Question 1092108: Betsy, a recent retiree, requires $5000 per year in extra income. She has $50000 to invest and can invest in B-rated bonds paying 17% per year or in a certificate of deposit (CD) paying 7% per year. How much money should be invested in each to realize exactly $5000 in interest per year?
Answer by Boreal(15235)   (Show Source):
You can put this solution on YOUR website! x amount is invested in bonds and at 17% interest per year (i=prt), the interest is x*0.17
The remainder is not known and could be called y, but since I know the two add to $50,000, I can call it $50000-x, since x +50000-x=50000. This way, I can use one variable. The interest for the other is the principal, or (50000-x)*7%
The interest on each is the product
x in Bonds at 17% or .17x interest per year
50000-x at 7% or 3500-.07x interest per year, multiplying 50000 by 0.07 and -x by 0.07. That is 3500-0.07x
That sum is $5000; in other words, .17x+3500-0.07x=3500+0.10x.
3500+0.10x=5000, because $5000 total interest is desired.
0.10x=1500; divide both sides by 0.10
x=$15,000 in bonds, and 17% of that is $2550
50000-x is $35000 in CDs, and 7% of that is $2450
They add to $5000.
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