Multiplication of Polynomials Application Help Needed

Discussion in 'Algebra' started by NMJim, Aug 24, 2022.

  1. NMJim


    Aug 24, 2022
    Likes Received:

    I am hoping someone can help me to see what I'm doing wrong. I am an adult trying to learn algebra on my own after having been out of school for a long time. There is a textbook applied algebra problem in the Polynomials and Exponents chapter. The answer is given, but I can't see what I'm doing wrong in getting a different answer. Here is the problem:

    Periodic Deposits.
    At the beginning of each year for five years, an investor invests $10 in a mutual fund with an average annual return of r.
    If we let x = 1 + r, then at the end of the first year (just before the next investment), the value is 10x dollars.
    Because $10 is then added to the 10x dollars, the amount at the end of the second year is (10x + 10)x dollars.
    Find a polynomial that represents the value of the investment at the end of the fifth year.
    Evaluate this polynomial if r = 10%.

    The given answer is 10x^5 + 10x^4 + 10x^3 + 10x^2 + 10x, $67.16.

    The answer I got was 10x^5 + 10x^4.

    A chart of my thinking (x = 1 + r):

    Beginning of Year -I- Avg Return -I- End of Year Value
    1 r 10x
    2 r (10x + 10)x
    3 r (10x^2 + 10x)x
    4 r (10x^3 + 10x^2)x
    5 r (10x^4 + 10x^3)x

    And that final Value = 10x^5 + 10x^4.

    Please, what am I doing wrong? Thank you so much to anyone who spends the time to help me.

    Have a great day.

    NMJim, Aug 24, 2022
  2. NMJim

    Phrzby Phil

    Mar 8, 2022
    Likes Received:
    You are correct: at end of year 1, value = 10x.
    You are correct: at end of year 2, value = (10x + 10)x [note: first term is prior year end value]
    So - end of year 3, first term is its prior year end value, which = (10x + 10)x
    giving [(10x + 10)x + 10]x = 10x^3 + 10x^2 + 10x
    Rinse and repeat.
    Phrzby Phil, Sep 9, 2022
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