Solve.
-A $78,000 trust is to be invested in bonds paying 7%, CDs paying 5%, and mortgages paying 10%. The sum of the bond and CD investment must equal the mortgage investment. To earn an $6310 annual income from the
Investments, how much should the bank invest in bonds?
A) $23,000
B) $21,000
C) $39,000
D) $16,000

Question

Quizplus · Accepted Answer

The total investment is $78,000, and the annual income is $6,310. Let's denote the amount invested in bonds, CDs, and mortgages as B, C, and M, respectively. We have two conditions: B + C = M, and the total investment is B + C + M = $78,000. From the first condition, we can substitute M in the second equation to get B + C + (B + C) = $78,000, which simplifies to 2(B + C) = $78,000, so B + C = $39,000. Since B + C = M, M also equals $39,000. The annual income from the investments is given by 0.07B + 0.05C + 0.10M = $6,310. Substituting M = $39,000 into the income equation gives 0.07B + 0.05C + 0.10($39,000) = $6,310. Since B + C = $39,000, we can solve for B by rearranging the terms and using the total income equation. The correct allocation that satisfies these conditions with the given annual income is $23,000 in bonds.

Solve. -A $78,000 Trust Is to Be Invested in Bonds Paying