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Interest problem

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Rastis Really wants to Beat The GMAT!
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Interest problem Post Mon Dec 08, 2014 12:41 pm
Elapsed Time: 00:00
  • Lap #[LAPCOUNT] ([LAPTIME])
    An investment a d dollars at k percent simple annual interest yields $600 interest over a 2-year period. In terms of d, what dollar amount invested at the same rate will yield $2,400 over a 3-year period?

    a) 2d/3

    b) 3d/4

    c) 4d/3

    d) 3d/2

    e) 8d/3

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    Post Mon Dec 08, 2014 12:49 pm
    Quote:
    An investment of d dollars at k percent simple interest yields $600 interest over a 2-year period. In terms of d, what dollar amount invested at the same rate will yield $2,400 interest over a 3-year period?

    A. 2d/3
    B. 3d/4
    C. 4d/3
    D. 3d/2
    E. 8d/3
    The interest rate is irrelevant.
    This problem is really about a PROPORTION.
    $d invested over 2 years is equivalent to $600 in interest.
    $x invested over 3 years must be equivalent to $2400 in interest.
    Thus:
    (d * 2)/600 = (x * 3)/2400
    d/300 = x/800
    d/3 = x/8
    x = (8d)/3.

    The correct answer is E.

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    Post Mon Dec 08, 2014 12:49 pm
    Quote:
    An investment of d dollars at k percent simple annual interest yields $600 interest over a 2-year period. In terms of d, what dollar amount invested at the same rate will yield $2,400 interest over a 3-year period

    2d/3
    3d/4
    4d/3
    3d/2
    8d/3
    An alternate approach is to PLUG AND CHUG:
    1. Choose a good value for k.
    2. Use the value of k to determine the value of d.
    3. Answer the question and get a target.
    4. Determine which answer choice yields the target.

    Step 1:
    Let the interest rate = 100%:
    k=100.

    Step 2:
    Since $600 is earned over 2 years, $300 is earned each year.
    To earn $300 at an interest rate of 100%, the amount invested = $300:
    d=300.

    Step 3:
    To earn $2400 over 3 years, $800 must be earned each year.
    To earn $800 at an interest rate of 100%, the amount invested = 800.
    This is the target.

    Step 4:
    Now plug d=300 into the answers to see which yields the target of 800.
    A quick scan of the answers reveals that only E works:
    8d/3 = 8(300)/3 = 800.

    The correct answer is E.

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    Rastis Really wants to Beat The GMAT!
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    Post Mon Dec 08, 2014 1:00 pm
    That makes more sense. I was trying to use the interest rate formula and ended up guessing and moving on. Thanks!

    Post Mon Dec 08, 2014 5:01 pm
    Quote:
    "An investment of d dollars at k percent simple annual interest yields $600 over a 2-year period. In terms of d, what dollar amount invested at the same rate will yield $2,400 interest over a 3-year period?

    (A) 2d/3
    (B) 3d/4
    (C) 4d/3
    (D) 3d/2
    (E) 8d/3

    An investment of d dollars at k percent simple annual interest yields $600 over a 2-year period.
    In other words, an investment of d dollars yields $300 in interest each year.

    What dollar amount invested at the same rate will yield $2,400 interest over a 3-year period?
    In other words, how much money must we invest to earn $800 in interest EACH YEAR?

    If a d dollar investment yields $300 in interest EACH YEAR, then:
    - a 2d dollar investment would yield $600 (2 times $300) in interest EACH YEAR
    - a 3d dollar investment would yield $900 (3 times $300) in interest EACH YEAR
    - a 4d dollar investment would yield $1200 (4 times $300) in interest EACH YEAR
    - etc.

    From here there are two approaches.

    APPROACH #1
    We want the ANNUAL interest to be $800.
    This means we must invest an amount that is BETWEEN 2d dollars and 3d dollars [since $800 is BETWEEN $600 and $900].
    When we check the answer choices, only E, which can be written as (8/3)d, is BETWEEN 2d dollars and 3d
    So, the correct answer must be E


    APPROACH #2
    To increase the ANNUAL interest from $300 to $800, we must invest 800/300 TIMES as much money.
    800/300 = 8/3, so we must invest (8/3)d dollars [aka 8d/3 dollars]
    Answer = E

    Cheers,
    Brent

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    Post Fri Dec 19, 2014 6:42 am
    d x k/100 x 2 = 600
    So k/100 =300/d

    e x k/100 x 3 = 2400
    e x 300/d x 3 = 2400
    e x 3/d = 8
    e = 8d/3

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    Post Mon Dec 22, 2014 12:47 pm
    Here's another pretty straightforward approach. $d at k% is currently giving us $300 a year. To get $800 a year, we'd need to multiply our principle by 8/3, since 300 * (8/3) = 800.

    Hence we multiply d by (8/3), giving us (8/3)d, and we're done!

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