HullFund7eCh04ProblemSolutions
CHAPTER 4
Interest Rates
Practice Questions
Problem 4.8.
The cash prices of six-month and one-year Treasury bills are 94.0 and 89.0. A 1.5-year bond that will pay coupons of $4 every six months currently sells for $94.84. A two-year bond that will pay coupons of $5 every six months currently sells for $97.12. Calculate the six-month, one-year, 1.5-year, and two-year zero rates.
The 6-month Treasury bill provides a return of in six months. This is per annum with semiannual compounding or per annum with continuous compounding. The 12-month rate is with annual compounding or with continuous compounding.
For the 1 year bond we must have where is the 1 year zero rate. It follows that or 11.5%. For the 2-year bond we must have where is the 2-year zero rate. It follows that or 11.3%.
Problem 4.9.
What rate of interest with continuous compounding is equivalent to 15% per annum with monthly compounding?
The rate of interest is where: i.e.,
The rate of interest is therefore 14.91% per annum.
Problem 4.10.
A deposit account pays 12% per annum with continuous compounding, but interest is actually paid quarterly. How much interest will be paid each quarter on a $10,000 deposit?
The equivalent rate of interest with quarterly compounding is where or
The amount of interest paid each quarter is therefore: or $304.55.
Problem 4.11.
Suppose that 6-month, 12-month, 18-month, 24-month, and 30-month zero rates are 4%, 4.2%, 4.4%, 4.6%, and 4.8% per annum with continuous compounding respectively. Estimate the cash price of a bond with a face value of 100 that will mature in 30 months and pays a coupon of 4% per annum semiannually.
The bond pays $2 in 6, 12, 18, and 24 months, and $102 in 30 months. The cash price is
Problem 4.12.
A three-year bond provides a coupon of 8% semiannually and has a cash price of 104. What is the bond’s yield?
The bond pays $4 in 6, 12, 18, 24, and 30 months, and $104 in 36 months. The bond
Interest Rates
Practice Questions
Problem 4.8.
The cash prices of six-month and one-year Treasury bills are 94.0 and 89.0. A 1.5-year bond that will pay coupons of $4 every six months currently sells for $94.84. A two-year bond that will pay coupons of $5 every six months currently sells for $97.12. Calculate the six-month, one-year, 1.5-year, and two-year zero rates.
The 6-month Treasury bill provides a return of in six months. This is per annum with semiannual compounding or per annum with continuous compounding. The 12-month rate is with annual compounding or with continuous compounding.
For the 1 year bond we must have where is the 1 year zero rate. It follows that or 11.5%. For the 2-year bond we must have where is the 2-year zero rate. It follows that or 11.3%.
Problem 4.9.
What rate of interest with continuous compounding is equivalent to 15% per annum with monthly compounding?
The rate of interest is where: i.e.,
The rate of interest is therefore 14.91% per annum.
Problem 4.10.
A deposit account pays 12% per annum with continuous compounding, but interest is actually paid quarterly. How much interest will be paid each quarter on a $10,000 deposit?
The equivalent rate of interest with quarterly compounding is where or
The amount of interest paid each quarter is therefore: or $304.55.
Problem 4.11.
Suppose that 6-month, 12-month, 18-month, 24-month, and 30-month zero rates are 4%, 4.2%, 4.4%, 4.6%, and 4.8% per annum with continuous compounding respectively. Estimate the cash price of a bond with a face value of 100 that will mature in 30 months and pays a coupon of 4% per annum semiannually.
The bond pays $2 in 6, 12, 18, and 24 months, and $102 in 30 months. The cash price is
Problem 4.12.
A three-year bond provides a coupon of 8% semiannually and has a cash price of 104. What is the bond’s yield?
The bond pays $4 in 6, 12, 18, 24, and 30 months, and $104 in 36 months. The bond