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31 January, 06:47

Joe must pay liabilities of 2000 due one year from now and another 1000 due two years from now. He exactly matches his liabilities with the following two investments: Mortgage I: A one year mortgage in which X is lent. It is repaid with a single payment at time one. The annual effective interest rate is 6%. Mortgage II: A two-year mortgage in which Y is lent. It is repaid with two equal annual payments. The annual effective interest rate is 7%. Calculate X + Y.

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  1. 31 January, 08:31
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    The value of X+Y=2,769

    Explanation:

    According to the given data we have the following:

    x=present value of 2,000

    =2,000 / (1+0.06) = 1,886.79

    y=present value of 1,000

    =1,000 (1+0.07) ∧2=873.44

    x+y=1,886.79+873.44

    =2,760.23

    =2,769

    The value of X+Y=2,769
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