Suppose you are looking to buy a $10,000 face value 13-week T-bill. If you want to earn at least 3% annual interest, what is the most you should pay for the bill?
Round your answer to the nearest penny.
9,925.56
To determine the maximum amount you should pay for the T-bill, you need to calculate the discounted price considering the desired annual interest rate of 3%. Here is how you can calculate it:
1. First, convert the 3% annual interest rate into a weekly interest rate. Since there are 52 weeks in a year, divide 3% by 52 to get the weekly interest rate.
Weekly interest rate = 3% / 52 = 0.0577%
2. Next, calculate the interest amount you would earn over the 13-week period by multiplying the face value of the T-bill by the weekly interest rate and the number of weeks.
Interest amount = $10,000 * 0.0577% * 13
3. Subtract the interest amount from the face value to determine the maximum amount you should pay for the T-bill.
Max price = $10,000 - Interest amount
Now, let's calculate the values to find the maximum amount you should pay for the T-bill:
Interest amount = $10,000 * 0.0577% * 13
Interest amount = $75.01
Max price = $10,000 - $75.01
Max price = $9924.99