MA170wk2solns

# The amount of interest earned over the fourth year i

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the amount of interest earned over the fourth year; I 4 = S (4) ° S (3) = 150 + 0 : 75 ² 4 2 ³ ° 150 ° 0 : 75 ² 3 2 ³ = 162 ° 156 : 75 = \$5 : 25 (d) i 4 ; the effective interest rate over the fourth year, as a percentage to two decimal places. i 4 = S (4) ° S (3) S (3) = 5 : 25 156 : 75 : = 0 : 03349282297 : = 3 : 35% 4. [8 marks ] Kim has a promissory note for \$1000. It is due in 120 days and bears an interest rate of 9%. Kim decides to sell the note 50 days after it is written to a bank that discounts at a simple interest rate of 11%. (a) Determine the price paid by the bank. The maturity date is 120 + 3 = 123 days later. ) S = 1000 ° 1 + 0 : 09 ° 123 365 ±± : = 1030 : 33 P = S (1 + rt ) ° 1 : = 1030 : 33 ° 1 + 0 : 11 ° 73 365 ±± ° 1 : = \$1008 : 15 2

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(b) If the seller of the note wishes to gain \$20.00 by selling the note to the bank, how many days before maturity should the note be sold to the bank? (Your answer should be a whole number) To gain \$20.00, the note must be sold for a price of \$1020.00 1020 = 1030 : 33 ° 1 + 0 : 11 ° t 365 ±± ° 1 1 + 0 : 11 ° t 365 ± = 1030 : 33 1020 0 : 11 ° t 365 ± = 1030 : 33 1020 ° 1 ) t = 365 ° 1030 : 33 1020 ° 1 ± 0 : 11 : = 33 : 605 : = 33 ) the note must be sold 33 days before the maturity date to ensure that the seller gains \$20.00 by selling the note to the bank. 5. [8 marks ] Investor A purchases a 91-day treasury bill with a face value of \$25 000. (a) If the note is purchased for \$24 771.49, what was the implied yield rate? Express your answer as a percentage with one decimal place.
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