SOLUTION: two bond funds pay interest at rates that differ by 2%. Money invested for one year in the first fund earns $315 interest. The same amount invested in the second fund earns $405.
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Question 1072679: two bond funds pay interest at rates that differ by 2%. Money invested for one year in the first fund earns $315 interest. The same amount invested in the second fund earns $405. Find the lower rate of interest.
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
let y = the investment.
let x = the lower interest rate.
the higher interest rate is 2% more than the lower interest rate.
that makes the higher interest rate equal to x + .02
the interest using the lower interest rate is 315.
the interest using the higher interest rate is 405.
you get:
y * x = 315
y * (x + .02) = 405
subtract the first equation from the second to get:
y * (x + .02) - y * x = 405 - 315
simplify to get:
y * x + .02 * y - y * x = 405 - 315
combine like terms to get:
.02 * y = 90
solve for y to get y = 90 / .02 = 4500.
this makes the investment equal to 4500.
now that you know y, you can solve for x.
the first equation is y * x = 315
replace y with 4500 and you get 4500 * x = 315
solve for x to get x = 315 / 4500 = .07
that's the smaller rate.
the larger rate is .02 more than that.
this makes the larger rate = .09
4500 * .07 = 315
4500 * .09 = 405
solution is confirmed to be good.
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