Question: 5) Dimitri borrows $100,000 at 6 % compounded semi-annually. He plans to pay the interest only every 6 months for 10 years. He plans to

5) Dimitri borrows $100,000 at 6 % compounded semi-annually. He plans to pay the interest only every 6 months for 10 years. He plans to make monthly deposits of X into a sinking fund paying 4% compounded quarterly to pay off the principal at maturity.

a) Find X.

b) How much money does he have in the sinking fund after 5 years?

After 5 years, the interest earned on the sinking fund increases to 5% compounded quarterly, so Dimitri adjusts his monthly deposit. For the next 5 years he makes monthly deposits of Y into the sinking fund so that he will still end up with 100,000 at maturity to pay back the loan.

c) Is Y bigger or smaller than X?

d) Find Y.

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