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A retired woman has $70,000 to invest but needs to make $6,000 a year from the interest to meet certain living expenses. One bond investment pays 15% annual interest. The rest of it she wants to put in a CD that pays 7%. Set up and solve the equation for how much the woman should invest in each option to sustain exactly a $6,000 annual return.

Respuesta :

Answer:

Retired woman needs to invest $13,750 into 15% bonds and 56,250 into 7% CD to meet exactly $6,000 annual return.

Please, note that this calculation is assuming only first year or linear returns as the answer would get more sophisticated if the bonds/CDs terms would include perpetuity terms, compound interest etc.

Step-by-step explanation:

Two equations to be linked:

(1) 0.15*x + 0.07*y = 6,000

(2) x + y = 70,000

Resolving the linkage:

(2) x = 70,000 - y

(1) 0.15 * (70,000 - y) + 0.07*y = 6,000

0.15*70,000 - 0.15*y + 0.07*y = 6,000

0.08*y = 10,500 - 6,000

0.08*y = 4,500

y = 56,250

(2) x = 13,750

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