Question

An investment firm recommends that a client invest in bonds rated​ AAA, A, and B. The average yield on AAA bonds is 5​%, on A bonds 6​%, and on B bonds 9​%. 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 ​$14,000​, and the investor wants an annual return of ​$870 on the three investments. The client should invest ​$ in AAA​ bonds, ​$ in A​ bonds, and ​$ in B bonds.

Answer 1

The average yield on AAA bonds = 5​%.

The average yield on A bonds = 6%

The average yield on B bonds = 9%

Invest twice as much in AAA bonds as in B bonds

the total investment =  ​$14,000​   Annual return required = ​$870

Let investment in AAA bonds = 2X

As, investment in B bonds = X

investment in A bonds = 14000 - investment in AAA bonds - investment in B bonds = 14000 - 2X -X = 14000 - 3X

Annual return required = ​5% * investment in AAA bonds + 6% * investment in A bonds + 9% * investment in B bonds

$870 = 0.05 * 2X + 0.06 * (14000 - 3X) + 0.09 * X

$870 = 0.1X + $840 - 0.18X + 0.09X

$870 - $840 = 0.1X + 0.09X - 0.18X

$30 = 0.01X

X = 30/0.01 = 3000

Required investment in AAA bonds = 2X = $6000

Required investment in A bonds = 14000 - 3X = 14000 - 3*200 = 14000-9000 = $5000

Required investment in B bonds = X = $3000