Problem 5 [20 points]:

Answering the following questions.

a.     What's the future value of an initial $100 after 3 years if it is invested in an account paying 8% annual interest and compounded annually? How about if the interest is compounded hourly?

b.     What is the present value of $100 to be received in 3 years if the annual interest rate is 8% and compounded annually? How about if the interest is compounded daily?

c.     Suppose someone offered to sell you a note calling for the payment of $1,200 in three years. They offer to sell it to you for $880. You have $880 deposit in a bank that pays a 9.5% nominal rate with daily compounding, and you plan to leave the money in the bank unless you buy the note. The note is not risky--you are sure it will be paid on schedule. Should you buy the note? Check the decision in three ways: (1) by comparing your future value if you buy the note versus leaving your money in the bank, (2) by comparing the present value of the note with your current bank account, and (3) by comparing the effective annual rate on the note versus that of the bank account.

Problem 6 [20 points]:

Answering the following questions.

a.     What is the value of a 5-year, $1,000 par value bond with a 9 percent annual coupon if its required annual rate of return is 10 percent? Does the bond sell at par?

b.     What would happen to the value of the above 5-year bond over time if the required annual rate of return remained at 10 percent?

c.     What is the yield to maturity (YTM) on a 10-year, 9 percent annual coupon, $1,000 par value bond that sells for $1,050?

d.     Suppose a 10-year, 10 percent, semiannual coupon bond with a par value of $1,000 is currently selling for $1,135.90, producing a yield to maturity (YTM) of 8 percent. However, the bond can be called after 5 years for a price of $1,025.

1.     What is the bond's yield to call (YTC)?

2.     If you bought this bond, do you think you would be more likely to earn the YTM or the YTC? Why?

Problem 7 [20 points]

You borrow a GPM of $450,000 with annual payments and 15-year term. The interest rate is 4.5% and the payment factors from year 1 to year 15 are: 50%, 50%, 50%, 50%, 50%, 75%, 75%, 75%, 75%, 75%, 100%, …, 100%.  

Questions:

1.     What are the annual payments for years 1 to 15?

2.     What is remaining balance at the end of each year?

3.     What are the interest payment and principal payment for years 1 to 15?