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

$A = P(1 + rt)$

Where:

• $A$ is the amount of money in the account after time $t$,
• $P$ is the initial principal (the starting amount),
• $r$ is the interest rate (as a decimal),
• $t$ is the time (in years).

Given:

• $A = 1500$ (the final balance),
• $P = 1000$ (the initial investment),
• $r = 2.5\% = 0.025$.

We need to find $t$, the number of years it will take for Emmanuel's account to reach $1,500.

Step 1: Substitute the known values into the formula

$1500 = 1000(1 + 0.025 \times t)$

Step 2: Simplify the equation

$1500 = 1000(1 + 0.025t)$

Step 3: Divide both sides by 1000

$1.5 = 1 + 0.025t$

Step 4: Subtract 1 from both sides

$0.5 = 0.025t$

Step 5: Solve for $t$ by dividing both sides by 0.025

$t = \frac{0.5}{0.025} = 20$

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

Would you like further details or have any questions?

Here are 5 related questions:

1. How much interest will Emmanuel have earned after 20 years?
2. What would be the balance after 10 years in the same account?
3. What if Emmanuel started with $2,000? How long would it take to reach $1,500?
4. How would the time change if the interest rate were 3% instead of 2.5%?
5. What if the interest were compounded annually instead of simple interest?

Tip: In simple interest problems, the interest amount grows linearly with time, unlike compound interest, where the growth is exponential.