Final Answer:
a. Principal amount: $12,000
Term: 3 years
Coupon rate: 5%
Coupon payment: $600
b. When the one-year interest rate is 3%, Arjay can expect the bond to be priced at approximately $12,527. At an 8% one-year interest rate, the expected bond price would be approximately $11,757. For a 10% one-year interest rate, the expected price would be approximately $11,578.
Step-by-step explanation:
a. The principal amount of Arjay's bond is the amount he paid initially, which is $12,000. The bond's term is 3 years, signifying the duration until maturity. The coupon rate, calculated as the annual coupon payment divided by the principal amount, is 5%. The coupon payment, which is the periodic interest payment the bondholder receives, is $600, calculated as 5% of $12,000.
b. To calculate the bond price under different one-year interest rates, we use the bond pricing formula. At a 3% one-year interest rate, the expected bond price is approximately $12,527. When the one-year interest rate rises to 8%, the bond's expected price drops to about $11,757. At a higher one-year interest rate of 10%, the bond price further decreases to around $11,578. These calculations involve discounting the future cash flows (coupon payments and face value) at the respective interest rates to find the present value of the bond.
The bond price moves inversely to prevailing interest rates; as interest rates increase, bond prices tend to decrease, and vice versa. When the one-year interest rates rise, the bond's fixed coupon payments become less attractive relative to the higher rates available in the market, causing the bond price to decline to align with the market's new interest rate.