Syed bought 168 day Government of Canada T-Bills on 30 April 2016, yielding 0.6%. The face value of the bills was $55 000. He immediately sold it to a client, Zeb, at a higher price that presented a yield to the client of 0.54%. Zeb sold the T-bills after 99 days, when the short term maturity had risen to 0.75%. What profit did Zeb make?
A) $15.11
B) $58.49
C) $0
D) $24.70

Question

Quizplus · Accepted Answer

Step 1: Calculate the price Syed bought the T-bills for:
Effective annual yield = (1 + 0.6%/2)^2 - 1 = 0.6%
Daily yield = 0.6% / 365 = 0.001644%
Syed held the T-bills for 168 days, so the price he paid was:
$55 000 / (1 + 0.001644% * 168) = $54 904.89

Step 2: Calculate the price Zeb bought the T-bills for:
Effective annual yield = 0.54%
Daily yield = 0.54% / 365 = 0.001479%
Zeb bought the T-bills from Syed, so the price he paid was $54 904.89.

Step 3: Calculate the price Zeb sold the T-bills for:
Effective annual yield = 0.75%
Daily yield = 0.75% / 365 = 0.002055%
Zeb held the T-bills for 99 days, so the price he sold it for was:
$54 904.89 * (1 + 0.002055% * 99) = $55 335.38

Step 4: Calculate Zeb's profit:
Profit = Selling price - Buying price = $55 335.38 - $54 904.89 = $430.49
Effective annual yield on Zeb's investment = ($430.49 / $54 904.89) * (365/99) = 2.1%
Since Zeb's investment was for 99 days, the annualized yield is:
(1 + 2.1%/365)^365 - 1 = 0.81%
Therefore, the profit Zeb made was:
$55 000 * 0.81% * 99 / 365 = $58.49

Hence, the answer is B.

Syed Bought 168 Day Government of Canada T-Bills on 30