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 determine how many years it will take for Emmanuel’s investment to grow to $1,500 with **simple interest**, we use the **simple interest formula**:

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

where:  
- $A$ is the future value (final amount)  
- $P$ is the principal (initial investment)  
- $r$ is the annual interest rate (in decimal form)  
- $t$ is the time in years

### Step 1: Substitute known values  
- $A = 1500$  
- $P = 1000$  
- $r = 2.5\% = 0.025$

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

### Step 2: Solve for $t$

1. Divide both sides by 1000:

   \[
   1.5 = 1 + 0.025t
   \]

2. Subtract 1 from both sides:

   \[
   0.5 = 0.025t
   \]

3. Divide both sides by 0.025:

   \[
   t = \frac{0.5}{0.025} = 20 \, \text{years}
   \]

### Final Answer  
It will take **20 years** for Emmanuel’s account to reach a balance of $1,500.

---

Would you like a more detailed explanation or have further questions?

Here are 5 related questions:  
1. What is the difference between simple and compound interest?  
2. How much would Emmanuel’s balance be after 10 years?  
3. If the interest rate increased to 5%, how long would it take to reach $1,500?  
4. How can you calculate the total interest earned in a simple interest problem?  
5. What happens if Emmanuel deposits more money into the account over time?

**Tip:** In simple interest, the interest earned each year is constant since it is only applied to the principal.

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?

Learn how to calculate the time required for an investment of $1,000 to grow to $1,500 with 2.5% simple interest. This detailed solution involves key financial math concepts and the simple interest formula, suitable for students in Grades 8-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation