Solve the problem. Round dollar amounts to the nearest cent. Use 360 days.
-What is the purchase price of a 26-week T-bill with a maturity value of $1000 that earns an annual interest rate of 5.25%?
A) $1000
B) $25.58
C) $974.42
D) $1025.58

Question

Quizplus · Accepted Answer

First, determine the annual interest rate equivalent for a 26-week T-bill using the following formula: 
(360 / maturity period) x discount rate = annualized discount yield
(360 / 26) x 0.0525 = 0.725%

Next, calculate the purchase price of the T-bill using the following formula:
Purchase price = maturity value / (1 + annualized discount yield)
Purchase price = $1000 / (1 + 0.00725)
Purchase price = $974.42

Therefore, the best choice is C, with an explanation that shows the calculation process used to arrive at the answer. First, we need to calculate the interest earned by the T-bill:
Annual interest rate = 5.25%
Maturity value = $1000
Time period = 26 weeks = 182 days
Using the formula: Interest = (Annual interest rate x Maturity value x Time period) / Number of days in a year
Interest = (0.0525 x 1000 x 182) / 360
Interest = $26.67 (rounded to the nearest cent)
Now, we can calculate the purchase price of the T-bill:
Purchase price = Maturity value - Interest
Purchase price = $1000 - $26.67
Purchase price = $973.33 (rounded to the nearest cent)
Since we need to round to the nearest cent, the closest option is C: $974.42

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