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Continuous annuities

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  • Continuous annuities

    Hi everyone,

    I have a question and hope hope that you can help.

    An investment fund is started with an initial deposit of 1 at time 0. New deposits are made continuously at the annual rate 1 + t at time t over the next 10 years. The force of interest at time t is given by delta = (1 + t)^(-1). Find the accumulated value in the fund at the end of 10 years.
    Here is what I did:

    a := accumulate 1 to the end of 10 years : exp(integral(1+t)^(-1),t=0..10)=11
    b := accumulate (1+t) to the end of 10 years :Integral(a*(1+t),t=0..10)=443.67
    then ac. value is a+b= 454.67 but the answer given is 121

    What is wrong in my solution?
    Thanks alot.
    Bye
    Ckota
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