Question

On June 3, first city bank loaned a local sandwich shop $1,800 discounted at 8% for two months. On July 14, first city sold the discount note to second national bank which re discounted it at 9%. How much profit did first city bank make on this transaction?

Answer 1

Face value = $1,800

First city bank interest = FV x rate of interest x period

=> Discount by first city bank= 1800 x 0.08 x (2/12) = $24

Hence the maturity value for first city bank = 1800-24 = 1776

Discounted period : June 3 : 30-3 = 27

July 14 : 14 = 14

Discounted period = 27+14 = 41 days days passed before note is discounted

first city bank has to wait for 61-41 = 20 days for the note to come due

For second national bank : PV = (1776)/(1+0.09*20/365) = 1767.28

Profit that first national bank made = 1776-1767.28 = $8.715