SOLUTION: A retired woman has $80,000 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 i
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Question 1189528: A retired woman has $80,000 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.
Bond =
CD = Answer by Theo(13342) (Show Source):
You can put this solution on YOUR website! x + y = 80,000
.15 * x + .07 * y = 6000
x is the amount invested at 15%.
y is the amount invested at 7%.
these are to equations that need to be solved simultaneously.
multiply both sides of the first equation by .15 and leave the second equation as is to get:
.15x + .15y = 12000
.15x + .07y = 6000
subtract the second equation from the first to get:
.08y = 6000
solve for y to get:
y = 6000 / .08 = 75000.
this means x = 5000 because x + y = 80000
.15x + .07y becomes .15 * 5000 .07 * 15000 = 6000.
she should invest 5000 in the 15% bond and 75000 in the 7% bond.
that's your solution.
