Problem

A one-year $\$ 9600$ treasury bill sold for $\$ 8311$. What was the simple annual discount rate?
The discount rate was $\%$.
(Type an integer or decimal rounded to two decimal places as needed.)

Answer

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Answer

Final Answer: The treasury bill had a simple annual discount rate of \(\boxed{13.43\%}\)

Steps

Step 1 :Given that the face value (F) is $9600, the purchase price (P) is $8311, and the time (T) is 1 year.

Step 2 :We can find the discount (D) by subtracting the purchase price from the face value: \(D = 9600 - 8311 = 1289\)

Step 3 :We then use the formula for simple discount, \(D = FRT\), to solve for the annual discount rate (R): \(R = \frac{D}{FT} = \frac{1289}{9600 \times 1} = 0.13427\)

Step 4 :The result R is the annual discount rate in decimal form. To convert it to a percentage, we need to multiply it by 100: \(R_{\%} = 0.13427 \times 100 = 13.427\%\)

Step 5 :Final Answer: The treasury bill had a simple annual discount rate of \(\boxed{13.43\%}\)

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