Final answer:
The price of a bond is calculated using the present value of its future coupon payments and face value, discounted by the current yield. For the provided bond with a 6% semiannual coupon rate, the bond's price can be found by discounting the $1,530 semiannual payments and $51,000 face value at the current yield of 6.9105%.
Step-by-step explanation:
To determine the price of a bond, we need to calculate the present value of the future coupon payments and the face value, discounted by the current yield. Since coupons are paid semiannually, the annual coupon rate should be divided by two, and the current yield should be applied semiannually as well.
Given:
Face value (FV) = $51,000
Semiannual coupon rate = 3% (Half of 6%)
Current yield = 6.9105%
Number of periods (n) = 12 (6 years * 2)
The semiannual coupon payment (C) is:
C = FV * Semiannual coupon rate = $51,000 * 0.03 = $1,530
The bond's price (P) is the sum of the present values of all future coupon payments and the face value:
P = C * [1 - (1 + r)^-n]/r + FV / (1 + r)^n
where 'r' is the semiannual current yield (6.9105% / 2).
The bond's realized maturity profile (rmp) is typically associated with a calculation involving the bond’s yield to maturity (YTM), which is different from the current yield and would require a different set of calculations.