Question

A bond is issued with a coupon of 6% paid annually, a maturity of 35 years, and a yield to maturity of 9%. What rate of return will be earned by an investor who purchases the bond for $683.00 and holds it for 1 year if the bond’s yield to maturity at the end of the year is 10%? (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places. Negative amount should be indicated by a minus sign.)

Answer 1

Price after 1 year = PV of Coupon Payment + PV of Maturity Value

= [Periodic Coupon Payment * {(1 - (1 + r)^-n) / r}] + [Face Value / (1 + r)^n]

= [6%*$1,000} * {(1 - (1 + 0.10)^-(35-1)) / 0.10}] + [$1,000 / {1 + 0.10}^(35-1)]

= [$60 * {0.9609 / 0.10}] + [$1,000 / 25.5477]

= [$60 * 9.6086] + $39.14

= $576.51 + $39.14 = $615.66

Rate of Return = [Price after 1 year - Purchase Price + Coupon Payment] / Purchase Price

= [$615.66 - $683 + $60] / $683 = -$7.34 / $683 = -0.0108, or -1.08%