Independent solution

How to solve this Coupon Reinvestment Yield question

Setup

Setup

At maturity, redemption plus accumulated coupons must equal the stated target 1,000(1.07)¹⁰. There are twenty semiannual coupons of 30.

1000(1.07)10=30s20‾∣ j+10001000(1.07)^{10}=30s_{\overline{20}|\,j}+1000

Model

Model

Solve the accumulated-value annuity equation for the semiannual coupon-reinvestment rate j. Then convert j to an annual effective rate rather than merely doubling it.

s20‾∣ j=32.238s_{\overline{20}|\,j}=32.238

Compute

Compute

The annuity factor requires j = 0.0476. Thus (1 + j)² − 1 = 0.0975, or 9.75% annually.

j=0.0476,i=(1+j)2−1=0.0975j=0.0476,\quad i=(1+j)^2-1=0.0975

Answer

Answer

The calculation gives 9.75% for coupon reinvestment yield, matching published choice B.

i=9.75%(B)\boxed{i=9.75\%\quad\text{(B)}}