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University of Connecticut
Math 3615: Financial Mathematics Problems
Fall 2008
9/9/08 Examples – Module 4
- You pay 10,000 to purchase a newly-issued 10-year bond with a face amount of 10, that pays semi-annual coupons at an 8% annual rate. As each coupon payment is received, you deposit it into a savings account that pays a 4% nominal interest rate, convertible semi-annually.
At the end of 10 years, after you receive the final coupon payment and the redemption value of the bond (10,000), what annual effective rate of return have you earned on your investment of 10,000? 7.026%
Suppose that you had paid 10,500 for the bond. What would your annual effective rate of return be in that case? 6.505%
- A 20-year bond has a face amount (and redemption value) of 1,000 and 6% annual coupons.
Five years after its issue date, Bonnie purchases the bond at a price that will provide a yield to maturity of 7% (an annual effective rate). What is the purchase price? 908.
Bonnie holds the bond for 5 years and then sells it to Bennie, who buys the bond at a price that will yield 7.5% to maturity. Assuming that Bonnie adjusted the bond’s “book value” each year based on a 7% yield to maturity, was the bond’s sale price more or less than its book value on the date of sale? By how much? 32.
What annual effective rate of return did Bonnie earn on her investment in this bond over the 5 years that she owned it? 6.371%
- A 20-year bond issued on September 1, 2008, is callable at par at any time after 5 years. The bond pays semi-annual coupons and its (annual) coupon rate is 7%. The bond is purchased on the issue date at a price that will provide a yield to maturity of 6% (convertible semi-annually). What is the bond’s “yield to first call”? 4.400%
What is the earliest coupon date that the bond could be called and still provide the original purchaser a yield of at least 5% (convertible semi-annually)? 9/1/
- A 20-year bond with a 10,000 par value and a 10,000 redemption value was issued on July 1, 2002. The bond pays semi-annual coupons at a 6% (annual) coupon rate.
The bond is purchased on September 8, 2008, at a price that will provide the buyer a 7.2% yield to maturity (convertible semi-annually).
What is the total price paid for the bond on September 8, 2008? 9,071. (Use the “actual days” method to determine the price.)
What is the accrued interest on the bond on the purchase date? 112. (Use the “simple interest” method with “actual days” to determine the accrued interest.)
What is the quoted price of this bond on the purchase date? 8,959.
