Final answer:
Calculating the bond's price with a semiannual coupon rate and current yield involves determining the coupon payments and understanding the relationship between yield and price. With the provided rates, the price of the bond is calculated to be approximately $2,113.82, meaning it is trading at a premium due to higher coupon payments compared to the market yield.
Step-by-step explanation:
Calculating the Bond's Price
To calculate the bond's price given a semiannual coupon rate and a current yield, you must understand the relationship between the coupon payments, yield, and bond price. For a bond with a par value of $2,000 with 16 years to maturity, a semiannual coupon rate of 5.89%, and a current yield of 5.57%, the coupon payments would be calculated as follows: $2,000 * (5.89% / 2) = $58.90 per period. There are 32 periods because the bonds mature in 16 years and there are two periods per year.
The current yield is given by the annual coupon payment divided by the bond price. So, we can rearrange the formula to find the bond price: Bond Price = Annual Coupon Payment / Current Yield. Since the current yield is 5.57% annually, and the annual coupon payment is $117.80 ($58.90 * 2 periods), we get: Bond Price = $117.80 / 0.0557 = $2,113.82 approximately.
Thus, even though the current yield is slightly lower than the coupon rate, the bond price reflects the fact that it pays a higher coupon rate than currently available yields. This price indicates the bond is trading at a premium. When interest rates change, the bond price fluctuates to align the current yield with prevailing market rates.