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8 September, 23:01

Paul has $90,000 to invest. His intent is to earn 12% interest on his investment. He can invest part of his money at 7% interest and part at 13% interest. How much does Paul need to invest in each option to make a total 12% return on his $90,000?

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  1. 9 September, 02:11
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    If Paul wants to gain 12% interest, he would expect that the money he will have after a certain period of time is:

    Future worth = 90000 (1+0.12) = $100,800

    Let's distribute the future worth to the different interest rates. The solution is as follows:

    x + y = 90,000 - - > eqn 1

    100,800 = x (1+0.07) + y (1+0.13) - - > eqn 2

    Solving the equations simultaneously,

    100,800 = x (1+0.07) + (90,000 - x) (1+0.13)

    Solving for x:

    x = 15,000

    y = 90 000 - 15 000 = 75,000

    Therefore, Paul should place $15,000 to the 7% interest and $75,000 to the 13% interest.
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