economics Leann just sold a 10,000 par value bond for 9,800. The bond interest r
ID: 1189056 • Letter: E
Question
economics Leann just sold a 10,000 par value bond for 9,800. The bond interest rate was 4.5% 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. Carry all interim calculations to 5 decimal places and then round your final answer to the nearest dollar. The tolerance is plusminus5.Explanation / Answer
Annual bond interest = $10,000 x 4.5% = $450 per year = $112.5 per quarter
Leann received total 12 quarterly coupons, hence total $(112.5 x 12) = $1,350 as coupon payment in 3 years (Her investment term).
Hence, if the purchase price of the bond is P, then
Selling price, $9,800 = P x [1 + (0.125 / 4)]4 x 3
$9,800 = P x (1.03125)12
P = $9,800 / (1.03125)12 = $6,774
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