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Actuarial math question

  1. Sep 21, 2006 #1
    I've found b by doing this:

    a(t) = at² + b
    A(t) = A(0)a(t)
    at time t = 0:
    A(0) = A(0)(0 + b)
    b = 1

    Now is it correct to say the following:
    172 = 100(a*3² + 1)
    thus a = 0.08
    and then the accumulated value at time 10 of $100 invested at time 5 is:
    A(10) = 100(0.08(10²)+1) - 100(0.08(5²)+1)
    A(10) = 900 - 300 = $600?
     
  2. jcsd
  3. Sep 22, 2006 #2

    HallsofIvy

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    Staff Emeritus
    Science Advisor

    Your question makes no sense. You say that a(t)= at2+ b. How can you use "a" inside an equation for "a"? Did you mean A(t)? But then you say A(t)= A(0)a(t).

    If you meant A(t)= at2+ b with a and b constants, then
    A(0)= a(0)+ b= b= 100 so b= 100. Then A(3)= a(32)+ 100= 100+ 9a= 172 so 9a= 72 and a= 8.
    That is, A(t)= 8t2+ 100.
    I'm not sure what is meant here. Are we to recalculate b, so that A(5)= 100, assuming the same a, and then calculate A(10)?
     
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