Three years ago, you purchased a bond for $974.69. The bond had three years to maturity, a coupon rate of 8%, paid annually, and a face value of $1,000. Each year, you reinvested all coupon interest at the prevailing reinvestment rate shown in the table below. Today is the bond's maturity date. What is your realized compound yield on the bond? $\begin{array}{lc}
\text { Time } & \text { Prevalling Reinvestment Rate } \
0 \text { (purchase date) } & 6.0 \% \
1 & 7.2\% \
2&9.4\% \
3 \text { (maturity date) }&8.2\% \

\end{array}$

Question

Three years ago, you purchased a bond for $974.69. The bond had three years to maturity, a coupon rate of 8%, paid annually, and a face value of $1,000. Each year, you reinvested all coupon interest at the prevailing reinvestment rate shown in the table below. Today is the bond's maturity date. What is your realized compound yield on the bond? $\begin{array}{lc}
\text { Time } & \text { Prevalling Reinvestment Rate } \
0 \text { (purchase date) } & 6.0 \% \
1  & 7.2\% \
2&9.4\% \
3 \text { (maturity date) }&8.2\% \

\end{array}$

Quizplus · Accepted Answer

The realized compound yield can be calculated by finding the total value of the investment at maturity and then calculating the annual compound growth rate that would result in this final amount from the initial investment. 1. Calculate the coupon payment: 8% of $1,000 = $80.2. Reinvest the first coupon at 7.2% for two years: $80(1 + 0.072)^2 = $91.57.3. Reinvest the second coupon at 9.4% for one year: $80(1 + 0.094) = $87.52.4. The third coupon is not reinvested, so it remains $80.5. Add the face value of the bond at maturity: $1,000.Total value at maturity = $91.57 + $87.52 + $80 + $1,000 = $1,259.09.6. Calculate the annual compound growth rate: $(\frac{1259.09}{974.69})^{1/3} - 1 = 8.97\%$.Therefore, the realized compound yield on the bond is 8.97%.

Three Years Ago, You Purchased a Bond for $974 A) 643% B) 7

Three Years Ago, You Purchased a Bond for $974 A) 643%
B) 7