Question

Webster Digital received a promissory note of $8,000 for 9 months at 7% simple interest from one of its customers. After 4 months, the note was discounted at Bank of Aventura at a discount rate of 10%. What are the proceeds Webster Digital will receive from the discounted note? (Round to the nearest cent)

Answer 1

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 $8,000 for 9 months at 7% simple interest from one of its customers.

P = &8,000; t = 9 months = 9 / 12 = 0.75 years; r = 7% = 0.07


`FV=8000(1+(0.07*0.75)) \\ \\ =8000(1+0.0525)=8000(1.0525) \\ \\ =\$8,420`

The proceed from a discounted promisory 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 4 months, the note was discounted at Bank of Aventura at a discount rate of 10%.

t = 9 months - 4 months = 5 months = 5 / 12 years; d = 10% = 0.1; FV = $8,420


`X=8420\left(1-\left(0.1* (5)/(12) \right)\right) \\ \\ =8420\left(1- (1)/(24) \right)=8420\left( (23)/(24) \right) \\ \\ =\$8,069.17`

Therefore, the proceed is $8,069.17