Independent solution

How to solve this Bond Discount Amortization question

Setup

Setup

For discount amortization K, the amount recognized with m periods remaining is Kvᵐ. Apply that relation to the two quoted accrual amounts.

194.82=Kv26,306.69=Kv21194.82=Kv^{26},\quad306.69=Kv^{21}

Model

Model

Their ratio gives v⁵ = 194.82/306.69, hence i = 9.5%. Back-substitution gives K = 2,062.53.

v5=194.82/306.69=0.63523⟹i=0.095v^5=194.82/306.69=0.63523\Longrightarrow i=0.095

Compute

Compute

The original discount is the present value of forty level amortization amounts K, namely K times a-angle-40 at 9.5%. This equals 21,135.

K=194.82(1.095)26=2062.53,D=Ka40‾∣ 0.095=21135K=194.82(1.095)^{26}=2062.53,\quad D=Ka_{\overline{40}|\,0.095}=21135

Answer

Answer

The calculation gives 21,135 for bond discount amortization, matching published choice E.

D=21135(E)\boxed{D=21135\quad\text{(E)}}