https://file.aiquickdraw.com/mathbot/file/1726579798989rk3ir13n.jpg

To solve the problem, we need to compute the maturity value (also called the face value) of a note that is discounted at 8% for 126 days, given that the maker receives P20,023.20 as proceeds.

### Step-by-step Solution:

The formula to compute the proceeds (P) from the face value (F) when a note is discounted is:

\[
P = F - D
\]
where:
- \( P \) = Proceeds (P20,023.20)
- \( F \) = Maturity value or face value (unknown)
- \( D \) = Discount

The discount \( D \) can be computed as:

\[
D = F \times r \times \frac{t}{360}
\]
where:
- \( r \) = discount rate (8% or 0.08)
- \( t \) = time (126 days)
- \( F \) = face value

Now, substituting the expression for \( D \) into the first equation, we get:

\[
P = F - (F \times r \times \frac{t}{360})
\]

Factor out \( F \):

\[
P = F \times \left(1 - r \times \frac{t}{360}\right)
\]

We can now solve for \( F \):

\[
F = \frac{P}{1 - r \times \frac{t}{360}}
\]

### Substituting the known values:

- \( P = 20,023.20 \)
- \( r = 0.08 \)
- \( t = 126 \)

\[
F = \frac{20,023.20}{1 - 0.08 \times \frac{126}{360}}
\]

Let me calculate the maturity value \( F \).The maturity value (or face value) of the note is **P20,600.00**.

Would you like further details or have any additional questions? Here are 5 related questions to expand on this concept:

1. How would the result change if the discount rate was 10% instead of 8%?
2. What is the total discount applied to the note in this example?
3. How does the duration (126 days) affect the proceeds compared to a 90-day period?
4. What would the proceeds be if the face value was P25,000 and all other conditions remained the same?
5. How can we calculate the interest earned on a note like this?

**Tip:** The longer the note duration, the higher the discount applied, which reduces the proceeds received.

What is the maturity value of a note that is discounted at 8% for 126 days if the maker receives P20,023.20 as proceeds?

Learn how to calculate the maturity value (face value) of a note discounted at 8% for 126 days, given that the proceeds are P20,023.20. This finance problem involves key formulas for calculating discounts on notes. Ideal for senior high school and college students studying finance or business math.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation