To solve these problems, we can use the formula for simple interest:

$I = P \times r \times t$

where:

• $I$ is the interest earned,
• $P$ is the principal amount (initial investment),
• $r$ is the annual interest rate (in decimal form),
• $t$ is the time in years.

Part (a)

1. Calculate the interest earned: $I = 10,000 - 9,710 = 290$

2. Determine the time in years: Since the T-bill matures in 6 months, we convert that to years: $t = \frac{6}{12} = 0.5 \text{ years}$

3. Plug in the values into the formula: $290 = 9,710 \times r \times 0.5$

4. Solve for $r$: $r = \frac{290}{9,710 \times 0.5} = \frac{290}{4,855} \approx 0.0598$

5. Convert to percentage: $r \approx 0.0598 \times 100 \approx 5.98\%$

Rounded to one decimal place: $\text{Annual interest rate} \approx 6.0\%$

Part (b)

1. Adjust for the bank fee: The effective principal paid after the fee is: $P' = 9,710 + 30 = 9,740$

2. Calculate the new interest earned (remains the same): $I = 10,000 - 9,740 = 260$

3. Use the same time and plug in the new principal: $260 = 9,740 \times r' \times 0.5$

4. Solve for $r'$: $r' = \frac{260}{9,740 \times 0.5} = \frac{260}{4,870} \approx 0.0534$

5. Convert to percentage: $r' \approx 0.0534 \times 100 \approx 5.34\%$

Rounded to one decimal place: $\text{Actual interest rate} \approx 5.3\%$

Summary

• (a) The annual simple interest rate is 6.0%.
• (b) The actual interest rate after the bank fee is 5.3%.

Do you want details or have any questions? Here are some related questions you might consider:

1. What are the advantages of investing in T-bills?
2. How does the interest calculation differ for compound interest?
3. What factors influence the interest rates of Treasury bills?
4. How do fees affect overall investment returns?
5. What other investment options might provide higher returns than T-bills?

Tip: Always consider fees when calculating the actual return on any investment.