Chapter A.8, Problem 18AYU

To determine

To find: How should the money be reinvested?

Answer to Problem 18AYU

$15\%$ bonds, $\$38,500$; $7\%$ CD, $\$17,500$.

Explanation of Solution

Given:

After 2 years, Betsy finds that she will now require $\$7,000$ per year. Assuming that the remaining information is the same.

Calculation:

In Problem(19) we have,

$=0.15\left(\$31,250\right)+0.07\left(\$18,750\right)$

$=\$4,687.50+\$1,312.50$

$=\$6,000$

Assume she spent the interest for her subsistence:

Investment in $15\%$ bonds.

b:

$0.15b+0.07\left(\$50,000-b\right)=\$7,000$

$15b+7\left(\$50,000-b\right)=\$700,000$

$15b+\$350,000-7b=\$700,000$

$8b=\$350,000$

$b=\$43,750$

Investment in $7\%$ CD:

$=\$50,000-\$43,750$

$=\$6,250$

So, $15\%$ bonds, $\$43,750$; $7\%$ CD, $\$6,250$.

Proof (interest on 2 investments, $\$7,000$):

$=0.15\left(\$43,750\right)+0.07\left(\$6,250\right)$

$=\$6,562.50+\$437.50$

$=\$7,000$

Assume she didn’t spend interest but kept it for reinvestment:

Investment in $15\%$ bonds-b:

$15b+7\left(\$56,000-b\right)=\$700,000$

$15b+\$392,000-7b=\$700,000$

$8b=\$308,000$

$b=\$38,500$

Investment in $7\%$ CD:

$=\$56,000-\$38,500$

$=\$17,500$

So, $15\%$ bonds, $\$38,500$; $7\%$ CD, $\$17,500$.

Proof (interest on 2 investments, $\$7,000$):

$=0.15\left(\$38,500\right)+0.07\left(\$17,500\right)$

$=\$5,775+\$1,225$

$=\$7,000$