A $25,700, 91-day Province of Newfoundland Treasury bill was originally purchased at a price that would yield the investor a 5.438% rate of return if the T-bill is held until maturity. Thirty-four days later, the investor sold the T-bill through his broker for $25,575.

Question

A $25,700, 91-day Province of Newfoundland Treasury bill was originally purchased at a price that would yield the investor a 5.438% rate of return if the T-bill is held until maturity. Thirty-four days later, the investor sold the T-bill through his broker for $25,575.

a. What price did the original investor pay for the T-bill? (Do not round the intermediate calculations. Round your answer to the nearest cent.)

b. What rate of return did the first investor realize during his holding period? (Do not round the intermediate calculations. Round your answer to three decimal places.)

c. If the broker sells the t-bill to a second investor for $25,575, what rate of return will the second investor realize if he or she holds the t-bill until maturity? (Do not round the intermediate calculations. Round your answer to three decimal places.)

Answer 1

a. To find the price the original investor paid for the T-bill, we need to use the formula for the present value of a future cash flow. Let's break it down step by step:

1. Determine the future value (FV) of the T-bill when it matures. Given that the T-bill is worth $25,575 when sold, this is the FV.

2. Determine the time period (N) in years. The T-bill has a maturity period of 91 days, which is roughly 0.2486 years (91/365).

3. Determine the desired rate of return (R). The question states that the investor wants a rate of return of 5.438%.

Now, plug the values into the present value (PV) formula:

PV = FV / (1 + R)^N

PV = $25,575 / (1 + 0.05438)^0.2486

Using a calculator, evaluate the expression inside the parentheses first:

(1 + 0.05438)^0.2486 = 1.013802074

Now, divide the future value by this result:

PV = $25,575 / 1.013802074 = $25,205.88

Therefore, the original investor paid approximately $25,205.88 for the T-bill.

b. To calculate the rate of return the first investor realized during the holding period, we need to use the formula for the annualized rate of return. Again, step by step:

1. Determine the initial investment or purchase price (PV) of the T-bill. In this case, it is the price the original investor paid: $25,205.88.

2. Determine the final investment or selling price (FV) of the T-bill. In this case, it is the price at which the T-bill was sold: $25,575.

3. Determine the time period (N) in years. The investor held the T-bill for 34 days, which is roughly 0.0932 years (34/365).

Now, plug the values into the rate of return (R) formula:

R = (FV / PV)^(1 / N) - 1

R = ($25,575 / $25,205.88)^(1 / 0.0932) - 1

Using a calculator:

R = (1.016417161)^(1 / 0.0932) - 1

R = 0.058959084

Therefore, the first investor realized a rate of return of approximately 0.059 or 5.9% during the holding period.

c. To calculate the rate of return the second investor will realize if they hold the T-bill until maturity after buying it for $25,575, we can use the same formula as in part b.

1. Determine the initial investment or purchase price (PV) of the T-bill. In this case, it is the price the second investor paid: $25,575.

2. Determine the final investment or selling price (FV) of the T-bill. We already know it will be $25,575.

3. Determine the time period (N) in years. The question states that the T-bill has a maturity period of 91 days, which is 0.2486 years (91/365).

Now, plug the values into the rate of return (R) formula:

R = (FV / PV)^(1 / N) - 1

R = ($25,575 / $25,575)^(1 / 0.2486) - 1

Using a calculator:

R = 1^(1 / 0.2486) - 1

R = 0

Therefore, the second investor will realize a rate of return of 0% if they hold the T-bill until maturity.