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Math Help - Financial math- force of interest

  1. #1
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    Financial math- force of interest



    Smith makes deposits of 100$ at time 0, and X $ at time 3. the fund grows at a force of interest f= (t^2)/100, t>0. The amount of interest earned from time 3 to time 6 is X. Calculate X.

    Any help would be really appreciated.
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  2. #2
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    Have you considered the basic formulation? You can do it in stages if it is easier to keep track.

    \int_{0}^{3}\frac{t^{2}}{100} \; dt = \frac{9}{100} = 0.09


    100 \cdot e^{0.09} = 109.417


    \int_{3}^{6}\frac{t^{2}}{100} \; dt = \frac{63}{100} = 0.63


    (109.417 + X) \cdot e^{0.63} = (109.417 + X) + X


    Solve for X.

    Note: You may wish to eliminate some rounding. There really is no need to use the three decimal places for intermediate results. I get an error of about 0.3 due to the unnecessary rounding. The integrals are exact to two decimal places, so that creates no additional rounding problem.
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  3. #3
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    Hmpf! Let's see you do the next one. Only one for free.
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