Final answer:
The original face value of the promissory note is approximately $90,000, and it was issued sometime in April 2023.
Step-by-step explanation:
To answer the student's question regarding the promissory note, we need to determine two things: the original face value of the promissory note and the original issue date.
To find the face value, we have to backtrack from the maturity amount. The promissory note includes interest, so the face value will be less than the maturity amount.
Let's begin with the maturity amount: $96,480. The note was issued at a 12% per annum interest rate for 219 days. The formula for calculating the total interest I on a promissory note is I = P x r x t, where:
- P is the principal amount (the original face value)
- r is the annual interest rate (expressed as a decimal)
- t is the time in years
We also know that there are 365 days in a year. Thus, the time in years is 219 / 365. The interest I can be expressed as:
Interest I = P x 0.12 x (219 / 365)
We know that the maturity amount M is the sum of the principal and the interest: M = P + I. Therefore:
$96,480 = P + P x 0.12 x (219 / 365)
Now we can solve for P.
P = $96,480 / (1 + 0.12 x (219 / 365))
= $96,480 / 1.07205479
≈ $90,000
The original face value of the promissory note is approximately $90,000.
Next, to find the original issue date, we simply count back 219 days from the maturity date of November 28, 2023.
By calculating backward, we find the original issue date to be sometime in April 2023.