JAB Consulting received a promissory note of $11,500 at 9% simple interest for 15 months from one of its customers. After 6 months, Grove Isle Bank discounted the note at a discount rate of 8% Calculate the proceeds (in $) that JAB Consulting will receive from the discounted note. (Round your answer to the nearest cent.)

$ 

Answer:

• Proceeds = $12,026.13

Step-by-step explanation

Maturity value is given by

FV = P(1 + rt)

where: P is the initial value of the promissory note, r is the simple interest rate, and t is the time period (in years).

Given that Webster Digital received a promissory note of $11,500 for 15 months at 9% simple interest from one of its customers.

P = $11,500; t = 15 months = 15 / 12 = 1.25 years; r = 9% = 0.07

FV = $11,500(1 + (0.09 x 1.25))

FV = $11,500(1 + 0.1125

FV = $11,500 x 1.1125

FV = $12,793.75

The proceed from a discounted promissory note is given by

X = FV(1 - dt)

where: 

FV is the maturity value of the promissory note, d is the discount rate and t is the number of years remaining from the time the note was discounted to the maturity date.

Given that after 6 months, the note was discounted at Bank of Aventura at a discount rate of 8%.

t = 15 months - 6 months = 9 months = 9 / 12 months; d = 8% = 0.1; FV = $12,793.75
 

X = $12,793.75(1 - (8% x 9/12))

X = $12,793.75(1 - (0.06/12))

X = $12,793.75 x 0.94

X = $12,026.13