Investments Kelly has 20,000 dollar to invest. As her...

Investments Kelly has 20,000 dollar to invest. As her financial planner, you recommend that she diversify into three investments: Treasury bills that yield $5 \%$ simple interest, Treasury bonds that yield $7 \%$ simple interest, and corporate bonds that yield $10 \%$ simple interest. Kelly wishes to earn 1390 dollar per year in income. Also, Kelly wants her investment in Treasury bills to be 3000 dollar more than her investment in corporate bonds. How much money should Kelly place in each investment?

Key Concepts

Algebraic Modeling

Algebraic modeling is the process of translating a real-world situation into mathematical expressions and equations. This approach is used to set up relationships between unknown quantities and known parameters, allowing for the systematic solution of problems. It is fundamental in applying mathematical reasoning to financial planning and investment scenarios.

Simple Interest

Simple interest is a method for calculating the interest charge on a loan or investment based solely on the original principal amount. It is determined by multiplying the principal by the interest rate and time period, and does not compound. This concept is crucial in financial mathematics when comparing different investment options with fixed returns over time.

Systems of Linear Equations

A system of linear equations consists of multiple equations with multiple variables that are all linear in nature. Solving such systems involves finding the values for the unknowns that satisfy all the equations simultaneously, using methods such as substitution or elimination. This concept is particularly important in problems where multiple conditions or constraints must be met simultaneously.

Investment Diversification

Investment diversification is a strategy that involves spreading investments across different assets or instruments to reduce risk. By allocating funds among various investment options, an investor can potentially mitigate losses from any single underperforming asset. This concept is key in financial planning to balance risk and return according to specified financial goals.

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