Amy has a 10% interest bearing note dated 3 March 2020. The term of the note is 120 days.
On 15 May 2020, she discounts the note at 8%. If the proceeds received amounted to
RM15392.54.
i. The maturity date of the note.
ii. The maturity value of the note.
iii. The bank discount amount
iv. The face value of the note
v. The amount of interest Amy receives.
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To answer these questions, we need to understand the concepts of interest, discounting, and calculating the various values related to the note.
i. The maturity date of the note:
The term of the note is given as 120 days from 3 March 2020. To find the maturity date, we add 120 days to 3 March 2020. Let's calculate it:
3 March 2020 + 120 days = 2 July 2020
So, the maturity date of the note is 2 July 2020.
ii. The maturity value of the note:
The maturity value refers to the total amount that will be paid at the end of the term. Since the note is interest-bearing, we need to consider the interest in the calculation. The formula for calculating the maturity value is:
Maturity value = Face value + (Face value × Interest rate × Time)
Here, the face value is the amount of the note, and the interest rate is the percentage stated (10%). Let's calculate it:
Maturity value = RM15392.54 + (RM15392.54 × 10% × 120/365)
Maturity value = RM15392.54 + (RM15392.54 × 0.10 × 120/365)
Maturity value = RM15392.54 + (RM15392.54 × 0.0328)
Maturity value ≈ RM15902.86
So, the maturity value of the note is approximately RM15902.86.
iii. The bank discount amount:
When Amy discounts the note at 8%, she is essentially selling the note to the bank at a discounted price. The bank discount is the difference between the maturity value and the proceeds received. Let's calculate it:
Bank discount amount = Maturity value - Proceeds received
Bank discount amount = RM15902.86 - RM15392.54
Bank discount amount ≈ RM510.32
So, the bank discount amount is approximately RM510.32.
iv. The face value of the note:
The face value is the original amount mentioned in the note. In this case, it is not given explicitly. However, we can find it by rearranging the formula for maturity value:
Face value = Maturity value / (1 + Interest rate × Time)
Face value = RM15902.86 / (1 + (10% × 120/365))
Face value = RM15902.86 / (1 + 0.0328)
Face value ≈ RM15379.44
So, the face value of the note is approximately RM15379.44.
v. The amount of interest Amy receives:
The amount of interest can be calculated by subtracting the face value from the maturity value. Let's calculate it:
Interest amount = Maturity value - Face value
Interest amount = RM15902.86 - RM15379.44
Interest amount ≈ RM523.42
So, the amount of interest Amy receives is approximately RM523.42.