SOLUTION: Two bond funds pay interest at rates that differ by 4%. Money invested for one year in the first fund earns $420 interest. The same amount invested in the other fund earns $560. Fi
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Question 1143006: Two bond funds pay interest at rates that differ by 4%. Money invested for one year in the first fund earns $420 interest. The same amount invested in the other fund earns $560. Find the lower rate of interest
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
let x = the lower rate of interest.
then x + 4%/100 = the higher rate of interest.
let y equal the investment.
your two equations are:
x * y = 420
(x + .04) * y = 560
solve for y in the first equation to get y = 420/x
replace y with that in the second equation to get (x + .04) * 420/x = 560
multiply both sides of that equation by x to get (x + .04) * 420 = 560 * x
simplify to get 420 * x + .04 * 420 = 560 * x
subtract 420 * x from both sides of the equation to get .04 * 420 = 140 * x
divide both sides of the equation by 140 to get .04 * 420 / 140 = x
solve for x to get x = .12
x * y = 420 becomes .12 * y = 420
solve for y to get y = 420 / .12 = 3500
(x + 4) * y = 560 becomes .16 * y = 560
solve for y to get y = 560 / .16 = 3500
the lower rate of interest = .12 = 12%.
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