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2.5 EXERCISES

1. With r = 7%, calculate the future value of \$1,500 at the end of each year for 5 years.

2. You want to have \$25,000 in 5 year's time. As a one time investment how much would you have to invest now in a money market account paying 5.4% a year to reach this goal.

3. What is the arbitrage-free price of a zero coupon bond with two years left until maturity and has a face value equal to \$110,000. Assume that the market interest rate interest is 5%?

4. What is the yield from investing in a newly issued 3-year zero coupon bond (payable semi-annually) that has a face value equal to \$1,000 and price of \$960.04.

5. Suppose you buy a house today for \$350,000 by financing 50%. You want to keep you monthly payments down low so you enter into a 7 year mortgage loan with a "balloon payment" of \$100,000 at the end of 7 years. That is, you repay equal monthly amounts plus at the end of 7 years you pay a lump sum of \$100,000 to clear the loan.

A. If interest rates are 9% calculate your monthly repayments.

B. Suppose at the end of 6-months interest rates have fallen. You check into refinancing your loan and discover that you will have to pay \$4,500 in various refinancing charges. Ignoring any tax implications, at what level of interest rates are you indifferent between refinancing versus not. Provide working.

6. Contrast a 10 year and 30 year coupon bond that both have an 8% coupon rate payable semi-annually. Suppose the market rate of interest applicable to all cash flows is 10%.

A. What is the market price of each bond if the face value of each bond is \$10,000.

B. Compute the market price of each bond if interest rates increase by 1 basis point (0.01%).

C. Compute the market price of each bond if interest rates decrease by 1 basis point (0.01%).

D. Compare your answers to B) and C) above and explain why a constant increase/decrease in yields, leads to a non constant decrease/increase in values.

7. Consider a 10 year coupon bond with a 7% coupon rate payable semi annually and a face value equal to \$10,000. Suppose that the market rate of interest is 5%.

A. At the time of issue what percentage of the market price arises from future coupon values and what percentage is due to the face value?

B. Immediately after the coupon payment in 5 1/2 years time what percentage of the market price is due to future coupon payments and what % is due to the eventual receipt of the face value?

C. Suppose immediately after the coupon payment in 5 1/2 years time interest rates had declined by 55 basis points (.55 of 1%). What percentage of the market price is due to future coupon payments and what percentage is due to the eventual receipt of the face value?