Present value. A promissory note will pay $ 65 comma 000 at maturity 9 years from now. How much should you be willing to pay for the note now if money is worth 4.25 % compounded​ continuously?
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Part 1
​$

enter your response here ​(Round to the nearest​ dollar.)

To determine how much you should be willing to pay for the promissory note now (the present value), we can use the formula for continuously compounded interest:

\[
PV = \frac{FV}{e^{rt}}
\]

Where:
- $ PV $ is the present value (the amount you should pay now),
- $ FV $ is the future value (\$65,000),
- $ r $ is the annual interest rate (4.25% or 0.0425),
- $ t $ is the time in years (9 years),
- $ e $ is Euler's number, approximately 2.71828.

Now, let's calculate the present value.The present value of the promissory note is \$44,340 (rounded to the nearest dollar). This is the amount you should be willing to pay for the note now.

Would you like any further details on this calculation or have any questions? Here are five related questions that might help deepen your understanding:

1. How does the interest rate affect the present value of an investment?
2. What is the difference between continuously compounded interest and other compounding methods?
3. How does increasing the time period impact the present value?
4. How would the present value change if the interest rate was compounded annually instead of continuously?
5. What are some real-life examples where continuously compounded interest is applied?

**Tip:** Continuously compounded interest grows faster than interest compounded annually, semi-annually, or monthly due to its constant application.

A promissory note will pay $65,000 at maturity 9 years from now. How much should you be willing to pay for the note now if money is worth 4.25% compounded continuously? (Round to the nearest dollar.)

Learn how to calculate the present value of a promissory note that pays $65,000 at maturity in 9 years, with money worth 4.25% compounded continuously. This detailed solution uses the continuous compound interest formula and is suitable for Grades 11-12 or early college students.

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