Question

A person has ​$4000to invest. Part of the money is to be placed in a certificate of deposit paying ​%, per year. The rest is to be placed in corporate bonds paying ​%, per year. If he wishes to obtain an overall return of ​% per​ year, how much should be placed in each​ investment?

Answer 1

Answer:

Investment amount = $2666.67

Step by step solved:

To determine how much should be invested in each option to achieve the desired overall return, we can use the following formula:

Total Investment = Amount Invested in CD + Amount Invested in Bonds

Total Return = (Amount Invested in CD x CD Rate) + (Amount Invested in Bonds x Bond Rate)

We can plug in the given values and use algebra to solve for the unknowns:

Let x be the amount invested in the CD and y be the amount invested in the bonds.

x + y = 4000 (total investment is $4000)

0.05x + 0.08y = 0.06(4000) (desired overall return is 6%)

Simplifying the second equation:

0.05x + 0.08y = 240

Multiplying the first equation by 0.05 and subtracting from the second equation:

0.05x + 0.08y - 0.05x - 0.05y = 240 - 0.05(4000)

0.03y = 40

y = 40 / 0.03 = 1333.33

Substituting y back into the first equation:

x + 1333.33 = 4000

x = 2666.67

Therefore, $2666.67 should be invested in the certificate of deposit and $1333.33 should be invested in corporate bonds to achieve the desired overall return of 6% per year.

Answer 2

Let x = amount invested in certificate of deposit (in dollars)

Let y = amount invested in corporate bonds (in dollars)

Total amount invested = $100: x + y = 100

CD pays 2% per year, corporate bonds pay 4% per year, total return is 3% per year

Total return on investments = 3% of $100 = $3: 0.02x + 0.04y = 3

Simplifying the equations:

x + y = 100

2x + 4y = 300

Solving for x:

x + y = 100

x = 50

Therefore, the person should invest $50 in the certificate of deposit and $50 in corporate bonds to obtain an overall return of 3% per year.

Step-by-step explanation: