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27 May, 11:09

Taylor has $32000 a part of which he invested at 5% and the remainder at 3%. His annual return on each investment is the same. At what rate would he have to invest all her money to get the same interest?

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  1. 27 May, 13:24
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    Taylor have to invest the total money at 3.75%

    Step-by-step explanation:

    Let the part of money invested at 5% be 'a' and the part of money invested at 3% be (32000-a).

    To find (a):

    The annual income for both the 5% and 3% investment is equal.

    Interest = (amount x rate of interest x time) / 100

    Interest for 5% rate on investment

    Interest = (a x 5 x 1) / 100

    Interest for 3% rate on investment

    Interest = [ (32000-a) x 3 x 1]/100

    Both the interests are equal so equate both the equations.

    (a x 5 x 1) / 100 = [ (32000-a) x 3 x 1] / 100

    5a = (32000-a) 3

    5a = 96000-3a

    8a = 96000

    a = 96000/8

    a = 12000

    32000-a = 32000-12000

    = 20000

    The amount invested at 5% is $12000 and invested $20000 at 3%

    Interest = (12000 x 5 x 1) / 100

    = 60000/100

    = $600

    Interest = (20000 x 3 x 1) / 100

    = 60000/100

    = $600

    Total interest = $1200

    To find the rate at which the total money is to be invested to get the same annual income.

    1200 = (32000 x rate x 1) / 100

    1200 x 100 = 32000 x rate x 1

    120000 = 32000 x rate

    120000/32000 = rate

    Rate = 3.75%

    Taylor have to invest the total money at 3.75% to get the same annual income
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