A man has $ 10,000 to invest. He invests $ 4000 at 5 % and $ 3500 at 4 %. In order to have a yearly income of $ 500, he must invest the rema

Question

A man has $ 10,000 to invest. He invests $ 4000 at 5 % and $ 3500 at 4 %. In order to have a yearly income of $ 500, he must invest the remainder at:

(a) 6 % , (b) 6.1 %, (c) 6.2 %, (d) 6.3 %, (e) 6.4 %

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Abigail 1 month 2021-08-20T06:06:44+00:00 2 Answers 0 views 0

Answers ( )

    0
    2021-08-20T06:08:08+00:00

    Answer:

    Step-by-step explanation:

    Solution:

    Income from $ 4000 at 5 % in one year = $ 4000 of 5 %.

    = $ 4000 × 5/100.

    = $ 4000 × 0.05.

    = $ 200.

    Income from $ 3500 at 4 % in one year = $ 3500 of 4 %.

    = $ 3500 × 4/100.

    = $ 3500 × 0.04.

    = $ 140.

    Total income from 4000 at 5 % and 3500 at 4 % = $ 200 + $ 140 = $ 340.

    Remaining income amount in order to have a yearly income of $ 500 = $ 500 – $ 340.

    = $ 160.

    Total invested amount = $ 4000 + $ 3500 = $7500.

    Remaining invest amount = $ 10000 – $ 7500 = $ 2500.

    We know that, Interest = Principal × Rate × Time

    Interest = $ 160,

    Principal = $ 2500,

    Rate = r [we need to find the value of r],

    Time = 1 year.

    160 = 2500 × r × 1.

    160 = 2500r

    160/2500 = 2500r/2500 [divide both sides by 2500]

    0.064 = r

    r = 0.064

    Change it to a percent by moving the decimal to the right two places r = 6.4 %

    Therefore, he invested the remaining amount $ 2500 at 6.4 % in order to get $ 500 income every year.

    Answer: (e)

    0
    2021-08-20T06:08:10+00:00

    @@@

    its a.

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