What is the holding period yield for a 182 day $1 M T-Bill that is selling for $991,250?

Question

BlackTom AI · Accepted Answer

We begin by restating the problem to ensure clarity: a 182-day T-Bill with face value $1,000,000 is selling for $991,250. We want the holding period yield (HPR) over the 182-day holding period.

First, calculate the total dollar return over the holding period. The T-Bill will pay its face value at maturity, so the return is 1,000,000 − 991,250 = 8,750 dollars.

Next, determine the holding period yield as the return divided by the initial price: HPR = (Face − Price) / Price = 8,750 / 991,250.

Compute the ratio: 8,750 ÷ 991,250 ≈ 0.008835, which is about 0.8835%. When rounded to two decimals, this is approximately 0.88%.

Now evaluate the given options:
- 0.66%: This is too low. If the HPR were only 0.66%, the dollar gain would be 0.0066 × 991,250 ≈ 6,542, which is smaller than the actual $8,750 gain. Therefore this option underestimates the yield.
- 0.88%: This aligns with the calculated HPR of roughly 0.8835%. It matches the exact yield when rounded appropriately, reflecting the correct proportion of gain relative to the price over 182 days.
- 0.77%: This is also lower than the calculated 0.8835%. It would imply a smaller dollar gain on the same price, so it does not fit the data.
- 0.55%: This is substantially too low, representing a significantly smaller return and inconsistent with the actual $8,750 gain over $991,250 invested.

In summary, the option that corresponds to the computed holding period yield of about 0.8835% (rounded to 0.88%) is the correct match for the given numbers. The other options underestimate the yield based on the actual gain relative to the investment price over 182 days.

What is the holding period yield for a 182 day $1 M T-Bill that is selling for $991,250?单项选择题

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