SOLUTION: A professor wants to supplement her pension with investment interest. If she invests $34,000 at 4% interest, how much more would she have to invest at 9% to achieve a goal of $2,44

Question 661041: A professor wants to supplement her pension with investment interest. If she invests $34,000 at 4% interest, how much more would she have to invest at 9% to achieve a goal of $2,440 per year in supplemental income?
Answer by colliefan(242) (Show Source): You can put this solution on YOUR website!
The goal is $2440.
From the first account, she makes $34,000*4% = $1360
The amount she still needs is: $2440-1360 = $1080

Now, how much does she need to invest to have $1080 at the end of the year if the interest is at 9%?
The number 1080 is the amount invested plus the amount of the interest earned.
if x is the amount invested:
x + x*9% = 1080
1x + x*9% = 1080
x(1 + 9%) = 1080
x(1+.09) = 1080
x(1.09) = 1080
x(1.09)*1/1.09 = 1080*1/1.09
x = 1080/1.09
x = $990.83

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