Independent solution

How to solve this Premium and Discount Bonds question

Setup

Setup

Let C be the redemption amount. The semiannual coupon is 4% of C, and the half-year yield is 5%.

K=0.04CK=0.04C
j=0.10/2=0.05j=0.10/2=0.05
N=20N=20

Model

Model

Price equals redemption amount plus the present value of the coupon-rate shortfall relative to yield.

962.92=C+(0.04C−0.05C)a20‾∣0.05962.92=C+(0.04C-0.05C)a_{\overline{20}|0.05}

Compute

Compute

The annuity factor is 12.462210, so the price coefficient is 0.875378 and C is approximately 1,100.

962.92=0.8753779C962.92=0.8753779C
C=1100.0049C=1100.0049

Answer

Answer

Purchase discount is redemption minus price, or 137.08, which rounds to choice E.

C−962.92≈137(E)\boxed{C-962.92\approx137\quad\text{(E)}}

Calculator reproduction

BA II Plus keystrokes

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

  1. 2ND · CLR TVMTVM worksheet clearedFirst price one unit of redemption; use half-year periods and END mode.
  2. 20 · NN = 20
  3. 5 · I/YI/Y = 5
  4. 0.04 · PMTPMT = 0.04
  5. 1 · FVFV = 1
  6. CPT · PVPV = -0.8753779Then divide 962.92 by 0.8753779 to recover C = 1,100.00.