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This is a classic simple interest problem where you need to determine how much money was invested at each interest rate. Here's how we can solve it:

### Given:
- Total amount invested: \$14,000
- One account earns **4.5%** (4 1/2% = 4.5%) interest per year.
- The other account earns **5%** interest per year.
- Total interest earned after one year: **\$656**.

### Let:
- $ x $ = amount invested at 4.5%,
- $ 14,000 - x $ = amount invested at 5%.

### The simple interest formula is:
\[
\text{Interest} = \text{Principal} \times \text{Rate} \times \text{Time}
\]
where the time is in years, and for one year, it simplifies to:
\[
\text{Interest} = \text{Principal} \times \text{Rate}
\]

### Equation setup:
1. The interest from the account earning 4.5% is $ 0.045 \times x $.
2. The interest from the account earning 5% is $ 0.05 \times (14,000 - x) $.

The total interest from both accounts is \$656:
\[
0.045x + 0.05(14,000 - x) = 656
\]

Now, let's solve this equation to find $ x $.

I'll calculate this next.The amount invested at the 4.5% interest rate is **\$8,800**.

Since the total investment was \$14,000, the amount invested at the 5% interest rate is:
\[
14,000 - 8,800 = 5,200
\]

Thus, the amounts invested at each rate are:
- **\$8,800** at 4.5%
- **\$5,200** at 5%

Would you like more details on the steps, or do you have any questions?

Here are five related questions:
1. What is the formula for calculating compound interest?
2. How does simple interest differ from compound interest?
3. If the total interest earned was \$700 instead of \$656, how would that affect the investments?
4. How does the time period affect the total interest earned in simple interest?
5. What happens if both accounts earned the same interest rate?

**Tip:** Always double-check the rates when dealing with interest problems to avoid confusion between simple and compound interest.

An amount of $14,000 was invested in two accounts, one earning 4.5% per year and the other earning 5% per year. After one year, the total interest earned on these investments was $656. How much money (in dollars) was invested at each rate?

Learn how to solve an investment problem where $14,000 is split between two accounts, one earning 4.5% and the other 5%, to earn a total interest of $656. Includes step-by-step solutions using simple interest formulas. Suitable for high school students in Grades 9-12.

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