Precalculus Enhanced with Graphing Utilities
Precalculus Enhanced with Graphing Utilities
6th Edition
ISBN: 9780321795465
Author: Michael Sullivan, Michael III Sullivan
Publisher: PEARSON
Question
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Chapter A.8, Problem 18AYU
To determine

To find: How should the money be reinvested?

Expert Solution & Answer
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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( $31,250 ) + 0.07( $18,750 )

= $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( $50,000  b ) = $7,000

15b + 7( $50,000  b ) = $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( $43,750 ) + 0.07( $6,250 )

= $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( $56,000  b ) = $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( $38,500 ) + 0.07( $17,500 )

= $5,775 + $1,225

= $7,000

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