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?

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.

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?

Find out how many years it will take for a $1,000 investment to grow to $1,500 at 2.5% simple interest. This step-by-step guide covers basic algebra and the simple interest formula. Suitable for students in Grades 6-8.

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