A Treasury bill with a par value of 100000 due three months

A Treasury bill with a par value of $100,000 due three months from now is selling today for $97,087, with an effective annual yield of
A. 12.40%.
B. 12.55%.
C. 12.62%.
D. 12.68%.
E. None of the options

$2,913/$97,087 = 0.03; (1.03)⁴- 1.00 = 12.55%.

Could you please explain how the exponent \"4\" is determined in this sort of problem?

Thanks

Solution

Correct option is > B. 12.55%

Effective annual yield = (Maturity Value / Current Selling Price)^time -1

Effective annual yield = (100000 / 97087)^(12/3) -1

Effective annual yield = 12.55%

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This bond will mature in next 3 months, that means we have time = 12/3 = 4 for effective annual yield; if we annualize rate for effective annual rate then we would require 4 times hence, we are using time =4 or time =12/3