Final answer:
The bond price is calculated using the present value of its future cash flows given the yield to maturity. A zero coupon bond's price is the present value of its par value. As interest rates rise, the price of the existing bond falls to align with new, higher-yielding bonds.
Step-by-step explanation:
Bond Pricing Calculations
The student's question involves calculating bond prices given various conditions. To find the price of the bond with a 2 percent coupon and 5 percent yield to maturity, we need to use the present value formula for each cash flow and sum them up. This bond makes semiannual payments, so there will be six coupon payments of $10 each ($1,000 * 2% / 2), and a final payment of $1,000 at maturity. Using the semiannual yield to maturity of 2.5% (5% / 2), the present value of each cash flow is calculated and summed to get the bond price.
For a zero coupon bond, there are no coupon payments; it only pays its par value at maturity. To find its price, we discount the $1,000 back to the present using the yield to maturity.
If the interest rate rises to 8 percent, the yield to maturity increases, thus decreasing the bond's price. This is because the bond's fixed coupon payments are less attractive compared to new bonds issued at the higher prevailing rates, so the bond's price adjusts downward to offer a competitive yield. We recalculate the bond price using the new semiannual yield to maturity of 4% (8% / 2).
Throughout these calculations, the key principles are the present value formula and understanding that a bond's price reflects the present discounted value of its future cash flows in light of current interest rates.