a man holds a note of $6,000 that has an interest rate of 13% annually the note was made on march 17 and is due november 11 he sells the note to a bank on june 14 at a discount rate of 12% annually find the proceeds on the third-party discount rate.
56,600
To find the proceeds on the third-party discount rate, we need to use the formula:
Proceeds = Face value - Discount
First, let's calculate the face value of the note. The note was made on March 17 and is due on November 11, so the time period is from March 17 to November 11. To calculate the time period, we need to count the number of days.
March 17 to June 14 = 89 days
June 14 to November 11 = 150 days
Total number of days = 89 + 150 = 239 days
Now, we can calculate the face value of the note.
Face value = Principal + Interest
Principal = $6,000
Interest = Principal * Interest rate * (Time period/360)
Interest = $6,000 * 0.13 * (239/360)
Interest = $512.31 (approx.)
Face value = $6,000 + $512.31
Face value = $6,512.31
Next, let's calculate the discount.
Discount = Face value * Discount rate * (Time period/360)
Discount = $6,512.31 * 0.12 * (239/360)
Discount = $310.07 (approx.)
Finally, let's calculate the proceeds on the third-party discount rate.
Proceeds = Face value - Discount
Proceeds = $6,512.31 - $310.07
Proceeds = $6,202.24
Therefore, the proceeds on the third-party discount rate is approximately $6,202.24.
To find the proceeds on the third-party discount rate, we need to calculate the amount of discount applied to the note.
First, let's determine the time period between March 17 and June 14.
March 17 to April 17 = 1 month
April 17 to May 17 = 1 month
May 17 to June 14 = 28 days (approximately)
So, the time period between March 17 and June 14 is approximately 2 months and 28 days.
Next, let's calculate the interest accrued on the note during this period.
Principal Amount = $6,000
Interest Rate = 13% annually
To calculate the interest accrued, we can use the formula:
Interest Accrued = (Principal Amount * Interest Rate * Time) / 365
Time = 2 months + 28 days = 88 days
Interest Accrued = (6,000 * 0.13 * 88) / 365
= $358.90 (approximately)
Now, we need to calculate the discounted value of the note using the discount rate of 12% annually.
Discount Rate = 12% annually
To calculate the discounted value, we can use the formula:
Discounted Value = Principal Amount - (Principal Amount * Discount Rate * Time) / 365
Time = 2 months + 28 days = 88 days
Discounted Value = 6,000 - (6,000 * 0.12 * 88) / 365
= $5,894.19 (approximately)
Therefore, the proceeds on the third-party discount rate would be $5,894.19.