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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.

Recently, a certain bank offered six-month CDs at 7.0% compounded monthly. Find the annual yield, the maturity value of a $1,000 CD, and related calculations.

Learn how to calculate the annual yield for a six-month CD with 7.0% interest compounded monthly, find the maturity value of a $1,000 CD, and determine the interest earned as a percentage of the initial principal. This example uses the compound interest formula and percentage calculations.

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