
Ordinary Annuity
Annuity
Payment	Payment
Frequency	Time
Period (years)	Nominal
Rate (%)	Interest
Compounded	Future Value
of the Annuity (in $)
$9,000	every 6 months	7	7.0	semiannually	$ 


To find the future value of the ordinary annuity, we can use the following future value formula for an ordinary annuity:

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

Where:
- $FV$ = Future value of the annuity
- $P$ = Payment per period ($9,000)
- $r$ = Nominal annual interest rate (7% or 0.07)
- $n$ = Number of compounding periods per year (semiannually means 2 periods per year)
- $t$ = Time in years (7 years)

Now, let's calculate step-by-step:

1. **Given values:**
   - $P = 9,000$
   - $r = 0.07$
   - $n = 2$ (semiannually)
   - $t = 7$ years

2. **Plugging the values into the formula:**
   \[
   FV = 9000 \times \left( \frac{(1 + \frac{0.07}{2})^{2 \times 7} - 1}{\frac{0.07}{2}} \right)
   \]

3. **Simplify the expression inside the parentheses:**
   \[
   FV = 9000 \times \left( \frac{(1 + 0.035)^{14} - 1}{0.035} \right)
   \]
   \[
   FV = 9000 \times \left( \frac{(1.035)^{14} - 1}{0.035} \right)
   \]

4. **Compute $1.035^{14}$:**
   \[
   1.035^{14} \approx 1.647009
   \]
   \[
   FV = 9000 \times \left( \frac{1.647009 - 1}{0.035} \right)
   \]

5. **Subtract and divide:**
   \[
   FV = 9000 \times \left( \frac{0.647009}{0.035} \right)
   \]
   \[
   FV = 9000 \times 18.486
   \]

6. **Final calculation:**
   \[
   FV \approx 166,374.56
   \]

Thus, the future value of the ordinary annuity is approximately **$166,374.56**.

Would you like more details or have any questions? Here are some related questions:

1. How would the future value change if the interest rate increased?
2. What happens to the future value if payments are made annually instead of semiannually?
3. How does increasing the number of compounding periods affect the future value?
4. What if the time period was extended to 10 years?
5. What would the future value be with monthly payments?

**Tip:** The more frequently interest is compounded, the higher the future value of the annuity will be due to more frequent interest accumulation.

Ordinary Annuity: Payment $9,000 every 6 months, 7 years, 7.0% nominal interest rate, compounded semiannually. Find the future value of the annuity.

Learn how to calculate the future value of an ordinary annuity with $9,000 payments made semiannually for 7 years at a 7% nominal interest rate, compounded semiannually. The final future value is approximately $166,374.56.

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