What is the effective interest rate of an 8% 13-week Treasury bill? Assume it is a $10,000 Treasury bill, and round your answer to the nearest hundredth percent.
A. 8.20%
B. 9.00%
C. 8.17%
D. 8.16%
Answer: D??
Yes D!
Can you show the steps to figure this out?
Well, well, well, we're talking about Treasury bills here, fancy stuff! So, let me do some funny math for you. To calculate the effective interest rate, we need to consider the time it takes for the Treasury bill to mature. In this case, it's 13 weeks.
Now, we can multiply the interest rate by the number of periods in a year, which is 52 weeks. So, 8% times (52/13) = 32%. But wait, we're not done clowning around yet! We need to divide this by 4 because there are 4 quarters in a year.
Voilà! 32% divided by 4 gives us 8%. Therefore, the effective interest rate of an 8% 13-week Treasury bill is... D. 8.16%. Ta-da!
To calculate the effective interest rate of a Treasury bill, you need to use the formula for the discount yield, also known as the bank discount method.
The formula is:
Discount Yield = (Discount / Face Value) * (360 / Days until Maturity)
In this case, the discount is calculated by subtracting the present value from the face value:
Discount = Face Value - Present Value
To find the present value, you need to use the formula for continuous compounding:
Present Value = Face Value / (1 + r)^n
Where:
r = the annual interest rate
n = the number of periods
Let's calculate the present value first:
r = 8% (or 0.08)
n = 13 weeks (or 91 days) / 365 (since we need the annual rate)
Present Value = $10,000 / (1 + 0.08 * 91/365) = $9,630.07 (rounded to the nearest cent)
Next, we can calculate the discount:
Discount = $10,000 - $9,630.07 = $369.93
Finally, we can calculate the discount yield:
Discount Yield = ($369.93 / $10,000) * (360 / 91) = 0.036993 * 3.956 => 0.146045
To convert the discount yield to a percentage, we multiply by 100:
0.146045 * 100 ≈ 14.6045 ≈ 14.60%
Rounding the answer to the nearest hundredth percent, the effective interest rate of an 8% 13-week Treasury bill is 14.60%. Therefore, Option D (8.16%) is incorrect. The correct answer should be none of the given options.