 Solve by using formulas. (Round your answer to the nearest cent.)
Ordinary Annuity Annuity
Payment 	Payment
Frequency 	Time
Period (years) 	Nominal
Rate (%) 	Interest
Compounded 	Future Value
of the Annuity (in $)
$5,000 	every 6 months 	7 	7.0 	semiannually 

We are given an ordinary annuity, which means regular payments are made at the end of each period. The problem provides the following information:

- **Payment (PMT)**: $5,000 every 6 months
- **Payment Frequency**: Semiannually (every 6 months)
- **Time Period (years)**: 7 years
- **Nominal Rate (Annual Interest Rate)**: 7.0%
- **Interest Compounded**: Semiannually

We are asked to find the **Future Value (FV)** of this annuity. To do this, we will use the future value formula for an ordinary annuity:

\[
FV = PMT \times \frac{(1 + r)^n - 1}{r}
\]

Where:
- $ PMT $ is the payment amount per period (5,000)
- $ r $ is the interest rate per period
- $ n $ is the total number of periods

### Step 1: Determine $ r $ (the interest rate per period)

The nominal annual interest rate is 7.0%, but since the interest is compounded semiannually, we need to divide this rate by 2 to get the interest rate per period.

\[
r = \frac{7.0\%}{2} = 0.035 \text{ or } 3.5\%
\]

### Step 2: Determine $ n $ (the total number of periods)

Since payments are made every 6 months and the total time is 7 years, we need to calculate the number of payment periods. There are 2 periods per year, so:

\[
n = 7 \text{ years} \times 2 \text{ periods/year} = 14 \text{ periods}
\]

### Step 3: Calculate the Future Value (FV)

Now, we can substitute the values into the formula:

\[
FV = 5,000 \times \frac{(1 + 0.035)^{14} - 1}{0.035}
\]

First, calculate $ (1 + 0.035)^{14} $:

\[
(1 + 0.035)^{14} = 1.035^{14} \approx 1.60471
\]

Now, calculate the numerator $ 1.60471 - 1 = 0.60471 $.

Finally, calculate the Future Value:

\[
FV = 5,000 \times \frac{0.60471}{0.035} \approx 5,000 \times 17.2774 = 86,387.06
\]

### Final Answer:

The future value of the annuity is approximately **$86,387.06**.

---

Would you like any further details or clarifications?

Here are 5 related questions to expand your understanding:
1. How would the future value change if the payment was made annually instead of semiannually?
2. What happens to the future value if the interest rate increases to 8%?
3. How does the future value of an annuity compare to a lump-sum investment over the same period?
4. How do we compute the present value of an ordinary annuity with the same parameters?
5. What is the difference between an ordinary annuity and an annuity due in terms of future value?

**Tip:** For semiannual compounding, always divide the nominal interest rate and multiply the time period accordingly.

Solve by using formulas. (Round your answer to the nearest cent.) Ordinary Annuity Annuity Payment  Payment Frequency  Time Period (years)  Nominal Rate (%)  Interest Compounded  Future Value of the Annuity (in $) $5,000 every 6 months 7 7.0 semiannually

Learn how to calculate the future value of an ordinary annuity with semiannual payments of $5,000 over 7 years at an interest rate of 7% compounded semiannually. This problem covers key finance concepts including annuities and compound interest, suitable for college-level or advanced high school students.

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