A 4-month Bank of Canada Treasury Bill with a face value of $1,000 currently trades in the market with a YTM of 3%.

Calculate the bill’s market price today.

Round your final answer to the nearest cent. Enter two decimals, without punctuation e.g. enter 2500.35 for $2,500.3531

Question

A 4-month Bank of Canada Treasury Bill with a face value of $1,000 currently trades in the market with a YTM of 3%.

Calculate the bill’s market price today.

Round your final answer to the nearest cent. Enter two decimals, without punctuation e.g. enter 2500.35 for $2,500.3531

BlackTom AI · Accepted Answer

We’re pricing a 4-month Bank of Canada Treasury Bill given its annualized yield of 3%.

First, convert the time to a year fraction: 4 months is 4/12 = 0.3333 years, but for simple interest pricing we use the proportion of the year directly in the discount formula, which effectively yields a 1% increase in the denominator for 3% annual yield over 4 months (0.03 × 4/12 = 0.01).

Next, apply the standard T-bill pricing formula using simple interest: Price = Face Value / (1 + YTM × (days/365 or 12)). Here we use the 12-month convention consistent with the problem’s 4 months out of a year, giving Price = 1000 / (1 + 0.03 × (4/12)). This simplifies to Price = 1000 / (1 + 0.01) = 1000 / 1.01.

Compute the division: 1000 ÷ 1.01 ≈ 990.0990099...

Finally, round to the nearest cent as requested: 990.0990 rounds to 990.10.

In summary, the price you’d observe today, given a 3% annual yield and a 4-month maturity, is approximately $990.10.

Note: If a different day-count convention (e.g., 360-day year) were specified, the slight rounding could change, but with the 4/12 year fraction used here, the result aligns with common classroom conventions.

A 4-month Bank of Canada Treasury Bill with a face value of $1,000 currently trades in the market with a YTM of 3%. Calculate the bill’s market price today. Round your final answer to the nearest cent. Enter two decimals, without punctuation e.g. enter 2500.35 for $2,500.3531数值题

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