Suppose you are looking to buy a $10,000 face value 13-week T-bill. If you want to earn at least 4% annual interest, what is the most you should pay for the bill?
Round your answer to the nearest penny.
To find the maximum amount you should pay for a $10,000 face value 13-week T-bill, you need to determine the present value of the bill.
The first step is to determine the interest earned on the bill. A 13-week T-bill has a maturity of 13/52 = 0.25 years. Since you want to earn at least 4% annual interest, the interest earned over 0.25 years would be 0.25 * 4% = 1%.
Next, you need to calculate the present value of the bill by discounting the face value by the interest rate. Let's call the maximum amount you should pay P.
Using the present value formula: P = F / (1 + r)^n
Where:
P is the present value (what you are trying to find)
F is the face value of the T-bill ($10,000 in this case)
r is the interest rate (1% or 0.01 as a decimal)
n is the number of years to maturity (0.25 years)
Now, let's substitute the values into the formula: P = 10,000 / (1 + 0.01)^0.25
Calculating the expression in the parentheses: (1 + 0.01)^0.25 ≈ 1.0025
Now, plug in the values: P = 10,000 / 1.0025
Calculating P: P ≈ $9,975.12
Rounding to the nearest penny, the maximum amount you should pay for the T-bill is $9,975.12.
P = Po + Po*r*t = 10,000.
Po + Po*(0.04/52)*13 = 10,000.
Po + 0.01Po = 10,000.
1.01Po = 10,000.
Po = $9900.99