The Three Investments
14) Jill made three investments that yielded $2,260 as annual
interest. Her 7.5% investment was $7,000 more than the one at
5%, and her 8% investment was $1,000 less than six times the 5%
investment. What was the amount she paid for each of these investments?
"x" will be the variable for the 5% investment. We, therefore,
will figure the other investments on the bases of that.
.05(x) + .075(x + 7,000) + .08(6x - 1,000) = 2260.00
Now move the decimal point two places to the right:
5(x) + 7.5(x + 7,000) + 8(6x - 1,000) = 226,000
Then add:
5x + 7.5x + 52,500 + 48x -8,000 = 226,000
Combine like signs:
60.5x + 44,500 = 226,000
Isolate x to one side of the equal sign by performing the operation
of deleting 44,500 from both sides:
60.5x = 181,500
Divide both sides by 60.5 to find the value of x:
x = 3,000
We can now plug the value of x into the formula:
5(x) + 7.5(x + 7,000) + 8(6x - 1,000) = 226,000
5% = $3,000
7.5% = $10,000 (x + 7,000)
8% = $17,000 (6x - 1,000)
To find the annual interest yield of each one, convert the percents
back to decimals by dividing them by 100. Then multiply:
Investment Interest Earning
5% divided by 100 = .05 .05 * $3,000 = $150.00
7.5% divided by 100 = .075 .075 * $10,000 = $750.00
8% divided by 100 = .08 .08 * $17,000 = $1,360.00
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$30,000 $2,260.00
We can also divide 2,260 by 30,000 to find out what are average
percent rate was for all three investments: 7.53%