A $74,000 trust is to be invested in bonds paying 8%, CDs paying 5%, and mortgages paying 9%. The bond and CD investment together must equal the mortgage investment. To earn a $5930 annual income from the
Investments, how much should the bank invest in bonds?

Question

Quizplus · Accepted Answer

The total investment is $74,000, and the annual income goal is $5,930. Let's denote the amount invested in bonds as B, in CDs as C, and in mortgages as M. We have two conditions: B + C = M, and the total investment is B + C + M = $74,000. The income from these investments is 0.08B + 0.05C + 0.09M = $5,930. Given B + C = M, we can substitute M with B + C in the total investment equation: B + C + (B + C) = $74,000, simplifying to 2B + 2C = $74,000, or B + C = $37,000. Using the income equation, we substitute M with B + C, getting 0.08B + 0.05C + 0.09(B + C) = $5,930. Since B + C = $37,000, we can replace C with $37,000 - B in the income equation, leading to a single variable equation in terms of B. Solving this equation directly for B (given the constraints and the need for a specific solution) without the specific algebraic steps here (due to the format constraint), we find that B = $25,000 meets the conditions for the investment strategy to achieve the desired annual income.

A $74,000 Trust Is to Be Invested in Bonds Paying