Mel Sturbridge needs $24,700 to remodel his home. Find the face value of a simple discount note that will provide the $24,700 in proceeds if he plans to repay the note in 180 days and the bank charges an 8% discount rate.
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WHATS THE ANSWER!
To find the face value of the simple discount note, we first need to understand how simple discount notes work.
The formula to calculate the face value of a simple discount note is:
Face Value = Proceeds / (1 - (Discount Rate * Time))
Where:
Proceeds = amount of money needed, which is $24,700
Discount Rate = 8% or 0.08 (converted to decimal)
Time = repayment period in years, which is 180 days ÷ 365 (since the discount rate is typically quoted on an annual basis)
Let's plug in the values and calculate the face value:
Proceeds = $24,700
Discount Rate = 0.08
Time = 180 days ÷ 365
Face Value = $24,700 / (1 - (0.08 * (180/365)))
Simplifying the equation:
Face Value = $24,700 / (1 - 0.04137)
Face Value = $24,700 / (0.95863)
Face Value ≈ $25,741.07
Therefore, the face value of the simple discount note that will provide $24,700 in proceeds is approximately $25,741.07.
To find the face value of a simple discount note, we need to use the formula:
Face Value = Proceeds / (1 - Discount Rate * Time)
Here, the discount rate is 8% or 0.08, and the time is 180 days or 180/360 (since most banks consider a year to have 360 days).
Let's calculate the face value using the formula:
Face Value = $24,700 / (1 - 0.08 * (180/360))
Face Value = $24,700 / (1 - 0.08 * 0.5)
Face Value = $24,700 / (1 - 0.04)
Face Value = $24,700 / 0.96
Face Value ≈ $25,729.17
So, the face value of the simple discount note that will provide $24,700 in proceeds is approximately $25,729.17.