Question

Leann just sold a $10,000 par value bond for $9,800. The bond interest rate was 6.5% 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 12.5% per year compounded quarterly. Determine the price she paid when she purchased the bond

Answer 1

Quarterly bond interest = $10,000 x 6.5% x (1/4) = $162.5

Quarterly yield = 12.5%/4 = 3.125%

Number of quarters = 12

Therefore,

Purchase price ($) = Present value of bond coupon payments + Present value of selling price

= 162.5 x P/A(3.125%, 12) + 9,800 x P/F(3.125%, 12)

= 162.5 x 9.8801** + 9,800 x 0.6912**

= 1,605.52 + 6,773.76

= 8,379.28

**P/F(3.125%, 12) = (1.03125)^-12 = 0.6912

**P/A(3.125%, 12) = [1 - (1.03125)^-12] / 0.03125 = (1 - 0.6912) / 0.03125 = 0.3088 / 0.03125 = 9.8801