algebra/stressed

If $32,500 is invested at 6.9% for 3 years. Find the future value if the interest is compounded the following ways:
annually, semiannually, quarterly, monthly, daily, every minute (N-525,600), continuously, and simple (not compounded. I don't know to set this up or how to start it. If you can help Thank you and it is appreciated.

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  1. a) annually

    A = p(1+ r)^t
    A = 32500(1+ 0.069)^3
    A = 32500(1 .069)^3
    A = $39,702.37

    b) semiannually

    A = p(1+ r/n)^tn
    A = 32500(1 + 0.069/2)^(3*2)
    A = 32500(1.0345)^6
    A = $39,835.14

    c) quarterly

    A = p(1+ r/n)^tn
    A = 32500( 1+ 0.069/4)^(3*4)
    A = 32500(1.01725)^12
    A = $39,903.94

    d) Monthly

    A = p(1+ r/n)^tn
    A = 32500(1 + 0.069/12)^(12*3)
    A =32500(1.00575)^36
    A = $ 39,950.74

    e) Daily

    A = p(1+ r/n)^tn
    A = 32500(1+ .069/365)^(3*365)
    A = $39,973.65

    f) every minute

    A = p(1 + r/n)^tn
    A= 32500( 1+ 0.069/525600)^(525600*3)
    A = $39,974.43

    g) Continuously

    A = pe^rt
    A = 32500e^(0.069*3
    A = 32500e^0.207
    A = $ 39,974.43

    h) Simple (not compound)

    A = p(1+ r)^t
    A = 32500( 1+ 0.069)^3
    A = 32500( 1.069)^3
    A = $ 39,702.37

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    posted by Kuai
  2. in each case you divide the rate by the annual compounding frequence,
    and multiply the years by that annual compouding frequency
    e.g. if compounded quarterly, the annual compounding frequencey is 4

    I will do that one, you try the others.

    6.9 %>
    compounded quarterly
    i = .069/4 = .01725
    n = 3(4) = 12

    Amount = 32500( 1 + .01725)^12
    = 32500 (1.01725)^12 = $39,903.94

    for continuous, you use the formula

    amount = principal x e^(rate x time)
    = 32500 e^(.069(3))
    = $39,974.43

    For simple interest:
    amount = 32500 + 32500(.069)(3) = $39,227.50



    Give the others a good try.

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    posted by Reiny
  3. There is typo for simple interest
    Simple interest. =Prt
    = 32500(.069)(3)
    =$6,727.50

    Amount. = p + interest
    A = $ 32500 + $6727.50
    A = 39,227.50

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    posted by Kuai
  4. Thank you all so much for the time you give, to help others. I appreciate it so much.

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