$10,000 is invested for 3 months at an annual simple interest rate of 7%.

a) You will earn $ in interest (round to the nearest cent).

b) The future value is (round to the nearest cent).

To solve this problem, we can use the formula for **simple interest**:

\[
I = P \times r \times t
\]

Where:
- $ I $ is the interest earned,
- $ P $ is the principal (initial investment),
- $ r $ is the annual interest rate (as a decimal),
- $ t $ is the time the money is invested for, in years.

### Part a) Calculating Interest Earned
Given:
- $ P = 10,000 $ dollars,
- $ r = 7\% = 0.07 $ (as a decimal),
- $ t = \frac{3}{12} = 0.25 $ years (since 3 months is 1/4 of a year).

Using the simple interest formula:
\[
I = 10,000 \times 0.07 \times 0.25
\]
\[
I = 175 \, \text{dollars}
\]

Thus, the interest earned is **$175.00**.

### Part b) Calculating the Future Value
The **future value** $ A $ is given by the formula:
\[
A = P + I
\]

Substituting the known values:
\[
A = 10,000 + 175 = 10,175
\]

Thus, the future value is **$10,175.00**.

### Final Answers:
a) You will earn **$175.00** in interest.  
b) The future value is **$10,175.00**.

Would you like more details or have any questions?

Here are some related questions to deepen understanding:
1. How does the simple interest formula differ from compound interest?
2. How would the future value change if the investment was for 6 months?
3. What would be the interest if the annual interest rate were 8% instead of 7%?
4. How does the time period affect the interest earned in simple interest?
5. How can we convert an annual interest rate to a monthly or quarterly rate?

**Tip**: For simple interest, increasing the time or the rate directly increases the interest in a linear fashion, unlike compound interest where the effect is exponential.

$10,000 is invested for 3 months at an annual simple interest rate of 7%. a) You will earn $ in interest (round to the nearest cent). b) The future value is (round to the nearest cent).

Learn how to calculate the simple interest earned and future value of a $10,000 investment at an annual interest rate of 7% over 3 months. Using key financial mathematics formulas, this step-by-step guide is perfect for students in Grades 6-8.

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