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The problem you provided involves calculating the future value of an annuity due using a semiannual interest rate and periodic payments.

### Given Data:
- **Investment amount per payment:** $7,000
- **Number of payments per year:** 2 (since it's invested twice a year)
- **Number of years:** 7
- **Interest rate:** 4% compounded semiannually, which implies:
  - **Semiannual interest rate:** 2% (since 4%/2 = 2%)
- **Annuity type:** Annuity due (payments made at the beginning of each period)

### Steps to Solve:

We will use the future value formula for an annuity due, which is:

\[
FV = P \times \left( \dfrac{(1 + r)^n - 1}{r} \right) \times (1 + r)
\]

Where:
- $ FV $ is the future value of the annuity
- $ P $ is the payment amount per period
- $ r $ is the interest rate per period (semiannual in this case, so 2% = 0.02)
- $ n $ is the total number of periods (7 years × 2 periods/year = 14 periods)

Now, I will calculate the future value using this formula.The total value of the annuity due at the end of the 7-year period is approximately **$114,053.92**.

Would you like more details or have any other questions?

Here are 5 related questions to deepen your understanding:
1. How would the calculation change if the annuity was an ordinary annuity instead of an annuity due?
2. What effect would a higher interest rate have on the total value of the annuity?
3. How would reducing the number of payments per year to 1 impact the annuity's future value?
4. What formula should be used if the compounding period was quarterly instead of semiannual?
5. How does the future value of an annuity differ from the present value?

**Tip:** When dealing with annuities, always pay attention to the type (ordinary vs. due) and the compounding frequency, as both significantly affect the outcome.

Sam Gonzales invested $7,000 twice a year in an annuity due at Capital Appreciation, Inc. for a period of 7 years at an interest rate of 4% compounded semiannually. Using the ordinary annuity table, calculate the total value of the annuity due at the end of the 7-year period.

Learn how to calculate the future value of an annuity due with $7,000 invested twice a year for 7 years at a 4% interest rate compounded semiannually. Includes the annuity due formula and step-by-step solution.

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