Answer:To calculate the bond's yield to maturity (YTM), we need to solve for the interest rate that will make the present value of all the cash flows (coupon payments and face value) equal to the bond's current price.
Given:
Coupon Rate (C) = 8.8% (annual coupon rate)
Semiannual Coupon Rate (c) = C / 2 = 8.8% / 2 = 4.4%
Number of periods (n) = 10 years = 20 semiannual periods
Face Value (FV) = $1,000
Bond Current Price (P) = $1,035.38
a. To calculate the bond's yield to maturity (YTM):
We can use the formula for the present value of a bond with semiannual coupon payments:
P = (c/FV) * (1 - (1+r)^(-n)) / r + FV / (1+r)^n
Where r is the interest rate per period.
By substituting the given values and solving for r, we can find the yield to maturity (APR with semiannual compounding).
P = $1,035.38
c = 4.4% = 0.044
FV = $1,000
n = 20 periods
Using this information, you can solve for r (the yield to maturity).
b. To determine the bond's price when the yield to maturity changes to 9.1% APR, we can use the same formula as above, but with the new yield to maturity:
P = (c/FV) * (1 - (1+r)^(-n)) / r + FV / (1+r)^n
We can solve for P by substituting the new yield to maturity, which is 9.1% APR, into the equation.
Explanation: