Emmanuel begins saving for college tuition. He invests $1,000 in an account that pays 2.5% simple interest.

After how many years will Emmanuel’s account have a balance of $1,500?
A.2.5
B.12.5
C.20 
D.25

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

\[
A = P(1 + rt)
\]

Where:
- $ A $ is the final amount ($1,500),
- $ P $ is the initial principal ($1,000),
- $ r $ is the interest rate (2.5% or 0.025),
- $ t $ is the time in years (what we need to find).

Now, we can substitute the known values:

\[
1500 = 1000(1 + 0.025t)
\]

First, divide both sides by 1000:

\[
1.5 = 1 + 0.025t
\]

Next, subtract 1 from both sides:

\[
0.5 = 0.025t
\]

Now, divide both sides by 0.025 to solve for $ t $:

\[
t = \frac{0.5}{0.025} = 20
\]

Thus, it will take Emmanuel **20 years** for his account to have a balance of $1,500.

The correct answer is:

**C. 20**

Would you like more details or have any questions?

Here are 5 related questions:
1. What is the difference between simple interest and compound interest?
2. How would the time change if the interest rate were increased to 5%?
3. How would you calculate the interest earned after 10 years instead?
4. What if Emmanuel wanted $2,000 instead of $1,500—how long would that take?
5. How does the principal amount affect the time it takes to reach a goal balance?

**Tip**: Simple interest grows at a constant rate, unlike compound interest, which grows at an increasing rate!

Emmanuel begins saving for college tuition. He invests $1,000 in an account that pays 2.5% simple interest. After how many years will Emmanuel’s account have a balance of $1,500? A. 2.5 B. 12.5 C. 20 D. 25

Learn how to calculate simple interest and determine the time required to reach a target savings balance. In this problem, Emmanuel invests $1,000 at a 2.5% interest rate, and we calculate how long it will take for his account to grow to $1,500. The solution includes step-by-step explanations for solving linear equations using the simple interest formula.

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