What is the purchase price of a​ 50-day T-bill with a maturity value of 1451 ​$ that earns an annual interest rate of ​6.237%? ​(Assume a​ 360-day year.)

Answer 1

To calculate the purchase price of a 50-day T-bill, we need to use the formula:

Purchase price = Maturity value / (1 + (Interest rate * T/360))

Where:
Maturity value = $1451
Interest rate = 6.237% = 0.06237
T = Number of days until maturity = 50

Substituting the values into the formula, we have:

Purchase price = $1451 / (1 + (0.06237 * 50/360))

Calculating the numerator:
Purchase price = $1451 / (1 + 0.00868)

Calculating the denominator:
Purchase price = $1451 / 1.00868

Purchase price ≈ $1437.03

Therefore, the purchase price of a 50-day T-bill with a maturity value of $1451 and an annual interest rate of 6.237% is approximately $1437.03.