Your friend signs a promissory note for $2,000 for 30 days with a rate of 2.25% attached. After fifteen days, you realize you need the money and sell the promissory to another friend to yield you 3.00%. What was the value of the note when you sold it?
To find the value of the promissory note when you sold it, we need to calculate the remaining value of the note after fifteen days and then determine what amount would yield a 3.00% return in the remaining time.
First, let's calculate the interest accrued on the promissory note over fifteen days.
Interest = Principal × Rate × Time
Interest = $2,000 × 2.25% × (15/365) (since there are 365 days in a year)
Interest = $18.49 (rounded to two decimal places)
Next, subtract the interest accrued from the principal to get the remaining value of the note after fifteen days.
Remaining Value = Principal - Interest
Remaining Value = $2,000 - $18.49
Remaining Value = $1,981.51
Now we need to determine what amount would yield a 3.00% return over the remaining 15 days.
Let's use the formula to calculate the selling price based on the desired yield:
Selling Price = Remaining Value / (1 + (Yield / 100) × (Time / 365))
Selling Price = $1,981.51 / (1 + (3.00/100) × (15/365))
Selling Price ≈ $1,988.84 (rounded to two decimal places)
Therefore, the value of the promissory note when you sold it was approximately $1,988.84.