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.)
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.
To calculate the purchase price of a 50-day T-bill, we need to use the formula:
Purchase Price = Maturity Value / (1 + (Interest Rate * Days / 360))
Where:
- Maturity Value is $1451
- Interest Rate is 6.237%
- Days is 50
Let's calculate the purchase price step by step:
Step 1: Convert the interest rate to a decimal:
Interest Rate = 6.237 / 100 = 0.06237
Step 2: Calculate the fraction of the year that the T-bill is held for:
Fraction of Year = Days / 360 = 50 / 360 = 0.13889
Step 3: Calculate the purchase price:
Purchase Price = 1451 / (1 + (0.06237 * 0.13889))
Purchase Price = 1451 / (1 + 0.0086336)
Purchase Price = 1451 / 1.0086336
Purchase Price = $1437.80 (rounded to two decimal places)
Therefore, the purchase price of the 50-day T-bill is $1437.80.
To calculate the purchase price of a T-bill, we need to use the formula:
Purchase Price = Maturity Value / (1 + (Annual Interest Rate * Days to Maturity / 360))
In this case, the Maturity Value is given as $1451, the Annual Interest Rate is 6.237%, and the Days to Maturity is 50.
To calculate the purchase price using the formula:
Purchase Price = 1451 / (1 + (0.06237 * 50 / 360))
Firstly, let's calculate the value inside the parenthesis:
Value inside the parenthesis = 0.06237 * 50 / 360 = 0.008658333
Now, let's add 1 to the value inside the parenthesis:
1 + 0.008658333 = 1.008658333
Finally, let's divide the Maturity Value by the result:
Purchase Price = 1451 / 1.008658333 = $1439.7440 (rounded to four decimal places)
Therefore, the purchase price of the 50-day T-bill with a maturity value of $1451 and an annual interest rate of 6.237% is approximately $1439.7440.