Question

Suppose that you received an unexpected inheritance of $36,000. You have decided to invest the money by placing some of the money in stocks that pay 6.46% and the rest in bonds that pay 8%. How much should you place in each investment in order to earn 7%, or $2520 annually?

A) $14,400 in stocks and $21,600 in bonds
B) $21,600 in stocks and $14,400 in bonds
C) $18,000 in stocks and $18,000 in bonds
D) $12,000 in stocks and $24,000 in bonds

Answer 1

To find out how much should be placed in each investment to earn a 7% return on a $36,000 inheritance, set up and solve a system of equations. The correct distribution is $14,400 in stocks (6.46% return) and $21,600 in bonds (8% return) to achieve the desired $2520 annual income, matching option A.

Step-by-step explanation:

To determine how much to place in each investment to earn 7% on a $36,000 inheritance, we need to set up a system of equations representing the investments in stocks and bonds. Let x represent the amount invested in stocks and y represent the amount invested in bonds. We know that the total amount invested is $36,000, so x + y = 36,000. We also want to earn 7% annually, which is $2520, so the second equation is 0.0646x + 0.08y = 2520.

Subtracting the first equation from the second, we can calculate the amounts for each investment. After solving the system of equations, we find that $14,400 should be placed in stocks and $21,600 in bonds, which corresponds to option A.