e7 **Investment Decision Analysis**Investor Dan has $636,000 to invest in a Certificate of Deposit (CD) and a mutual fund. The CD yields 5.7% and the mutual fund yields an average of 8%. The mutual fund requires a minimum investment of $8,000, and Dan requires that at least 3 times as much money be invested in the CD as in the mutual fund. You must invest in order to maximize his return. How much should you invest in the CD? Enter 0 if no investment can be made satisfying the requirements.**Question:** $ ____________. Round to the nearest cent.### Solution Approach:To determine how much Dan should invest in the CD:Let $ x $ be the amount invested in the CD and $ y $ be the amount invested in the mutual fund.1. Given that the total investment is $636,000: \[ x + y = 636,000 \]2. He wants at least 3 times as much invested in the CD as in the mutual fund: \[ x \geq 3y \]3. The mutual fund requires a minimum investment of $8,000: \[ y \geq 8,000 \]By combining these constraints, solve for $ x $ and $ y $:- Substitute the minimum mutual fund investment: \[ y = 8,000 \]- Substitute $ y $ into $ x \geq 3y $: \[ x \geq 3(8,000) = 24,000 \]- Substitute $ y $ into the total investment equation: \[ x + 8,000 = 636,000 \] \[ x = 636,000 - 8,000 = 628,000 \]- Check that $ x $ meets the initial constraints: \[ 628,000 \geq 3(8,000) = 24,000 \]Thus, Dan should invest \$628,000 in the CD to maximize his return while meeting all the requirements.

Investor Dan has $636,000 to invest in a CD and a mutual fund. The CD yields 5.7% and the mutual fund yields an average of 8%. The mutual fund requires a minimum investment of $8,000, and Dan requires that at least 3 times as much money be invested in the CD as in the mutual fund. You must invest in order to maximize his return. How much should you invest in the CD? Enter O if no investment can be made satisfying the requirements. $ Round to the nearest cent.

Investor Dan has $636,000 to invest in a CD and a mutual fund. The CD yields 5.7% and the mutual fund yields an average of 8%. The mutual fund requires a minimum investment of $8,000, and Dan requires that at least 3 times as much money be invested in the CD as in the mutual fund. You must invest in order to maximize his return. How much should you invest in the CD? Enter O if no investment can be made satisfying the requirements. $ Round to the nearest cent.

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Question

**Investment Decision Analysis**

Investor Dan has $636,000 to invest in a Certificate of Deposit (CD) and a mutual fund. The CD yields 5.7% and the mutual fund yields an average of 8%. The mutual fund requires a minimum investment of $8,000, and Dan requires that at least 3 times as much money be invested in the CD as in the mutual fund. You must invest in order to maximize his return. How much should you invest in the CD? Enter 0 if no investment can be made satisfying the requirements.

**Question:**

$ ____________. Round to the nearest cent.

<Provided input box for student's answer>

### Solution Approach:

To determine how much Dan should invest in the CD:

Let $ x $ be the amount invested in the CD and $ y $ be the amount invested in the mutual fund.

1. Given that the total investment is $636,000:
\[
x + y = 636,000
\]

2. He wants at least 3 times as much invested in the CD as in the mutual fund:
\[
x \geq 3y
\]

3. The mutual fund requires a minimum investment of $8,000:
\[
y \geq 8,000
\]

By combining these constraints, solve for $ x $ and $ y $:

- Substitute the minimum mutual fund investment:
\[
y = 8,000
\]

- Substitute $ y $ into $ x \geq 3y $:
\[
x \geq 3(8,000) = 24,000
\]

- Substitute $ y $ into the total investment equation:
\[
x + 8,000 = 636,000
\]
\[
x = 636,000 - 8,000 = 628,000
\]

- Check that $ x $ meets the initial constraints:
\[
628,000 \geq 3(8,000) = 24,000
\]

Thus, Dan should invest \$628,000 in the CD to maximize his return while meeting all the requirements.

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