Question text 5Marks You purchased an annual coupon bond one year ago that had nine years remaining to maturity at that time. The coupon rate was 10%, and the par value was $1,000. At the time you purchased the bond, the yield to maturity was 8%. Annual coupons are paid at the end of each year. Today you sold the bond after receiving the first annual coupon payment and the yield to maturity continued to be 8%. Your annual total rate of return on holding the bond for that year would have been:Answer 13[select: , 8.00%., 7.82%., -7.00%., 11.95%., -6.88%] Selling price for the bond is: Answer 14[select: , $1,114.93, $1,124.94, $1,000, $948.75, $1,100]Notes Report question issue Question 4 Notes

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BlackTom AI · Accepted Answer

To tackle this problem, I will break down the key pieces and work through them step by step before identifying the final values.
First, recall the bond details: par value = $1,000, annual coupon rate = 10%, so annual coupon = $100. When you bought the bond, the yield to maturity (YTM) was 8%. One year has passed, you received the first $100 coupon, and you sell the bond right after that. The YTM at the time of sale remains 8%.
Next, determine the selling price. After one year, the bond has 8 years remaining to maturity. The price today (just after receiving the coupon) is the present value of 8 years of $100 coupons plus the $1,000 face value repaid at the end of year 8, all discounted at the new/continuing YTM of 8%. Mathematically:
- PV of coupons = 100 × a-angle-8 at 8% = 100 × [1 − (1.08)^−8] / 0.08
- PV of redemption = 1000 × (1.08)^−8
Using approximate present-value factors, (1.08)^−8 ≈ 0.540, so a-angle-8 ≈ (1 − 0.540)/0.08 ≈ 5.75, giving PV of coupons ≈ 575 and PV of redemption ≈ 540. Therefore, selling price ≈ 575 + 540 = $1,115 (specifically about $1,114.93 in precise calculation).
Now, compute the total return for the holding year. The holder received the $100 coupon during the year and then realized a capital loss of (selling price − initial purchase price).
- What was the initial purchase price? It was the price of the bond when YTM was 8% with 9 years to maturity. So: PV = 100 × a-angle-9 at 8% + 1000 × (1.08)^−9. Here (1.08)^−9 ≈ 0.500, and a-angle-9 ≈ (1 − 0.500)/0.08 = 6.25. Thus, initial price ≈ 100 × 6.25 + 1000 × 0.500 = 625 + 500 = $1,125.
- Price change over the year = selling price − purchase price ≈ 1,115 − 1,125 = −$10.
- Total dollar return over the year = coupon received + price change = $100 + (−$10) = $90.
- Total rate of return = $90 / $1,125 ≈ 0.08 = 8.0%.
With these calculations, the annual total rate of return for the holding year is 8.00%, and the selling price is about $1,114.93.
Now, addressing the other answer choices for the first blank:
- 7.82%: This would imply a slightly different sum of coupon and price-change relative to the initial price, but the precise cash flows and price path at a constant 8% yield yield exactly 8.0% return, not 7.82%.
- −7.00%: A negative return would require a large loss offsetting the coupon, which does not align with the calculated price movement and received coupon when yield stays at 8%.
- 11.95%: This would overstate the return; it would correspond to a much larger capital gain or coupon impact than actually realized when yield remains constant and price moves from about $1,125 to about $1,114 after one year.
- −6.88%: Similar to the negative options, this would imply a sizable loss relative to the coupon, incorrect given the actual cash flows and price trajectory under the same yield.
Regarding the second blank for selling price:
- $1,114.93 (the precise value): This matches the present value calculation for 8 years of $100 coupons plus $1,000 redemption discounted at 8%, yielding approximately $1,114.93.
- $1,114.93 is more accurate than $1,115 rounded, and other options like $1,124.94, $1,000, $948.75, or $1,100 do not align with the 8% yield scenario for 8 remaining years, either overvaluing or undervaluing the present value of future cash flows.
- The $1,125 figure would be the purchase price, not the selling price one year later after one coupon has been paid and with yield unchanged; thus, it is not the correct selling price.
In summary, the computed numbers fit together consistently: selling price ≈ $1,114.93 and total annual return = 8.00%.

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