results change with a higher interest rate?
3. What happens to the final amount if the CD is held for 2 years instead of 6 months?
4. How does the yield compare with other types of interest (e.g., simple interest)?
5. What is the impact of taxes on the interest earned in such investments?

Tip: Always double-check the interest compounding method to ensure you're using the correct formula for the financial product.