Chapter 11.2, Problem 86AYU

To determine

To find: A young couple has $\$25,000$ to invest. As their financial consultant, you recommend that they invest some money in Treasury bills that yield $7\%$, some money in corporate bonds that yield $9\%$, and some money in junk bonds that yield $11\%$. Prepare a table showing the various ways that this couple can achieve the following goals:

a. $\$1500$ per year in income

b. $\$2000$ per year in income

c. $\$2500$ per year in income

d. What advice would you give this couple regarding the income that they require and the choices available?

Answer to Problem 86AYU

a. They can exceed $\$1500$ per year with all $\$25,000$ in treasury bills.

b. $25,000 - 12,500 = 12,500$ to corporate bonds.

c. $25,000 - 12,500 = 12,500$ to corporate bonds.

d. The couple income should $\$ 2000$ and they can choose treasury bills.

Explanation of Solution

Given:

A young couple has $\$25,000$ to invest. As their financial consultant, you recommend that they invest some money in Treasury bills that yield $7\%$, some money in corporate bonds that yield $9\%$, and some money in junk bonds that yield $11\%$.

Calculation:

Start by determining how much income would result with all $\$25,000$ in each of the investments, one at a time.

Treasury Bills: $\$25,000 * 7\% = \$1750$

Corporate Bonds: $\$25,000 * 9\% = \$2250$

Junk Bonds: $\$25,000 * 11\% = \$2750$

a. Therefore, they can exceed $\$1500$ per year with all $\$25,000$ in treasury bills.

b. To earn $\$2000$ per year ,let’s try to see how much we need in treasury bills and how much in corporate bonds, assuming we don’t need the more risky junk bonds.

Let x be the amount into treasury bills .The amount put into corporate bonds ,then would be $\$25,000 - x$. We calculate the amounts like this:

$\text{Total interest} = x * 7\% + \left(25,000 - x\right) * 9\%$

Since $7\%$ is $0.07$ and $9\%$ is $0.09$.

Total interest desired is $\$2000$.

$2,000 = x * 0.07 + \left(25,000 - x\right) * 0.09$

$2000-25,000 * 0.09 = 0.07 x - 0.09x$

$250 = 0.02x$

$x = \$12,500$

$25,000 - x$ is amount to corporate bonds

$25,000 - 12,500 = 12,500$ to corporate bonds.

c. To earn $\$2500$ per year ,let’s try to see how much we need in treasury bills and how much in corporate bonds, assuming we don’t need the more risky junk bonds.

Let $x$ be the amount into treasury bills .The amount put into corporate bonds,then would be $\$25,000 - x$. We calculate the amounts like this:

$\text{Total interest} = x * 7\% + \left(25,000 - x\right) * 9\%$

Since $7\%$ is $0.07$ and $9\%$ is $0.09$.

Total interest desired is $\$2500$.

$2,500 = x * 0.07 + \left(25,000 - x\right) * 0.09$

$2500 - 25,000 * 0.09 = 0.07x - 0.09x$

$250 = 0.02x$

$x = \$12,500$

$25,000 - x$ is amount to corporate bonds

$25,000 - 12,500 = 12,500$ to corporate bonds.

d. The couple income should $\$ 2000$ and they can choose treasury bills.