A man has a total of $110,000 invested in three rental properties. One property earns 7.5% per year on its investment, the second earns 9%, and the third earns 10%. The three properties earn a total of $9600 per year.
What is the largest amount that could be invested at 7.5%?
A) $56,000
B) $110,000
C) $50,000
D) $54,000

Question

Quizplus · Accepted Answer

To maximize the amount invested at 7.5%, the remaining amounts should be invested at the higher rates to ensure the total income does not exceed $9600. Let x be the amount invested at 7.5%, y at 9%, and z at 10%. The total investment is $110,000, so x + y + z = $110,000. The total income from these investments is $9600, so 0.075x + 0.09y + 0.1z = $9600. To maximize x, minimize the amounts at higher interest rates, assuming they meet the total income requirement without exceeding it. If y and z are minimized while still achieving the $9600 total income, x can be maximized. Given the constraints, the largest amount that can be invested at 7.5% without the total income exceeding $9600 is $56,000.

A Man Has a Total of $110,000 Invested in Three