https://file.aiquickdraw.com/mathbot/file/17277844151405l4di41f.jpg

The problem in the image states:

- A couple invested $20,000 in two retirement accounts.
- One account has an annual simple interest rate of 5%, and the other has an interest rate of 4%.
- The combined interest earned from both investments after the first year is $940.
- The goal is to find out how much was invested in each account.

Let the amount invested at 5% be $ x $, and the amount invested at 4% be $ 20,000 - x $.

### Step-by-step solution:

1. The interest earned from the amount invested at 5% is:
   \[
   0.05 \times x = 0.05x
   \]

2. The interest earned from the amount invested at 4% is:
   \[
   0.04 \times (20,000 - x) = 0.04(20,000 - x)
   \]

3. The combined interest from both investments is given as $940. Therefore, we set up the equation:
   \[
   0.05x + 0.04(20,000 - x) = 940
   \]

4. Distribute the 0.04 on the second term:
   \[
   0.05x + 0.04 \times 20,000 - 0.04x = 940
   \]
   \[
   0.05x + 800 - 0.04x = 940
   \]

5. Combine like terms:
   \[
   (0.05x - 0.04x) + 800 = 940
   \]
   \[
   0.01x + 800 = 940
   \]

6. Subtract 800 from both sides:
   \[
   0.01x = 140
   \]

7. Divide by 0.01:
   \[
   x = \frac{140}{0.01} = 14,000
   \]

So, $14,000 was invested at 5%.

8. The amount invested at 4% is:
   \[
   20,000 - 14,000 = 6,000
   \]

### Final answer:
- \$14,000 was invested at 5%.
- \$6,000 was invested at 4%.

Would you like any more details or have any questions? 

Here are 5 related questions for further understanding:
1. What would happen if the combined interest was different, say $1000?
2. How does the formula for simple interest change if the interest rate is compounded annually?
3. What if one of the interest rates were negative or zero?
4. How can you calculate the interest for varying interest rates over multiple years?
5. What would be the interest earned if the $20,000 were split equally between both accounts?

**Tip:** When solving problems involving simple interest, it's essential to set up your equation carefully to represent the interest earned by each investment.

A couple invested $20,000 in two retirement accounts. One account has an annual simple interest rate of 5%, and the other has an interest rate of 4%. The combined interest earned from both investments after the first year is $940. Find the amount invested in each account.

Learn how to solve a problem where a couple invests $20,000 in two accounts at 5% and 4% interest, earning $940 in total interest. This step-by-step solution demonstrates how to use algebra to find the amount invested in each account. Suitable for Grades 9-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation