If you purchase $$ \$ 26,000 $$ in U.S. Treasury Bills with a discount rate of $$ 4.9 \% $$ for a period of 26 weeks, what is the effective interest rate (as a \%)? Round to the nearest hundredth percent.

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To find the effective interest rate for the U.S. Treasury Bills, we can follow these steps:

1. **Calculate the discount amount**: The discount amount can be calculated using the formula:
   $$
   \text{Discount} = \text{Face Value} \times \text{Discount Rate} \times \frac{\text{Time}}{52}
   $$
   where the time is in weeks.

2. **Calculate the purchase price**: The purchase price is given by:
   $$
   \text{Purchase Price} = \text{Face Value} - \text{Discount}
   $$

3. **Calculate the effective interest**: The effective interest can be calculated using the formula:
   $$
   \text{Effective Interest} = \frac{\text{Discount}}{\text{Purchase Price}} \times \frac{52}{\text{Time}} \times 100
   $$

Now, let's perform the calculations step by step.

### Step 1: Calculate the Discount Amount
- Face Value = $$ 26000 $$
- Discount Rate = $$ 0.049 $$
- Time = $$ 26 $$ weeks

Calculating the discount:
$$
\text{Discount} = 26000 \times 0.049 \times \frac{26}{52}
$$

### Step 2: Calculate the Purchase Price
$$
\text{Purchase Price} = 26000 - \text{Discount}
$$

### Step 3: Calculate the Effective Interest Rate
$$
\text{Effective Interest} = \frac{\text{Discount}}{\text{Purchase Price}} \times \frac{52}{26} \times 100
$$

Now, let's perform these calculations.
Calculate the value by following steps:
- step0: Calculate:
  $$26000\times 0.049\left(\frac{26}{52}\right)$$
- step1: Reduce the fraction:
  $$26000\times 0.049\times \frac{1}{2}$$
- step2: Multiply the terms:
  $$1274\times \frac{1}{2}$$
- step3: Reduce the numbers:
  $$637\times 1$$
- step4: Simplify:
  $$637$$
Calculate or simplify the expression $$ 26000 * 0.049 * (26 / 52) $$.
Calculate the value by following steps:
- step0: Calculate:
  $$26000\times 0.049\left(\frac{26}{52}\right)$$
- step1: Reduce the fraction:
  $$26000\times 0.049\times \frac{1}{2}$$
- step2: Multiply the terms:
  $$1274\times \frac{1}{2}$$
- step3: Reduce the numbers:
  $$637\times 1$$
- step4: Simplify:
  $$637$$
Calculate or simplify the expression $$ 26000 - 637 $$.
Calculate the value by following steps:
- step0: Calculate:
  $$26000-637$$
- step1: Subtract the numbers:
  $$25363$$
Calculate or simplify the expression $$ (637 / 25363) * (52 / 26) * 100 $$.
Calculate the value by following steps:
- step0: Calculate:
  $$\left(\frac{637}{25363}\right)\left(\frac{52}{26}\right)\times 100$$
- step1: Reduce the fraction:
  $$\frac{49}{1951}\left(\frac{52}{26}\right)\times 100$$
- step2: Divide the terms:
  $$\frac{49}{1951}\times 2\times 100$$
- step3: Multiply the terms:
  $$\frac{98}{1951}\times 100$$
- step4: Multiply:
  $$\frac{98\times 100}{1951}$$
- step5: Multiply:
  $$\frac{9800}{1951}$$
Let's summarize the calculations step by step:

1. **Calculate the Discount Amount**:
   $$
   \text{Discount} = 26000 \times 0.049 \times \frac{26}{52} = 637
   $$

2. **Calculate the Purchase Price**:
   $$
   \text{Purchase Price} = 26000 - 637 = 25363
   $$

3. **Calculate the Effective Interest Rate**:
   $$
   \text{Effective Interest} = \frac{637}{25363} \times \frac{52}{26} \times 100 \approx 5.02\%
   $$

Thus, the effective interest rate, rounded to the nearest hundredth percent, is approximately **5.02%**.
The effective interest rate is approximately 5.02%.

If you purchase \( \$ 26,000 \) in U.S. Treasury Bills with a discount rate of \( 4.9 \% \) for a period of 26 weeks, what is the effective interest rate (as a \%)? Round to the nearest hundredth percent.

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