Question

An investor has ​$60,000 to invest in a CD and a mutual fund. The CD yields 8​% and the mutual fund yields 7​%. The mutual fund requires a minimum investment of ​$8,000​, and the investor requires that at least twice as much should be invested in CDs as in the mutual fund. How much should be invested in CDs and how much in the mutual fund to maximize the​ return? What is the maximum​ return?

Answer 1

Explanation:

Let's start by defining some variables to represent the amount invested in the CD and the mutual fund. Let:

C = amount invested in the CD

M = amount invested in the mutual fund

From the problem statement, we know that:

C + M = 60,000 (the total investment amount is $60,000)

C >= 2M (twice as much should be invested in CDs as in the mutual fund)

M >= 8,000 (the mutual fund requires a minimum investment of $8,000)

We can use these constraints to write the objective function that we want to maximize, which is the total return on investment:

R = 0.08C + 0.07M

To solve this problem, we can use the following steps:

Substitute C = 2M into the first equation to get:

3M = 60,000

M = 20,000

Since M >= 8,000, we can invest the minimum required amount in the mutual fund and put the rest in the CD:

M = 8,000

C = 60,000 - M = 52,000

Calculate the total return on investment:

R = 0.08C + 0.07M = 0.08(52,000) + 0.07(8,000) = 4,960 + 560 = 5,520

Therefore, the investor should invest $52,000 in the CD and $8,000 in the mutual fund to maximize the return, and the maximum return is $5,520.