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.

Question

Nia Donaldson

Business

11 August, 00:25

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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Kinley · Answer 1

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