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Question 1137123: Two bond funds pay interest at rates that differ by 2%. Money invested for one year in the first fund earns $550 interest. The same amount invested in the other fund earns $660. Find the lower rate of interest.
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! let the rate of the first bond be equal to x.
then the rate of the second bond will be equal to x + .02.
this is because a rate of 2% is equal to .02.
since the interest on the first bond is 550, then the rate on the first bond must be the lower rate, so the rate on the first bond is x and the rate on the second bond is x + .02.
interest = interest rate * principal.
let i = interest and r = interest rate and p = principal and you get i = r * p.
when i = 550 and r = x, the equation becomes 550 = x * p.
when i = 660 and r = x + .02, the equation becomes 660 = (x + .02) * p
in the equation of 550 = x * p, solve for x to get x = 550 / p.
in the equation of 660 = (x + .02) * p, replace x with 550 / p to get 660 = (550 / p + .02) * p
simplify this equation to get 660 = 550 / p * p + .02 * p
simplify further to get 660 = 550 + .02 * p.
subtract 550 from both sides of this equation to get 110 = .02 * p
divide both sides of this equation by .02 to get 110 / .02 = p
solve for p to get p = 5500.
this means the principal is 5500.
your original equations are:
550 = x * p
660 = (x + .02) * p
replace p in these equations to get:
550 = x * 5500
660 = (x + .02) * 5500
solve for x in the first equation to get x = 550 / 5500 = .10.
since x is equal to .10, then x + .02 must be equal to .12.
the first equation becomes 550 = .10 * 5500 which becomes 550 = 550.
the second equation becomes 660 = .12 * 5500 which becomes 660 = 660.
the soluition is confirmed to be good.
the lower rate of interest is .1 which is equal to 10%.
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