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Thread: Force of Interest

  1. #1
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    Force of Interest

    An investment of $1000 accumulates to $1360.86 at the end of 5 years. If the force of interest is $\displaystyle \delta$ during the first year and $\displaystyle 1.5\delta $ in each subsequent year, find the equivalent effective annual interest rate in the second year.

    Not sure how to proceed, basically all i can think of is
    $\displaystyle 1360.86=1000\cdot exp\left( \int^5_0 (...)dt \right)$

    so cant think of a function for $\displaystyle \delta$ that i should be using to integrate..
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  2. #2
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    i = .04543
    [1000(1 + i)] * (1 + 3i/2)^4 = 1360.86738....
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