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Suppose you pay $9,400 for a $10,000 par Treasury bill maturing in 6 months. What is the effective annual rate of return for this investment?

A. 6.38%

B.12.77%

C. 13.17%

D. 14.25%

User DaveTurek
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Final answer:

The effective annual rate of return for the Treasury bill is 6.489%, which is obtained by annualizing the return earned over six months. The listed options do not include this calculated value, with the closest option being A. 6.38%.

Step-by-step explanation:

To calculate the effective annual rate of return for the Treasury bill, you need to consider the interest earned and the time period involved. When you purchase a Treasury bill at a discount, like paying $9,400 for a $10,000 par value (which you will receive on maturity), you will earn $600 ($10,000 - $9,400) over the six months. To find the annualized return, you can use the formula for the effective annual rate (EAR):

EAR = (1 + i/n)^n - 1,

where i is the interest rate per period and n is the number of periods per year. In this case:

i = $600 / $9,400 = 0.06383 (or 6.383%),

n = 2 (since the investment is for 6 months, there are two six-month periods in a year).

The calculation is as follows:

EAR = (1 + 0.06383/2)^2 - 1

EAR = (1 + 0.031915)^2 - 1

EAR = (1.031915)^2 - 1

EAR = 1.06489 - 1

EAR = 0.06489 or 6.489%

Therefore, the correct answer is not available in the listed options; the closest would be A. 6.38%, but that is slightly lower than the calculated effective annual rate of return of 6.489%. Remember that the EAR takes into account the effect of compounding, which is why the formula includes raising to the power of 'n'.

User Lizzett
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