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A retired couple has 190,000 to invest to obtain annual income. They want some of it invested in safe certificates of deposit yielding 7%. The rest they want to invest in AA bonds yielding 10% per year. How much should they invest in each to realize exactly $17,200 per year ?

 Oct 21, 2015

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 #1
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If "f" denotes the fraction of save bonds,

 

Then: 17.2 = 0.07 * (f*190) + 0.1 * (1-f) * 190

 

So f = (0.1 - 17.2 / 190) / 0.03

 

Therefore: about 31.5% of save bounds and 68.5% of the other bond.

 Oct 21, 2015
 #2
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x is invested in CD's @ 7%, then we have:

(190,000 - x) is invested in AA bonds. But, we have:

.07x + .10(190,000-x)=17,200

.07x + 19,000 - .1x=17,200

-.03x=-1,800

x=$60,000 is to be invested in CD's @ 7%, and $ $190,000-$60,000

=$130,000 is to be invested in AA bonds @ 10%

 Oct 21, 2015

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