Q:6 You pay $$ \$ 9850 $$ for a 91 -day T-bill. It is worth $$ \$ 10,000 $$ at maturity. What is its annualized yield?

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$$
\textbf{Step 1: Compute the discount or gain at maturity.}
$$

You paid $$ P = \$9850 $$ and will receive $$ F = \$10,\!000 $$ at maturity. The gain is:
$$
\text{Gain} = F - P = 10,\!000 - 9850 = 150.
$$

$$
\textbf{Step 2: Compute the rate of return over the 91-day period.}
$$

The simple rate of return over 91 days is:
$$
r_{91} = \frac{\text{Gain}}{P} = \frac{150}{9850}.
$$

$$
\textbf{Step 3: Convert the 91-day rate to an annualized yield.}
$$

Assuming a 365-day year, the annualized yield $$ r_{\text{annual}} $$ is:
$$
r_{\text{annual}} = r_{91} \times \frac{365}{91} = \frac{150}{9850} \times \frac{365}{91}.
$$

$$
\textbf{Step 4: Simplify and compute.}
$$

First, simplify $$\frac{150}{9850}$$:
$$
\frac{150}{9850} = \frac{3}{197} \quad \text{(dividing numerator and denominator by 50)}.
$$

Now substitute back:
$$
r_{\text{annual}} = \frac{3}{197} \times \frac{365}{91}.
$$

Multiplying the fractions:
$$
r_{\text{annual}} = \frac{3 \times 365}{197 \times 91}.
$$

$$
\textbf{Step 5: Compute numerical value.}
$$

Calculate the denominator and numerator:
$$
3 \times 365 = 1095,
$$
$$
197 \times 91 = 17927.
$$
Thus,
$$
r_{\text{annual}} = \frac{1095}{17927} \approx 0.06106.
$$

Expressed as a percentage:
$$
0.06106 \times 100\% \approx 6.11\%.
$$

$$
\boxed{6.11\%}
$$
The annualized yield is approximately 6.11%.

Q:6 You pay \( \$ 9850 \) for a 91 -day T-bill. It is worth \( \$ 10,000 \) at maturity. What is its annualized yield?

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