Final answer:
The total return of the bond in dollars would be $1,125.81.
Step-by-step explanation:
The total return of the bond can be calculated by considering the yield to maturity and the change in interest rates. In this case, the bond has a 6.60 percent coupon rate and a 5.3 percent yield to maturity. The yield to maturity is the average annual return you can expect from the bond if held until maturity. If the yield to maturity increases to 6.0 percent after one year, it means that the bond's price will decrease. Assuming semiannual interest payments, the total return of the bond in dollars can be determined by considering the interest payments and the change in bond prices.
To calculate the total return, we need to determine the bond price at the beginning and end of the period. The bond pays semiannual interest, so the annual coupon payment is $1,000 * (6.60%) = $66. The number of coupon payments over 15 years is 15 * 2 = 30. The present value of the coupon payments can be calculated using the yield to maturity of 5.3 percent as the discount rate. Using the formula for the present value of an annuity, the present value of the coupon payments is:
PV = PMT * (1 - (1 + r)^-n) / r
Where PV is the present value, PMT is the annual coupon payment, r is the discount rate (yield to maturity/2), and n is the number of periods (30).
The present value of the coupon payments is $66 * (1 - (1 + 0.053/2)^-30) / (0.053/2) = $827.10.
The future value of the bond at maturity is $1,000, so the total return would be the difference between the future value and the present value of the coupon payments, plus the change in bond price. Assuming the bond price decreases due to the increase in yield to maturity, the change in bond price can be calculated using the formula:
Change in bond price = Initial bond price - Final bond price
Where the initial bond price is $1,000 and the final bond price is the present value of the future value at the new yield to maturity. The present value of the future value can be calculated using the new yield to maturity of 6.0 percent as the discount rate. Using the formula for the present value of a single future amount, the present value of the future value is:
PV = FV / (1 + r)^n
Where PV is the present value, FV is the future value ($1,000), r is the discount rate (6.0%/2), and n is the number of periods remaining until maturity (15 * 2 = 30). The present value of the future value is $1,000 / (1 + 0.06/2)^30 = $701.29.
So, the change in bond price would be $1,000 - $701.29 = $298.71.
Therefore, the total return of the bond in dollars would be the sum of the change in bond price ($298.71) and the present value of the coupon payments ($827.10), which is $298.71 + $827.10 = $1,125.81.