What is the present value of ​$800 to be received 14 years from now discounted back to the present at 9 ​percent?

To calculate the present value (PV) of $800 to be received 14 years from now, discounted at a rate of 9%, we use the formula for present value:

\[
PV = \frac{FV}{(1 + r)^t}
\]

Where:
- $FV$ is the future value, which is $800.
- $r$ is the discount rate, which is 9% or 0.09.
- $t$ is the number of years, which is 14.

Substitute the given values into the formula:

\[
PV = \frac{800}{(1 + 0.09)^{14}} = \frac{800}{(1.09)^{14}}
\]

Now, I'll calculate this.

The present value of $800 to be received 14 years from now, discounted at a rate of 9%, is approximately **$239.40**.

Would you like more details or have any questions? 

Here are 5 related questions for further understanding:
1. What would the present value be if the interest rate were 8% instead of 9%?
2. How does increasing the number of years affect the present value?
3. What is the future value if you invest $239.40 today at 9% interest for 14 years?
4. How would compounding more frequently (e.g., monthly or quarterly) change the present value?
5. Can the present value formula be used for continuous compounding, and how would it differ?

**Tip:** When interest rates increase, the present value of future amounts decreases.

What is the present value of $800 to be received 14 years from now discounted back to the present at 9 percent?

Discover how to calculate the present value of $800 received 14 years from now with a 9% discount rate. This example covers the present value formula and explains key concepts like discounting and the time value of money. Ideal for advanced high school and college students.

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