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Betsy, a recent​ retiree, requires ​$5000 per year in extra income. She has ​$70000 to invest and can invest in​ B-rated bonds paying 15​% per year or in a certificate of deposit​ (CD) paying 5​% per year. How much money should be invested in each to realize exactly ​$5000 in interest per​ year?

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sqdancefan

Answer:

$15000 in bonds, $55000 in a CD

Step-by-step explanation:

Let x represent the amount Betsy invests in the B-rated bonds (in thousands). Then she will invest 70-x in a CD. Her interest (in thousands) will be ...

0.15x + .05(70 -x) = 5

0.10x + 3.5 = 5 . . . . . . . eliminate parentheses, collect terms

x + 35 = 50 . . . . . . . . . . multiply by 10

x = 15 . . . . . . . . . . . . . . . subtract 35

Then 70-x = 70-15 = 55

Betsy should invest $15000 in bonds, and $55000 in a CD.

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