An investor purchases a T-bill with a face value (maturity value) of $1,000 for $986. If the term of the T-bill is 8 months, what is the annual simple interest rate (in percent)? Round to the nearest tenth of a percent.

To find the annual simple interest rate, we use the formula for simple interest:

\[
I = \frac{P \cdot r \cdot t}{100}
\]

Where:
- $ I $ is the interest earned (in this case, the difference between the face value and the purchase price),
- $ P $ is the principal or the purchase price of the T-bill,
- $ r $ is the annual simple interest rate (what we're solving for),
- $ t $ is the time the investment is held in years.

### Step 1: Calculate the Interest Earned

The interest earned on the T-bill is the difference between the face value and the purchase price:

\[
I = 1000 - 986 = 14 \text{ dollars}
\]

### Step 2: Convert the Term to Years

Since the term of the T-bill is 8 months, we convert this to years:

\[
t = \frac{8}{12} = \frac{2}{3} \text{ years}
\]

### Step 3: Use the Simple Interest Formula

Rearranging the simple interest formula to solve for the interest rate $ r $:

\[
r = \frac{I \cdot 100}{P \cdot t}
\]

Substitute the values:

\[
r = \frac{14 \cdot 100}{986 \cdot \frac{2}{3}} = \frac{1400}{986 \cdot \frac{2}{3}} = \frac{1400 \cdot 3}{986 \cdot 2} = \frac{4200}{1972}
\]

### Step 4: Calculate $ r $

\[
r \approx 2.13 \text{ percent}
\]

Thus, the annual simple interest rate is approximately **2.1%**.

---

Would you like further details on this or have any questions? Here are five related questions you might find interesting:

1. How would the rate change if the purchase price was lower?
2. How does simple interest differ from compound interest for T-bills?
3. What is the difference between Treasury bills and Treasury bonds?
4. How would you calculate the interest rate if the term was in days instead of months?
5. What factors affect the price of T-bills on the secondary market?

**Tip**: Always check whether the interest rate is quoted on a simple or compound basis when evaluating investment returns!

Learn how to calculate the annual simple interest rate for a T-bill purchased at $986 with a face value of $1,000 and an 8-month term. This problem involves the simple interest formula and converting time from months to years. Suitable for Grades 10-12 students.

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