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:
- be the amount invested in the 4% account.
- be the amount invested in the 6% account.
We have two key equations:
- The total investment equation:
- The total interest equation:
Solve the system of equations:
-
From the first equation, express in terms of :
-
Substitute in the second equation:
-
Expand and simplify:
-
Solve for :
So, .
- Find using the first equation:
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:
- How would the total interest change if the amount invested at 6% increased by $1,000?
- What would be the interest earned if all $11,000 were invested at 5%?
- How do you calculate the interest rate if the total interest and amounts invested are known?
- How does the duration of investment impact the total interest earned?
- 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
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