Jim lends $8000 to Sally on September 23,2006.Sally signs a promissory note,with the note due in 10 months.The maturity value of the note is $8536.55.Jim sells the note to a bank on February 23,2007.If the bank wishes to earn r = 8%,what price does Jim get for the note?
A)$8259.57
B)$8261.18
C)$8264.83
D)$8268.27

Question

Quizplus · Accepted Answer

The price Jim gets for the note is calculated based on the discount of the maturity value for the remaining period until maturity, at the bank's desired rate of 8%. The note matures in 10 months from September 23, 2006, which is July 23, 2007. Jim sells the note to the bank on February 23, 2007, which means there are 5 months left until maturity. The discount is calculated using the formula for the present value of a single sum due in the future: $PV = FV / (1 + r)^n$, where $PV$ is the present value (price Jim gets), $FV$ is the future value (maturity value of the note, $8536.55), $r$ is the monthly interest rate (annual rate of 8% divided by 12 months = 0.08/12), and $n$ is the number of periods (months) until maturity (5 months). Calculating this gives the price Jim gets for the note, which is closest to option A, $8259.57.

Jim Lends $8000 to Sally on September 23,2006