Find the present value for the amount given in the table.
Amount
Nominal Rate
Frequency of Conversion
Time
​$6789.49
3.7​%
semi dash annually
8 years
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Part 1
The present value is ​$
  
enter your response here.
​(Round to the nearest cent as needed. Round all intermediate values to six decimal places as​ needed.)

To find the present value (PV) of the given amount, we can use the formula for the present value of a future sum when interest is compounded periodically:

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

Where:
- $ A $ is the future amount: $ A = 6789.49 $
- $ r $ is the nominal annual interest rate: $ r = 3.7\% = 0.037 $
- $ n $ is the number of times the interest is compounded per year: Since it's semi-annually, $ n = 2 $
- $ t $ is the time in years: $ t = 8 $

Now, let's plug in the values and calculate the present value:

\[
PV = \frac{6789.49}{\left(1 + \frac{0.037}{2}\right)^{2 \times 8}}
\]

We'll calculate this step by step:

1. Calculate the interest rate per period:  
   \[
   \frac{0.037}{2} = 0.0185
   \]

2. Calculate the total number of compounding periods:  
   \[
   2 \times 8 = 16
   \]

3. Calculate the compound factor:  
   \[
   \left(1 + 0.0185\right)^{16} 
   \]

4. Finally, divide the future amount by the compound factor to find the present value.

Let's compute that.The present value of the amount is **$5,063.61**.

Would you like any further details or have any questions? Here are some related questions to consider:

1. How does changing the interest rate affect the present value?
2. What happens to the present value if the compounding frequency is changed to quarterly?
3. How would the present value change if the time was reduced to 5 years?
4. What if the amount was compounded annually instead of semi-annually?
5. How does the present value formula differ for continuous compounding?
6. What is the impact of increasing the future value on the present value?
7. Can you calculate the future value given the present value using the same parameters?
8. How does the number of compounding periods affect the present value?

**Tip:** Understanding how different variables impact the present value can help in financial planning and investment decisions.

Learn how to calculate the present value (PV) of $6789.49 with compound interest. Use our step-by-step solution and formula to understand the process. Includes details on nominal interest rates, compounding frequencies, and time periods. Round to the nearest cent as needed.

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