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Math Help - Compounded Interest Question

  1. #1
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    Compounded Interest Question

    Hello everyone! How are you all doing today? I am having two questions as of now regarding compounded interest.

    First one: A small hardware store makes a profit of $20,000 during its first year. The store owner sets a goal of increasing profits by $5000 each year for 4 years. Assuming that this goal is met, find the total profit during the first 5 years of business.

    Second One: A principal of $2500 is invested at $% interest. Find the amount after 20 years if the interest is compounded a. annually, b. semi-annually, c. quarterly, d. monthly, and e. daily

    I understand how to do it annually, but I'm not sure about b-e. Thank you all for the help and I'm very grateful for it!
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  2. #2
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    Quote Originally Posted by Norman Smith View Post
    Hello everyone! How are you all doing today? I am having two questions as of now regarding compounded interest.

    First one: A small hardware store makes a profit of $20,000 during its first year. The store owner sets a goal of increasing profits by $5000 each year for 4 years. Assuming that this goal is met, find the total profit during the first 5 years of business.

    Second One: A principal of $2500 is invested at $% interest. Find the amount after 20 years if the interest is compounded a. annually, b. semi-annually, c. quarterly, d. monthly, and e. daily

    I understand how to do it annually, but I'm not sure about b-e. Thank you all for the help and I'm very grateful for it!
    First one: A small hardware store makes a profit of $20,000 during its first year. The store owner sets a goal of increasing profits by $5000 each year for 4 years. Assuming that this goal is met, find the total profit during the first 5 years of business.

    1st year, $20,000.
    2nd year, 25,000.
    3rd year, 30,000.
    4th year, 35,000.
    5th year, 40,000.
    Add them all ---> $150,000 -----answer.

    If you want another way, Arithmetic series way,
    a1 = 20,000
    d = 5,000
    an = a1 +(n-1)d
    a5 = 20,000 +(5-1)(5,000) = 40,000
    Sn = (n/2)(a1 +an)
    S5 = (5/2)(20,000 +40,000) = 5(30,000) = 150,000 dollars.

    ---------------------------------------------------

    Second One: A principal of $2500 is invested at $% interest. Find the amount after 20 years if the interest is compounded a. annually, b. semi-annually, c. quarterly, d. monthly, and e. daily

    I bet you the $% interest should be 4% interest.

    Compound Interest fpormula:
    A = P(1 +i)^n
    where
    A = amount after n compundings.
    P = principal = initial amount, at 0 compoundings.
    i = interest at each compounding.
    n = number of compoundings.

    r = interest rate per year, = 4% = 0.04 here.
    So,
    annual i = 0.04 per compounding
    semi-annual i = 0.04/2 = 0.02 per compounding
    quarterly i = 0.04/4 = 0.01 per compounding
    monthly i = 0.04/12 = 0.0033333... per compounding
    daily i = 0.04/365 = 0.000109589 per compounding

    For n,
    annual, n = 1 compounding per year
    semi-annual = 2 compoundings per year
    quarterly = 4 compoundings per year
    monthly = 12 compoundings per year
    daily = 365 compoundings per year

    So, for 5 years:

    a) Compounding annually,
    A = $2500(1 +0.04)^(1*5) = $3041.63

    b) Compounding semi-annually,
    A = $2500(1 +0.02)^(2*5) = $3047.49

    c) Compounding quarterly,
    A = $2500(1 +0.01)^(4*5) = $3050.48

    d) Compounding monthly,
    A = $2500(1 +0.0033333...)^(12*5) = $3052.49

    e) Compounding daily,
    A = $2500(1 +0.000109589)^(365*5) = $3053.47
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