Independent solution

How to solve this Accumulation of Bond Discount question

Setup

Setup

The first discount accumulation is 50. Successive amounts grow by one plus the yield, so cumulative discount through coupon k is 50 times s-angle-k.

Bk−20,000=50sk‾∣iB_k-20{,}000=50s_{\overline k|i}

Model

Model

Use the two stated book values to eliminate the scale 50.

491.51=50s8‾∣i491.51=50s_{\overline8|i}
1,263.74=50s16‾∣i1{,}263.74=50s_{\overline{16}|i}

Compute

Compute

The annuity ratio yields the eight-year accumulation factor. Extend cumulative discount to coupon 25.

(1+i)8=1,263.74491.51−1=1.5711379(1+i)^8=\frac{1{,}263.74}{491.51}-1=1.5711379
i=0.0581002i=0.0581002
50s25‾∣i=2,670.9450s_{\overline{25}|i}=2{,}670.94

Answer

Answer

Add the total accumulated discount to purchase price to obtain redemption 22671, choice D.

C=20,000+2,670.94≈22,671(D)\boxed{C=20{,}000+2{,}670.94\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/Y5.80994This solves 50 times s-angle-8 equals 491.51.