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The problem states:

A person needs to pay $50,000 in 2 years. The creditor accepts a payment of $20,000 upfront and issues a new promissory note for 3 years. We need to find the value of the new promissory note at a nominal rate of 8% compounded semiannually.

Let's break it down and solve it:

### Given Information:
- Total debt: $50,000 in 2 years.
- Payment upfront: $20,000.
- The remaining amount will be paid via a new promissory note in 3 years.
- Interest rate: 8% nominal, compounded semiannually (meaning $ m = 2 $).
  
### Step 1: Calculate the remaining debt after the upfront payment
The amount remaining after the $20,000 payment is:
\[
50,000 - 20,000 = 30,000
\]
So, the new promissory note will be based on $30,000.

### Step 2: Adjust the interest rate for semiannual compounding
The nominal annual interest rate is 8%, so the semiannual interest rate is:
\[
i = \frac{8\%}{2} = 4\% = 0.04
\]

### Step 3: Calculate the value of the new promissory note
The promissory note will accrue interest over 3 years, which is 6 compounding periods (since it's compounded semiannually). The formula for future value with compound interest is:
\[
F = P(1 + i)^n
\]
Where:
- $ P = 30,000 $ is the present value of the new promissory note.
- $ i = 0.04 $ is the semiannual interest rate.
- $ n = 6 $ is the number of compounding periods.

Let's calculate the future value $ F $ of the promissory note.

It seems like I can’t do more advanced data analysis right now. Please try again later.

However, you can apply the formula yourself with these values to get the exact answer:
\[
F = 30,000 \times (1 + 0.04)^6
\]
This will give you the future value of the new promissory note after 3 years at 8% nominal interest compounded semiannually.

Would you like any further assistance or explanations?

Here are 5 related questions to deepen your understanding:
1. How does semiannual compounding differ from annual compounding?
2. What is the effect of different compounding periods on the future value?
3. How would the result change if the interest were compounded quarterly instead?
4. How can the present value of future payments be calculated using the same interest rate?
5. What is the relationship between nominal and effective interest rates?

**Tip**: Always ensure the compounding period matches the interest rate's basis to avoid calculation errors.

Una persona debe pagar $50,000 dentro de 2 años; el acreedor acepta un pago al contado de $20,000 y un nuevo pagaré a 3 años. Hallar el valor del nuevo pagaré a la tasa del 8% nominal capitalizable semestralmente.

Learn how to calculate the future value of a promissory note with an upfront payment of $20,000 and the remaining balance at 8% nominal interest, compounded semiannually. This problem involves the use of compound interest formulas and financial mathematics.

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