ryan discounts an 80-day note for $15,000 at 12 percent. the bank discount is: (assume ordinary interest)
To find the bank discount, we need to use the formula:
Bank Discount = Face Value * Rate * Time
Here,
Face Value = $15,000
Rate = 12% (or 0.12 as a decimal)
Time = 80 days
Let's substitute these values into the formula:
Bank Discount = $15,000 * 0.12 * (80/360)
Note that we divide the time by 360 because 360 days is a standard convention for calculating interest on short-term notes.
Now, let's solve the equation:
Bank Discount = $15,000 * 0.12 * (80/360)
Bank Discount = $15,000 * 0.12 * 0.2222
Bank Discount = $399.96 (rounded to the nearest cent)
Therefore, the bank discount is $399.96.
To find the bank discount on a note, you need to know the face value of the note, the interest rate, and the time period.
In this case, the face value of the note is not given, but we can find it using the formula for bank discount:
Bank Discount = Face Value - Discount
Discount = Face Value x Interest Rate x Time
Let's calculate the face value first:
Discount = $15,000
Interest Rate = 12% or 0.12
Time = 80 days
Discount = Face Value x 0.12 x 80
Solving for Face Value:
Face Value = Discount / (0.12 x 80)
Now we can calculate the face value:
Face Value = $15,000 / (0.12 x 80)
Face Value = $15,000 / 9.6
Face Value = $1,562.50
Now that we have determined the face value of the note, we can find the bank discount:
Bank Discount = Face Value - Discount
Bank Discount = $1,562.50 - $15,000
Bank Discount = -$13,437.50
Since the bank discount is negative, it means that the amount discounted is greater than the face value of the note. In this case, Ryan is actually paying $13,437.50 less than the face value of the note.