Independent solution

How to solve this Discount Amortization Schedule question

Setup

Setup

Let d1 = 50 be the discount accumulated in the first coupon. Under effective-interest amortization, later increments compound at the bond yield.

dk=50(1+i)k−1d_k=50(1+i)^{k-1}

Model

Model

Sum the first eight increments and match the observed increase in book value.

20,491.51−20,000=50s8‾∣i20{,}491.51-20{,}000=50s_{\overline8|i}

Compute

Compute

Solving gives i = 5.80994%. Sum all twenty-five discount increments to reach redemption.

i=0.0580994i=0.0580994
C=20,000+50s25‾∣i=22,670.91C=20{,}000+50s_{\overline{25}|i}=22{,}670.91

Answer

Answer

The redemption value rounds to 22671, choice D.

C≈22,671(D)\boxed{C\approx22{,}671\quad\text{(D)}}

Calculator reproduction

BA II Plus keystrokes

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

  1. 8 · N; 0 · PV; 50 · +/− · PMT; 491.51 · FV; CPT · I/Y5.80994Then use N = 25 with the solved I/Y to accumulate the discount series.