what is the effective interest rate of an 8% 13-week treasury bill? assume it is a $10,00 treasury bill, and round to the nearest hundredth percent

The rate i=8% is for 1 year (52 weeks).

There are n=4 terms in a year.
The value of the bill ($10) is not used in this problem.

The effect interest rate (EAR)
EAR=(1+i/n)^n - 1
=(1+0.08/4)^4 - 1
=1.08243 - 1
=0.08243
=8.24% (to hundredth %)

To calculate the effective interest rate of a treasury bill, you can use the formula:

Effective Interest Rate = (1 + (Discount / Price)) ^ (365 / Days) - 1

where:
- Discount is the difference between the face value and the price of the bill
- Price is the amount you paid for the bill
- Days is the number of days until the bill matures

In this case, the discount can be calculated as:
Discount = Face Value - Price
Discount = $10,000 - $10,000 * (8% / 100)
Discount = $10,000 - $800
Discount = $9,200

The days until the bill matures is 13 weeks, which is equal to 13 * 7 = 91 days.

Now, we can calculate the effective interest rate:
Effective Interest Rate = (1 + (Discount / Price)) ^ (365 / Days) - 1
Effective Interest Rate = (1 + ($9,200 / $10,000)) ^ (365 / 91) - 1
Effective Interest Rate = (1 + 0.92) ^ (365 / 91) - 1
Effective Interest Rate = (1.92) ^ (365 / 91) - 1
Effective Interest Rate ≈ (1.92) ^ 4 - 1
Effective Interest Rate ≈ 7.09 - 1
Effective Interest Rate ≈ 6.09%

Rounded to the nearest hundredth percent, the effective interest rate of an 8% 13-week treasury bill is approximately 6.09%.

To calculate the effective interest rate of a treasury bill, you need to consider the discount yield. The discount yield represents the difference between the original price of the treasury bill and its face value.

Here's how you can calculate the effective interest rate:

1. Determine the discount value: Multiply the face value of the treasury bill by the discount rate. In this case, the treasury bill has a face value of $10,000 and an 8% interest rate. So, the discount value is $10,000 multiplied by 0.08, which equals $800.

2. Calculate the purchase price: Subtract the discount value from the face value of the treasury bill to get the purchase price. In this case, subtract $800 from $10,000 to get a purchase price of $9,200.

3. Determine the number of periods: The question states that the treasury bill has a 13-week maturity period. To calculate the effective interest rate, divide the number of weeks by 52 weeks to get the decimal representation of the number of years. In this case, 13 weeks divided by 52 weeks equals 0.25 years.

4. Calculate the effective interest rate: Use the following formula to calculate the effective interest rate:

Effective Interest Rate = (Discount Value / Purchase Price) * (1 / Number of Periods)

Substituting the values:
Effective Interest Rate = ($800 / $9,200) * (1 / 0.25)
Effective Interest Rate ≈ 0.08695652173913043 * 4
Effective Interest Rate ≈ 0.34782608695652173

5. Round to the nearest hundredth percent: The effective interest rate calculated above is approximately 0.34782608695652173. When rounded to the nearest hundredth percent, it becomes 0.35%.

Therefore, the effective interest rate of an 8% 13-week treasury bill is approximately 0.35%.