Tristan Sandino was given a 20-year bond when he was twelve years old and would like to sell it on his 21st birthday. The bond has a coupon rate of 4.8% and was purchased for $580. Tristan receives interest checks every six months. If Tristan sells the bond for $1,040, less brokerage fees of $28, what will be his yield during ownership? (Assume the bond is sold just after receiving the 18th interest check.) Round your answer to the nearest tenth of a percent.
To calculate the yield during ownership of the bond, we need to determine the total interest received and the total cost of the bond.
First, let's calculate the total interest received over the 18 interest check periods:
Number of interest checks per year = 2 (checks received every 6 months)
Number of years from age 12 to 21 = 9 years
Total interest checks received = Number of interest checks per year * Number of years
= 2 * 9
= 18 checks
Next, we'll calculate the total interest received:
Coupon rate = 4.8%
Face value of the bond = $580 (purchase price)
Interest payment per check = Coupon rate * Face value of the bond
= 4.8% * $580
= $27.84 (rounded to the nearest cent)
Total interest received = Interest payment per check * Number of interest checks received
= $27.84 * 18
= $501.12 (rounded to the nearest cent)
Now, let's calculate the total cost of the bond:
Sale price of the bond = $1,040
Brokerage fees = $28
Total cost of the bond = Sale price of the bond - Brokerage fees
= $1,040 - $28
= $1,012
Finally, we can calculate the yield during ownership:
Yield during ownership = (Total interest received / Total cost of the bond) * 100%
= ($501.12 / $1,012) * 100%
= 49.51% (rounded to the nearest tenth of a percent)
Therefore, Tristan's yield during ownership of the bond is approximately 49.5%.
To calculate Tristan's yield during ownership, we need to determine the total interest he received throughout the bond's ownership and divide it by the total cost of the bond, including brokerage fees.
First, let's calculate the total interest received. Tristan receives interest checks every six months, so the bond's term of 20 years equals 40 six-month periods.
The coupon rate of the bond is 4.8%, which means Tristan will receive 4.8% of the bond's face value as interest every six months. To find the bond's face value, we need to find the price Tristan paid for it.
Given that the bond's price was $580, and the coupon rate is 4.8%, we can calculate the face value using the following formula:
Face Value = Bond Price / (1 + Coupon Rate/2)^(Number of Periods)
Face Value = $580 / (1 + 4.8%/2)^(40)
Evaluating the expression:
Face Value = $580 / (1 + 0.048/2)^(40)
= $580 / (1.024)^(40)
= $580 / (1.471518)
Face Value ≈ $393.66
Since Tristan's bond paid interest every six months, the total interest received is:
Total Interest = Face Value * Coupon Rate/2 * Number of Periods
Total Interest = $393.66 * 4.8%/2 * 40
= $9,449.92
Now, let's calculate the total cost of the bond, including brokerage fees:
Total Cost = Bond Price + Brokerage Fees
Total Cost = $580 + $28
= $608
Finally, we can calculate the yield during ownership:
Yield = (Total Interest / Total Cost) * 100
Yield = ($9,449.92 / $608) * 100
≈ 1554.273%
Rounded to the nearest tenth of a percent, Tristan's yield during ownership is approximately 1554.3%.