1. A $2,500 14% six-year bond with annual coupons is bought to yield 6% annually. The price is $3,432.26. Find its clean and dirty values at the end of each quarter of the forth year after issue, by the practical method and also by the theoretical method.
2. As in Problem (6.5,5) we are concerned with three-year $1,000 6% bond with semiannual coupons and redemption amount $1,040. Suppose that the bond was purchased on January 1, 2000. Make a chart showing the theoretical and practical dirty and clean values of the bond at the end of each quarter if the bond was purchased at the discount to yield a nominal rate of 7% convertible semiannually. Use the "30/360" basis for accounting.
3. Miguel purchases a $22,000 9% fifteen-year par-value bond having annual coupons for a price to provide a 7% annual yield if the bond is held to maturity. Five years later, just after the receipt of the fifth coupon, he sells it at a price to provide the new purchaser a yield to maturity of 8%. Find the difference between Miguel's book value B5 and the invoice price. What was Miguel's actual yield for the five-year period?
4. A $1,000 seven-year 6% bond with semiannual coupons is redeemable for $1,065. It was originally purchased at issue for $970. It is sold after 45 months for $995. Find the accrued interest by the practical method and again by the theoretical method using the new yield to maturity.
5. Jiayin purchases a ten-year 8% $62,000 par-value bond with annual coupons eighty months after its issue. The original purchaser paid a price to yield 8.5% if the bond was held until maturity, as does Jiayin. Compute the accrued interest by the theoretical method at 8.5% and also by the practical method. Find the split of the accrued interest by the theoretical method at 8.5% into interest and principal.
6. Dominique LeBlanc is the owner of a new ten-year %50,000 8% par-value bond with Bermuda option and annual coupons. Allowable call dates are at the end of years 6 through 10, and the call premium at the end of year n is $300(10-n). Dominique purchased the bond for $51,248.(a) Find the lowest yield the Dominique may receive during the period she holds the bond as well as the highest.(b) Upon receipt, Dominique deposits each coupon and the redemption amount in an account earning 6%. Find the lowest yield that Diminique may receive during the ten-year period and also the highest.
7. Drew purchases a new $20,000 9% twelve-year bond with semiannual coupons. If held to maturity, the redemption payment is $18,500, and the bond would yield Mr. Jefferson 8% convertible semiannually. The bond has an American option and is callable beginning at three years from issue. If the bond is called at time T, where T is measured in coupon periods, the call premium is p(T). Find an expression for the amount p(T) so that Mr. Jefferson yield is 8% no matter when the bond is called.
8. Sofia purchases a $6,000 7% eight-year par-value bond with annual coupons. If held to maturity, her yield is 6.6%. The bond is callable at the end of two years for $6,300 and at the end of years five, six, and seven for $6,200.(a) Find sofia's minimal yield for the period she holds the bond.(b) If the bond is called prior to maturity, Sofia has made arrangements to have the redemption amount accumulate in her i=5.5% savings account until the end of the eight years. What is her minimal yield for the eight-year period of the bond? (Coupons are not reinvested.)