Question 1193719: Please help with a homework.
A promissory note dated 1 April 2021 for 1500, borrowed at a simple discount rate of 16%p.a. due on the 1 October 2021 is sold on the 1 July 2021.
1.1. what is the maturity value of the note?
1.2. what is the present value on the date of the sale?
Answer by parmen(42)   (Show Source):
You can put this solution on YOUR website! ### 1.1 Maturity Value of the Note
The **maturity value** of the note is the amount payable at the end of the term of the loan. For a promissory note, this is simply the face value, as the simple discount applies at the start or upon sale, not to the maturity value itself.
\[
\text{Maturity Value} = 1500 \, (\text{face value of the note})
\]
### 1.2 Present Value on the Date of the Sale
The **present value** of a note under a simple discount is calculated using the formula:
\[
PV = M \times (1 - d \times t)
\]
Where:
- \( M \) = Maturity value = \( 1500 \)
- \( d \) = Discount rate = \( 16\% = 0.16 \)
- \( t \) = Time remaining to maturity in years (from 1 July 2021 to 1 October 2021) = \( \frac{3}{12} = 0.25 \)
Substitute the values:
\[
PV = 1500 \times (1 - 0.16 \times 0.25)
\]
\[
PV = 1500 \times (1 - 0.04)
\]
\[
PV = 1500 \times 0.96
\]
\[
PV = 1440
\]
### Summary
1. **Maturity Value**: \( 1500 \)
2. **Present Value on 1 July 2021**: \( 1440 \)
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