Math

Ginny Katz has decided to invest $700 quarterly for 10 years in an ordinary annuity at 8 percent. The total cash value of the annuity at end of year 10 is?

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  1. i = .08/4 = .02
    n = 10(4) = 40

    amount = 700( 1.02)^ 40 - 1)/.02

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  2. This Compound interest
    using
    Amount =
    principle * ((Rate + 100)/100)^time

    Here Rate is per time period
    i.e 8% per annum will be 2% per quater
    Time period is 10 years = 40 quater year
    P=700 $

    Putting values
    Amount = 700 * ((2+100)/100)^40
    =700 * (51/50)^40
    using scientific calculator
    (51/50)^40 = 2.208

    =700 * 2.208
    =1545.6 $ =7728/5 $ (ans)

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  3. The answer to my
    700 (1.02^40 - 1)/.02 is $42,281.39

    Your solution makes no sense at all.
    Even without any interest, there would be 40 payments of 700 for $28,000

    Unless you are sure of the math for compound interest, you are just confusing students more by giving them incorrect solutions.

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  4. 700 $ make 42281 $ in ten years
    Totally wrong this cant be true
    He had invested money that will be get in a collection not in payment

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  5. Fact:
    quarterly deposits for 10 years ---> 40 payments
    quarterly rate --- .08/2
    standard formula that has been used for hundreds of years
    Amount = deposit ( (1+i)^n - 1)/i , where i is the rate as a decimal and n is the number of payments or deposits

    = 700( 1.02^40 - 1)/.02
    = 42281.39

    Fact:
    my answer is right and you are wrong.
    To convince yourself, complete the following table for 40 rows

    time, deposit, interest on balance, increase in balance, balance
    1 --- 700 ---0.00 ------------ 700.00 ---------- 700.00
    2 --- 700 ---14.00------------714.00-----------1414.00
    3 ----700 ---28.28------------728.28-----------2142.28
    4 ----700 ---42.85 -----------742.85 -----------2885.13
    ........ that is at the end of the 1st year..........
    etc.

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