To find how many years it will take for Emmanuel's account to grow to $1,500, we use the formula for simple interest:

$A = P(1 + rt)$

Where:

• $A$ is the final amount ($1,500),
• $P$ is the principal (initial investment of $1,000),
• $r$ is the annual interest rate (2.5% = 0.025),
• $t$ is the time in years.

We are solving for $t$.

1. Plug in the known values:

$1500 = 1000(1 + 0.025t)$

2. Simplify and solve for $t$:

$1500 = 1000(1 + 0.025t)$ $\frac{1500}{1000} = 1 + 0.025t$ $1.5 = 1 + 0.025t$ $1.5 - 1 = 0.025t$ $0.5 = 0.025t$ $t = \frac{0.5}{0.025}$ $t = 20$

So, it will take Emmanuel 20 years for his account to reach a balance of $1,500.

Would you like any further details or clarification on the steps?

Here are 5 related questions:

1. What is the formula for compound interest and how does it differ from simple interest?
2. How much interest will Emmanuel have earned after 10 years at the same rate?
3. If Emmanuel wanted to reach $2,000 instead of $1,500, how long would it take?
4. How would the time change if the interest rate were increased to 5%?
5. How does inflation affect the value of money in long-term investments like this one?

Tip: Simple interest grows linearly, so the total interest earned depends directly on both time and the principal amount.