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.

FA25-BL-BUS-F307-1134

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

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