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Thread: Forces of interest

  1. #1
    Junior Member
    Sep 2009

    Forces of interest

    Tawny makes a deposit into a bank account that credits interest at a nominal interest rate of 10% per year, compounded semiannually. At the same time, Fabio deposits 1000 into a different bank account, which is credited with simple interest. At the end of 5 years, the forces of interest on the two accounts are equal, and Fabio’s account has accumulated to Z. Determine Z.

    Here is what I have ...
    For Fabio, the accumulation function would be 1000(1 + 5i) and the force of interest at time t would be i/(1 + 5i)
    The force of interest for Tawny would be ln(1 + i) = ln(1.1) for all t
    So I think you set i/(1 + 5i) = ln(1.1) , which would give i = .1821
    Then Fabio's account would equal 1000(1 + 5*.1821) = 1910.5 at 5 years
    But our teacher said the answer is 1953 so I'm a little off somewhere and can't figure out where. Any help would be great thanks!
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  2. #2
    Mar 2009
    You forgot to factor in that the nominal interest is compounded semi-annually. If you make this conversion, you get the answer your teacher provided;
    so the force of interst for twany should have been $\displaystyle ln(1.1025)=0.09758$ once you take into account the semi-annual compounding.

    This gives $\displaystyle i=0.19055$; $\displaystyle 1000\cdot (1+5\cdot 0.19055)=1952.749$
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