### What rate of return would you earn if you bought the bond

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Money and Banking

1. Consider the example used in class. Project 1 pays \$5.25 million the first year, \$21 million the second year, and \$57.75 million the third year. Project 2 pays \$52.5 million the first year, \$13,125,000 the second year, and \$10.5 million in the third. Project 3 pays \$26.25 million per year for three years. If the going interest rate is 5% we found that Project 1 is the best. Suppose that the interest rate changes to 15%. Reevaluate the three projects.

2. Suppose you could buy a three year bond for \$2000 that had a face value of \$1000 and paid a coupon rate of 10%. What rate of return would you earn if you bought this bond?

3. For each of the following situations graph the supply and demand curves for the loan market, for the bond market and show the primary movement in the curves as a result of the given action. Show the effect this would have on interest rates, bond prices, quantity of loans and quantity of bonds?

a) The government increases the corporate tax rate, which decreases the return on new business investments.

b) The new US Congress and the president come to an agreement on a bill to increase the debt ceiling, thus reducing the risk of a government debt default.

c) The recent financial crisis and recession makes Americans more skeptical of debt and increases the national savings rate, and generally more conscious of the need to think about the future.

d) A first time home buyer tax credit make is affordable for more families to purchase a house.

e) Federal spending increases leading to a larger federal deficit.

f) Federal Reserve chairman announces in a press conference that he will implement a new anti-inflation program and the financial markets believe that he will follow through on this promise.

4. Suppose that on Jan 1 you lend \$2,500 to a bank (deposit \$2,500 in a savings account). The savings account is paying 4% annual interest rate paid quarterly.

a.) How much interest will be paid on April 1? What is the new account balance? (Hint: you will receive only a quarter of the annual interest)

b.) How much interest is paid on July 1? What is the new account balance?

c.) How much interest is paid on Oct 1? What is the new account balance?

d.) How much interest is paid on Jan 1? What is the new account balance?

e.) Use the simple interest rate formula: PV = FV/(1+i) to calculate the interest rate that you actually received. In banking jargon the 4% shown above is called the interest "rate" and what you are calculating here is called the "yield".

f.) The difference between the interest "rate" and the "yield" is due to compounding; that is, how often the interest is paid. Since it is paid in the spring the July interest payment includes interest paid on the April interest. If the interest is paid more often, say monthly, will the yield be higher or lower or unchanged?

g.) Calculate the yield if interest is compounded monthly.

h.) Calculate the yield if interest is compounded weekly.

i.) Calculate the yield if interest is compounded daily.

j.) Bonus: Is there a simple way of calculating this, a formula? Can you figure it out?

k.) Calculate the yield if interest is compounded continuously. Is his higher or lower than when quarterly, monthly, weekly, daily compounding is used?

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