1Cademy - Solving an Investment Fund Interest Application Using a System of Equations

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Solving an Investment Fund Interest Application Using a System of Equations

Apply the seven-step problem-solving strategy and a mixture table to solve an interest application involving two investments. Problem: Adnan has $\$40{,}000$ to invest and hopes to earn $7.1\%$ interest per year. He will put some of the money into a stock fund that earns $8\%$ per year and the rest into bonds that earns $3\%$ per year. How much money should he put into each fund? 1. Read the problem. A chart will help organize the information. 2. Identify what to find: the amount to invest in each fund. 3. Name the unknowns. Let $s$ = the amount invested in stocks, and $b$ = the amount invested in bonds. Multiply Principal $\cdot$ Rate $\cdot$ Time ( $t=1$ ) to get the Interest. Organize into a table: / Fund / Principal ($) / Rate / Interest ($) / /---/---/---/---/ / Stocks / $s$ / $0.08$ / $0.08s$ / / Bonds / $b$ / $0.03$ / $0.03b$ / / Total / $40{,}000$ / $0.071$ / $0.071(40{,}000)$ / 4. Translate into a system of equations from the Principal and Interest columns: $\left\{\begin{array}{l} s + b = 40{,}000 \ 0.08s + 0.03b = 0.071(40{,}000) \end{array} ight.$ 5. Solve the system by elimination. Multiply the top equation by $-0.03$ : $-0.03s - 0.03b = -1{,}200$ $0.08s + 0.03b = 2{,}840$ Add the equations: $0.05s = 1{,}640$ $s = 32{,}800$ Substitute $s = 32{,}800$ into the first equation: $32{,}800 + b = 40{,}000$ $b = 7{,}200$ 6. Check the answer. $32{,}800 + 7{,}200 = 40{,}000$ $\checkmark$ $0.08(32{,}800) + 0.03(7{,}200) = 2{,}624 + 216 = 2{,}840$ $0.071(40{,}000) = 2{,}840$ $\checkmark$ 7. Answer the question. Adnan should invest $\$32{,}800$ in stock and $\$7{,}200$ in bonds.

Updated 2026-05-26

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OpenStax Intermediate Algebra

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