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Math  /  Numbers & Operations

Question1.5 Promissory Notes 1) The maturity value of a 280 day non-interest bearing promissory note is $5,554.84\$ 5,554.84. What would the proceeds of the note be 100 days after it was issued if the interest rate is 9.75%9.75 \% ?

Studdy Solution

STEP 1

1. The promissory note is non-interest bearing, meaning it is issued at a discount.
2. The maturity value of the note is \$5,554.84.
3. The note matures in 280 days.
4. The interest rate is \(9.75\%\) per annum.
5. We need to find the proceeds of the note 100 days after issuance.

STEP 2

1. Calculate the discount rate.
2. Determine the discount amount.
3. Calculate the proceeds of the note 100 days after issuance.

STEP 3

Calculate the discount rate for the 280-day period using the annual interest rate.
Discount Rate=9.75%100×280365\text{Discount Rate} = \frac{9.75\%}{100} \times \frac{280}{365}

STEP 4

Convert the percentage to a decimal and calculate the discount rate.
Discount Rate=0.0975×280365≈0.0748\text{Discount Rate} = 0.0975 \times \frac{280}{365} \approx 0.0748

STEP 5

Calculate the discount amount using the maturity value and the discount rate.
Discount Amount=Maturity Value×Discount Rate=5554.84×0.0748\text{Discount Amount} = \text{Maturity Value} \times \text{Discount Rate} = 5554.84 \times 0.0748

STEP 6

Compute the discount amount.
Discount Amount≈5554.84×0.0748≈415.50\text{Discount Amount} \approx 5554.84 \times 0.0748 \approx 415.50

STEP 7

Calculate the proceeds of the note 100 days after issuance by subtracting the proportionate discount from the maturity value.
First, find the proportionate discount for 100 days:
Proportionate Discount=100280×415.50\text{Proportionate Discount} = \frac{100}{280} \times 415.50

STEP 8

Calculate the proportionate discount.
Proportionate Discount≈100280×415.50≈148.39\text{Proportionate Discount} \approx \frac{100}{280} \times 415.50 \approx 148.39

STEP 9

Subtract the proportionate discount from the maturity value to find the proceeds.
Proceeds=5554.84−148.39≈5406.45\text{Proceeds} = 5554.84 - 148.39 \approx 5406.45
The proceeds of the note 100 days after issuance are approximately:
5406.45\boxed{5406.45}

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