Jane borrows $10,000 and writes a promissory note on July 10,2011.The due date is December 12,2011.The value on the maturity date is $10,472.00.Prior to the maturity date,it is sold to a bank that discounts the note at r = 5%.If the bank pays $10,383.81 for the note,on what day was it sold?
A)October 11
B)October 14
C)October 17
D)October 20

Question

Quizplus · Accepted Answer

We can use the formula for simple discount interest to solve this problem:

P = M/(1+rt)

where P is the discounted price paid by the bank, M is the maturity value of the note, r is the discount rate (5% or 0.05), and t is the time between the sale and maturity dates in years. We can solve for t by rearranging the formula:

t = (M/P - 1)/(r)

Plugging in the values given, we get:

t = (10,472/10,383.81 - 1)/(0.05) = 0.168

This means that the note was sold 0.168 years or about 61 days before the maturity date of December 12, 2011. Counting backwards from December 12, we get:

October 13, 2011 
October 12, 2011 
October 11, 2011

So the note was sold on October 11, 2011. Therefore, the answer is B) October 14.

Jane Borrows $10,000 and Writes a Promissory Note on July