Independent solution

How to solve this Bond Book Value and Discount Growth question

Setup

Setup

The quarterly coupon is 30.25. Relate the book value after coupon 4 to the value after coupon 19 by the book-value recursion.

Cq=2,500(0.0484)/4=30.25C_q=2{,}500(0.0484)/4=30.25
B19=B4(1+j)15−Cqs15‾∣jB_{19}=B_4(1+j)^{15}-C_qs_{\overline{15}|j}

Model

Model

Insert the two observed book values and solve for the quarterly yield j.

2,316.30=2,092.88(1+j)15−30.25s15‾∣j2{,}316.30=2{,}092.88(1+j)^{15}-30.25s_{\overline{15}|j}
j=0.02060006j=0.02060006

Compute

Compute

The coupon-20 discount increment is interest on B19 minus coupon. Later increments grow geometrically at one plus j.

d20=2,316.30j−30.25=17.46592d_{20}=2{,}316.30j-30.25=17.46592
d48=d20(1+j)28=30.91349d_{48}=d_{20}(1+j)^{28}=30.91349

Answer

Answer

The last discount accumulation is 30.91, choice D.

d48≈30.91(D)\boxed{d_{48}\approx30.91\quad\text{(D)}}

Calculator reproduction

BA II Plus keystrokes

Check END/BGN, period, sign, TVM, and cash-flow setup

  1. 15 · N; 2092.88 · PV; 30.25 · +/− · PMT; 2316.30 · +/− · FV; CPT · I/Y2.060006Signs may be reversed consistently; the result is the quarterly yield.