You invested $20,000 in two accounts paying 1.45% and 1.59% annual interest. If the total interest earned for the year was $307.50, how much was invested at each rate?
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1
Let x be the amount invested at 1.45% interest rate.
Then, the amount invested at 1.59% interest rate is 20000 - x.
The interest from the first account is 0.0145x.
The interest from the second account is 0.0159(20000 - x).
Set up the equation: 0.0145x + 0.0159(20000 - x) = 307.50 and solve for x.
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Systems of Equations
A system of equations consists of two or more equations with the same variables. In this problem, we can set up two equations to represent the total investment and the total interest earned. Solving this system will help us find the amounts invested at each interest rate.
Interest calculation involves determining the amount earned on an investment over a period of time, typically expressed as a percentage of the principal. In this scenario, the interest earned from each account can be calculated using the formula: Interest = Principal × Rate. This is essential for setting up the equations.
Variable representation is the practice of using symbols to denote unknown quantities in mathematical problems. In this case, we can let 'x' represent the amount invested at 1.45% and 'y' represent the amount at 1.59%. This allows us to create equations that can be solved to find the values of 'x' and 'y'.