Leann just sold a 10000 par value bond for 9800 The bond int

Leann just sold a $10,000 par value bond for $9,800. The bond interest rate was 7 % per year payable quarterly. Leann owned the bond for 3 years. The 1st interest payment she received was 3 months after she bought the bond. She sold it immediately after receiving her 12th interest payment. Leann’s yield on the bond was 11 % per year compounded quarterly. Determine the price she paid when she purchased the bond.

Solution

Quarterly coupon (C) = $10,000 x 7% x (3/12) = $175

Face value (F) = $10,000

Number of quarters held (N) = 3 x 4 = 12

Quarterly Yield (Y) = 11%/4 = 2.75%

If Price paid = P, then

Y = [C + (F - P) / N] / [(F + P) / 2)]

0.0275 = [175 + (10,000 - P) / 12] / [(10,000 + P) / 2]

0.0275 x [(10,000 + P) / 2] = [175 + (10,000 - P) / 12]

137.5 + 0.0138P = 175 + (10,000 - P) / 12

12 x (137.5 + 0.0138P) = 12 x 175 + (10,000 - P)

1,650 + 0.1656P = 2,100 + 10,000 - P

1.1656P = 10,450

P = 10,450 / 1.1656 = 8,965.34

Bond purchase price was $8,965.34.