Math Problem Statement

You invested $11,000 and two accounts paying 4% and 6% annual interest, interest, respectively. If the total interest earned for the year was $620, how much was invested at each rate?

Solution

Let's solve the problem step by step.

Problem Breakdown:

  • You invested a total of $11,000 in two accounts.
  • One account earns 4% annual interest, and the other earns 6% annual interest.
  • The total interest earned from both accounts in one year is $620.

We need to determine how much was invested in each account.

Let:

  • xx be the amount invested in the 4% account.
  • yy be the amount invested in the 6% account.

We have two key equations:

  1. The total investment equation: x+y=11,000x + y = 11,000
  2. The total interest equation: 0.04x+0.06y=6200.04x + 0.06y = 620

Solve the system of equations:

  1. From the first equation, express yy in terms of xx: y=11,000xy = 11,000 - x

  2. Substitute yy in the second equation: 0.04x+0.06(11,000x)=6200.04x + 0.06(11,000 - x) = 620

  3. Expand and simplify: 0.04x+6600.06x=6200.04x + 660 - 0.06x = 620 0.02x+660=620-0.02x + 660 = 620

  4. Solve for xx: 0.02x=620660-0.02x = 620 - 660 0.02x=40-0.02x = -40 x=400.02=2,000x = \frac{-40}{-0.02} = 2,000

So, x=2,000x = 2,000.

  1. Find yy using the first equation: y=11,0002,000=9,000y = 11,000 - 2,000 = 9,000

Final Answer:

  • $2,000 was invested at 4% interest.
  • $9,000 was invested at 6% interest.

Would you like more details or have any questions?

Here are five related questions to explore further:

  1. How would the total interest change if the amount invested at 6% increased by $1,000?
  2. What would be the interest earned if all $11,000 were invested at 5%?
  3. How do you calculate the interest rate if the total interest and amounts invested are known?
  4. How does the duration of investment impact the total interest earned?
  5. What if the interest rates were compounded monthly instead of annually?

Tip: Always double-check your final equations to ensure accuracy in problem-solving, especially in investment-related questions.

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Math Problem Analysis

Mathematical Concepts

Systems of linear equations
Interest calculations

Formulas

Linear equations
Interest formula

Theorems

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Suitable Grade Level

Grades 9-12