Final answer:
To find the face value of the three-month promissory note, the maturity value needs to be discounted by the interest earned over the given period using the simple interest formula. The detailed explanation includes the mathematical steps necessary to determine the original amount loaned, known as the face value.
Step-by-step explanation:
The question asks about the face value of a three-month promissory note with a known maturity value. To find the face value, we need to discount the maturity value by the interest that was earned over the three-month period. Given an interest rate of 4.5% and ignoring any grace period, we will apply the simple interest formula to solve for the face value.
Since the maturity value is the sum of the face value and the interest earned, we can denote the face value as FV, the maturity value as MV, and the annual interest rate as r. The time period in years, t, is three months or 0.25 years.
The formula for calculating the maturity value (MV) with simple interest is:
MV = FV + (FV × r × t)
Given that MV = $950.899, r = 4.5%, and t = 0.25, we can rewrite the formula as:
$950.899 = FV + (FV × 0.045 × 0.25)
By isolating FV in the equation, we can calculate the exact face value of the promissory note.