SOLUTION: The annual interest on a $19,000 investment exceeds the interest earned on a $5000 investment by $617. The $19,000 is invested at a 0.3% higher rate of interest than the $5000. W
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Question 1108965: The annual interest on a $19,000 investment exceeds the interest earned on a $5000 investment by $617. The $19,000 is invested at a 0.3% higher rate of interest than the $5000. What is the interest rate of each investment? Found 2 solutions by josmiceli, Theo:Answer by josmiceli(19441) (Show Source):
You can put this solution on YOUR website! This is a simple interest problem
Use
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(1)
(2)
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Plug (2) into (1)
(1)
(1)
(1)
and
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The rate for $19,000 investment is 4.3%
The rate for $5,000 investment is 4%
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check:
(1)
(1)
(1)
and
(2)
(2)
OK
let y = the interest rate on the 5000 dollar investment.
you get 19000 * x - 5000 * y = 617
that means that the annual interest on the 19000 dollar investment is 617 dollars higher than the annual interest on the 5000 dollar investment.
you are given that the interest rate on the 19000 dollar investment is .3% higher than the interest rate on the 5000 dollar investment.
.3% is equal to .003.
this results in x = y + .003
you have 2 equations that need to be solved simultaneously.
they are:
19000 * x - 5000 * y = 617
x = y + .003
replace x in the first equation with the equivalent value of y + .003 from the second equation to get:
19000 * (y + .003) - 5000 * y = 617
simplify to get 19000 * y + 57 - 5000 * y = 617.
combine like terms to get:
14000 * y + 57 = 617.
subtract 57 from both sides to get:
14000 * y = 560.
solve for y to get y = 560 / 14000 = .04.
you have y = .04 and x = .043, since x is .003 more than .04.
go back to your original problem to see if it makes sense when x = .043 and y = .04
the original problem says that the difference between the interest on the 19000 dollar investment and the interest on the 5000 dollar investment is 617 dollars.
the original problem also states that the interest rate on the 19000 dollar investment is .3% higher than the interest rate on the 5000 dollar investment.
19000 * .043 - 5000 * .04 is equal to 617 dollars, confirming the solution is correct.
the solution is that the interest rate on the 19000 investment is 4.3% and the interest rate on the 5000 dollar investment is 4.0%.
