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!