Assume the $10,000 Treasury bill, 4% for 13 weeks. Calculate the effective rate of interest.(Use calendar year. Round your answer to 2 decimal places. Omit the "%" sign in your response.)
To calculate the effective rate of interest on a Treasury bill, you need to consider the discount rate applied to the bill and the number of compounding periods in a year.
In this case, we have a $10,000 Treasury bill with a 4% discount rate for 13 weeks. First, let's determine the number of compounding periods in a year. Since there are 52 weeks in a year, we divide the given 13 weeks by 52.
Number of compounding periods (n) = 13 weeks รท 52 weeks = 0.25
Next, we calculate the effective rate of interest using the formula:
Effective Rate of Interest = (1 - Discount Rate) ^ (1/n) - 1
Plugging in the values:
Effective Rate of Interest = (1 - 0.04) ^ (1/0.25) - 1
Calculating this expression will give us the effective rate of interest. Let me calculate it for you.
To calculate the effective rate of interest, we need to use the formula:
Effective Rate = (1 + Nominal Rate)^n - 1
Where the Nominal Rate is the quoted rate and n is the number of compounding periods in a year.
In this case, the Nominal Rate is 4% or 0.04, and there are 13 weeks in a quarter. Since we need to calculate the effective rate for a calendar year, we assume there are 52 weeks in a year.
Let's plug in the values into the formula:
Effective Rate = (1 + 0.04)^(52/13) - 1
= (1.04)^(4) - 1
= 1.169858 - 1
= 0.169858
Rounding the answer to 2 decimal places, the effective rate of interest on the $10,000 Treasury bill is approximately 16.99%.