Final answer:
Using the effective interest method and present value calculations, a two-year bond with an 8% interest rate would have the same value as its face value if discounted at 8%. When the discount rate rises to 11%, the bond's present value decreases. Similarly, a $10,000 bond yielding 6% would be worth $9,633.03 one year before maturity if the market interest rate is 9%.
Step-by-step explanation:
When assessing the value of a bond with the effective interest method, we use the time value of money to determine present value. For a $3,000 bond with an 8% interest rate, annual payments are $240. Using an 8% discount rate, the present value of the first year’s interest is calculated as $240/(1+0.08) = $222.22. The second year’s payment is both interest and principal, so $3,240 discounted at 8% for two years is $3,240/(1+0.08)^2 = $2,777.78. Summing these gives us the bond's present value at the 8% discount rate: $222.22 + $2,777.78 = $3,000, which makes sense as the bond's yield matches the discount rate.
If the discount rate increases to 11%, the calculations adjust to $240/(1+0.11) = $216.22 for the first year and $3,240/(1+0.11)^2 = $2,624.73 for the second year, totaling $216.22 + $2,624.73 = $2,840.95. This shows the bond's value decreases as the discount rate exceeds the bond's yield, reflecting increased market rates and reduced attractiveness of holding the bond at the previous rate.
Similarly, when considering whether to buy a $10,000 bond yielding 6% one year before maturity when market rates are at 9%, you'd pay less than the face value due to the change in interest rates. The bond will pay $600 in interest plus the $10,000 principle in one year, and at a 9% discount rate, the present value would be ($600 + $10,000) / (1+0.09) = $9,633.03, which is what you'd be willing to pay for the bond.