Answer:
the face value of the loan is $5,263.16.
Explanation:
To determine the face value of the loan, we need to use the formula:
Face Value = Proceeds / (1 - Discount Rate * Time)
where "Time" is the time period of the loan in years.
Since the loan is for 6 months, we need to convert this time to years by dividing it by 12. Therefore, "Time" = 6/12 = 0.5 years.
Now, we can substitute the given values into the formula:
Face Value = 5,000 / (1 - 0.1 * 0.5)
Face Value = 5,000 / (1 - 0.05)
Face Value = 5,000 / 0.95
Face Value = $5,263.16 (rounded to the nearest cent)
Therefore, the face value of the loan is $5,263.16.