Question

Leann just sold a $10,000 par value bond for $9,800. The bond interest rate was 8% 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 9% per year compounded quarterly. Determine the price she paid when she purchased the bond.

Answer 1

ANSWER:

Coupon payment = par value * interest rate / payments per year = 10,000 * 8% / 2 = 200

no of payments in 3 years = 3 * 4 = 12 quarters

i = 9% per year or 9% / 4 = 2.25% per quarter

Price when bond was purchased = selling price(p/f,i,n) + coupon payment(p/a,i,n)

Price when bond was purchased = 9,800(p/f,2.25%,12) + 200(p/a,2.25%,12)

Price when bond was purchased = 9,800 * 0.7657 + 200 * 10.41

Price when bond was purchased = 7,503.54 + 2,082.96

Price when bond was purchased = 9,586.50

so the price when bond was purchased is $9,586.50