272 Chapter 6 Investments
- Sybil owns several U.S. Treasury Bonds (bonds issued by the U.S. federal government). On the radio she hears
a well-known fi nancial commentator predict that interest rates are going to rise signifi cantly over the next few months.
Would this be good news or bad news for the market value of her investments?
E. Zero Coupon Bonds
Recall that a zero coupon bond is a note with a fi xed future value and maturity date, on which the borrower makes no
payments until maturity, and on which compound interest is earned. Zero coupon bonds resemble simple discount notes,
except that the interest is calculated by using compound interest instead of simple discount. For example, to fi nd the selling
price for a $10,000 zero coupon bond with 5 years to maturity and an interest rate of 7.2% compounded daily (bankers’ rule):
$10,000 PV(1.0002)1,800
$10,000 PV(1.433277823)
PV $6,977.01
So the zero coupon bond would sell for $6,977.01 today.
Exercises 18–22 deal with zero coupon bonds.
- Find the selling price for a zero coupon bond with 8 years to maturity and a $100,000 maturity value if:
a. The interest rate is 7.7% compounded monthly
b. The interest rate is 5.5% compounded daily.
c. The effective interest rate is 6.3%.- Find the selling price for a zero coupon bond with 3½ years to maturity and a $10,000 maturity value if
a. The interest rate is 6.25% compounded quarterly
b. The interest rate is 7.35% compounded daily (bankers’ rule)
c. The APY is 12.72%- Find the selling price for a zero coupon bond with 28 years to maturity and a $10,000 face value if:
a. The effective rate is 5.25%
b. The effective rate is 6.83%
c. The effective rate is 12.43%- Suppose that you buy a zero coupon bond, with the intention of selling it on the secondary market before it matures.
On the morning business news you hear that interest rates are going up. Would this be good news or bad news for you?
Explain. (Hint: Look at what happened in Exercises 19 and 20.) - Tom and Jerry both invested in zero coupon bonds. Tom bought a bond with 30 years to maturity, while Jerry bought
a bond with 2 years to maturity. After both bought, interest rates dropped dramatically. Who would be happier, Tom or
Jerry? Whose investment was riskier? (Hint: Compare Exercise 19 to 20. In which case did the changes in interest rates
make a bigger difference in the bond prices?)
F. Bonds and CAGR
- Eighteen years ago, Porshia’s grandmother bought her a $1,000 face value savings bond for $500. Today, she can cash
this bond in for $1,514.67. What is the effective interest rate earned by this bond?