An Australian company issued a 180-day bank-accepted bill domestically with a face value of $200000. The bill was discounted at a yield of 7.79% per annum, representing a price of $192600.96. After 21 days the discounter sells the bill in the short-term money market for $193778.75. The bill is not traded again in the market. The yield to the current holder at maturity is Answer Question 1[input]%

Question

An Australian company issued a  180-day bank-accepted bill domestically with a face value of $200000. The bill was discounted at a yield of 7.79% per annum, representing a price of $192600.96. After 21 days the discounter sells the bill in the short-term money market for $193778.75. The bill is not traded again in the market. The yield to the current holder at maturity is Answer Question 1[input]%

BlackTom AI · Accepted Answer

We start by identifying the key facts: the bill has a face value of 200,000 and was issued for 192,600.96 when the 7.79% per annum yield (discount yield) was applied for 180 days. After 21 days, there are 159 days remaining until maturity (180 − 21 = 159). The holder in possession sells the bill for 193,778.75, and at maturity the payoff will be 200,000.

We need to calculate the yield to maturity for the current holder based on the remaining time to maturity. The standard money market (bank-accepted bill) yield is typically expressed as a simple interest rate on a 365-day year (actual days to maturity used for the proportion).

Step 1: Compute the total gain from the current holder’s perspective from purchase price to maturity.
- Gain = Face value − Purchase price = 200,000 − 193,778.75 = 6,221.25.

Step 2: Compute the annualized yield using the 365-day year convention over the remaining 159 days.
- Period yield for the remaining term = Gain / Purchase price = 6,221.25 / 193,778.75 ≈ 0.032095 (3.2095%).
- Annualized yield = Period yield × (365 / 159) ≈ 0.032095 × 2.29434 ≈ 0.07356 (7.356%).

Step 3: Round to the requested precision.
- The calculated yield to maturity is approximately 7.36% when rounded to two decimal places.

Therefore, the yield to the current holder at maturity is about 7.36% per annum (using a 365-day year convention for the 159-day remaining period).

FINS5512-Financial Markets&Institutions - T2 2025

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