Final answer:
The price of a $5000 bond with a 6.4% coupon rate will increase if the yield to maturity decreases by 0.8%, as bonds become more valuable when interest rates fall, increasing their price above face value.
Step-by-step explanation:
If the yield to maturity on a $5000 bond with a coupon rate of 6.4% paid semi-annually decreases by 0.8%, the price of the bond will increase. This happens because as the bond's yield decreases, it becomes more valuable since its promised cash flows are discounted at a lower rate, making the present value of those cash flows higher.
When interest rates fall, bonds with higher coupon rates become more attractive to investors because they offer higher returns compared to the new bonds being issued at current lower rates. Consequently, the demand for the high-coupon bond increases, driving up its price. In essence, when the market interest rates decrease, the value of existing bonds that have a higher interest rate compared to the new market rate rises because they are offering higher income streams to their holders.
Using the provided example, bonds with a coupon rate higher than the current market rate will be sold for more than their face value if the interest rates decrease, just as a bond with an 8% coupon rate becomes more valuable if the market rate declines from what it was when the bond was issued.