Question

An investment firm recommends that a client invest in bonds rated AAA, A, and B. The average yield on AAA bonds is 4%, on A bonds 5%, and on B bonds 8%. The client wants to invest twice as much in AAA bonds as in B bonds. How much should be invested in each type of bond if the total investment is $29,000, and the investor wants an annual return of $1,510 on the three investments? The client should invest \$ in AA 1 bonds, $ in A bonds, and $ in B bonds.

Answer 1

The client should invest $10,000 in AAA bonds, $6,000 in A bonds, and $13,000 in B bonds.

Step-by-step explanation:

To find the amounts to invest in AAA, A, and B bonds, let's denote the investment in AAA bonds as x. According to the client's preference, the investment in B bonds should be twice that in AAA bonds, so the investment in B bonds is 2x. The investment in A bonds is not specified, so let's denote it as y.

The total investment is $29,000, so the equation is x + y + 2x = $29,000. Simplifying, we get 3x + y = $29,000.

Now, we need to consider the annual return. The annual return from AAA bonds is 4% of x, from A bonds is 5% of y, and from B bonds is 8% of 2x. The total annual return should be $1,510, so the equation is 0.04x + 0.05y + 0.08(2x) = $1,510. Simplifying, we get 0.04x + 0.05y + 0.16x = $1,510.

Now, we have a system of two equations:

1. 3x + y = $29,000

2. 0.20x + 0.05y = $1,510

Solving these equations simultaneously, we find x = $10,000, y = $6,000, and 2x = $20,000.

Therefore, the client should invest $10,000 in AAA bonds, $6,000 in A bonds, and $13,000 in B bonds to meet the total investment amount and achieve the desired annual return.