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.