Question

A retiree has $100,000 to invest between two accounts: a stock fund that earns 7% interest each month and a bond fund that earns 3% interest each month. They want to earn at least $5000 total in interest each month but their financial advisor tells them they should invest as much of their money in the bond fund as they can because it is more stable. How much money should they invest in each account? Create linear cost models and solve.

Answer 1

To create linear cost models and solve the problem, the retiree should invest $66666.67 in the bond fund and $33333.33 in the stock fund.

To create linear cost models and solve the problem, we can let x represent the amount invested in the stock fund and let y represent the amount invested in the bond fund. Since the retiree wants to earn at least $5000 in interest each month, we can set up the following equations:

0.07x + 0.03y = 5000

x + y = 100000

From the second equation, we can solve for x:

x = 100000 - y

Substituting this into the first equation, we get:

0.07(100000 - y) + 0.03y = 5000

7000 - 0.07y + 0.03y = 5000

0.03y = 2000

y = 2000 / 0.03 = 66666.67

Since the retiree cannot invest a fraction of a dollar, they should invest $66666.67 in the bond fund. The remaining amount, $33333.33, should be invested in the stock fund.