A 10-year bond pays a 5% annual coupon on a $1,000 face value. If market interest rates rise to 8%, what happens to the bond's price?
AIt rises above $1,000, because the coupon payments are now more valuable relative to new bonds
BIt stays at $1,000, because the face value is a contractual guarantee
CIt falls below $1,000, because investors can earn 8% on new bonds and will only buy this 5% bond at a discount
DIt cannot change until the bond matures
When market rates exceed the coupon rate, existing bonds must offer a compensating discount to attract buyers. Discounting the fixed cash flows (5% × $1,000 = $50 per year plus $1,000 at maturity) at 8% yields a present value below $1,000. The bond trades at a discount so that its effective return matches the 8% available in the market.
Question 2 True / False
A bond's coupon rate and its yield to maturity are generally the same number.
TTrue
FFalse
Answer: False
The coupon rate is fixed at issuance and determines the dollar amount of coupon payments. The yield to maturity reflects current market interest rates and changes continuously with supply and demand. They are equal only when the bond trades at exactly par (face value) — which happens only when market rates happen to equal the coupon rate, rarely the case after the initial issuance date.
Question 3 Short Answer
Explain intuitively, without using a formula, why a bond's price and prevailing interest rates move in opposite directions.
Think about your answer, then reveal below.
Model answer: A bond's cash flows are fixed in dollar terms. When market rates rise, investors can earn more from new bonds, so they will only buy the old bond at a lower price — a discount that compensates them for receiving below-market coupons.
Think of it as competition. If you own a bond paying $50/year and new bonds now pay $80/year on the same face value, no rational investor pays full price for yours. The price must fall until the effective yield (coupon divided by price, simplified) equals the market rate. The math of present-value discounting formalizes this intuition: discounting fixed cash flows at a higher rate always produces a lower present value.