a non interest bearing note of 1000 dated january 1, 2010 for 8 months was discounted at a dicounting rate of 10% after 2 months, how much cash is received
To calculate the amount of cash received for a non-interest bearing note, we need to determine the discounted value of the note and deduct any accrued interest.
First, let's calculate the discounted value of the note. The discounting rate is 10%, and the note was discounted after 2 months. Therefore, the remaining period until maturity is 8 - 2 = 6 months.
To find the discounted value, we'll use the formula:
Discounted Value = Face Value / (1 + Discount Rate * Time)
In this case:
Face Value = $1000
Discount Rate = 10% or 0.10
Time = 6/12 = 0.50 (since the remaining period is given in months)
Discounted Value = $1000 / (1 + 0.10 * 0.50)
Discounted Value = $1000 / (1 + 0.05)
Discounted Value = $1000 / 1.05
Discounted Value ≈ $952.38
Now, since it is a non-interest bearing note, there is no additional interest to deduct. Therefore, the cash received will be the discounted value of the note, which is approximately $952.38.