Use the ordinary annuity formula shown to the right to determine the accumulated amount in the annuity if ​$50 is invested semiannually for 10 years at 5.5​% compounded semiannually.
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Part 1
The accumulated amount will be ​$
  
enter your response here.
​(Round to the nearest cent as​ needed.)


To determine the accumulated amount in the annuity using the ordinary annuity formula, we need to use the following equation:

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

Where:
- $ A $ is the accumulated amount.
- $ P $ is the regular payment (in this case, $50).
- $ r $ is the annual interest rate (5.5%, or 0.055 as a decimal).
- $ n $ is the number of compounding periods per year (since it's compounded semiannually, $ n = 2 $).
- $ t $ is the time in years (10 years).

Now, let's plug the given values into the formula:
- $ P = 50 $
- $ r = 0.055 $
- $ n = 2 $
- $ t = 10 $

Let's calculate the accumulated amount.It seems like I can’t do more advanced data analysis right now. Please try again later. However, you can still follow the steps I provided and plug the values into a calculator or spreadsheet to determine the accumulated amount. If you need any further guidance or explanations, feel free to ask!

Would you like me to explain any part of the formula in more detail, or help with another question?

Here are five related questions to deepen your understanding:
1. How does compounding frequency affect the total accumulated amount?
2. What if the interest rate were compounded annually instead of semiannually?
3. How does the accumulated amount change if the regular payment increases to $100?
4. What is the formula for a future value of an annuity due, and how does it differ from the ordinary annuity?
5. How would the accumulated amount change if the investment period were extended to 15 years?

**Tip:** Always double-check whether an annuity is compounded at regular intervals (like annually, semiannually, or quarterly) to apply the right formula adjustments.

Use the ordinary annuity formula shown to the right to determine the accumulated amount in the annuity if $50 is invested semiannually for 10 years at 5.5% compounded semiannually.

Find out how to calculate the accumulated amount in an ordinary annuity when $50 is invested semiannually for 10 years at a 5.5% interest rate compounded semiannually. This problem involves key concepts of compound interest and annuities. Suitable for Grades 10-12 students.

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