You just bought a bond with 8 years to maturity, 8% annual coupon rate with semi-annual coupon payments. The bond currently sells at par (the face value of the bond is 1000$). Assume that the yield curve is flat at an 8% stated annual yield (with semi-annual compounding) and remains constant for five years. You reinvest all cash flows in the first five years at this rate. However, starting at the beginning of the sixth year, the interest rate drops to 5% stated annual rate (with semi-annual compounding). What will be your effective annualized rate of return if you sell the bond 5 years from now (just after the drop in the interest rate)?

I know to find the answer I need the math below, but I do not know why to use those formulas or what those formulas are?

The future value of reinvested coupons in 4 years is

FV(Coupons) = (40/0.04)(1-(1/1.04^10) * (1.04)^10 = 480.24

The price of the bond in 4 years

B = (40/0.025)(1-(1/1.025^6) + (1000/1.025^6) = 1082.62

R = [(480.24 + 1082.62)/1000]^(1/5) - 1 = 9.34%

Answer rating: 100% (QA)

The formulas you provided are used to calculate the future value of reinvested coupons the price of ... View the full answer