7.7 Review Exercises

1. A $100,000 face value bond has a 5.03% coupon.  The bond is purchased when there was 13.5 years to maturity and the yield to maturity was 4.29%.
   1. What is the purchase price of the bond?
   2. What is the premium or discount?
   Click to see Answer

   a. $107,523.91; b. Premium=$7,523.91

    

2. Greg purchased a $5,000 bond with a 4.3% coupon when there was 12 years to maturity and the yield to maturity was 5.7%. Four years later, Greg sold the bond when the yield rate was 3.9%.
   1. What did Greg pay to purchase the bond?
   2. What is the premium or discount?
   3. At what price did Greg sell the bond?
   4. What was Greg’s gain or loss on the sale of the bond?
   Click to see Answer

   a. $4,397.56; b. Discount=$602.44; c. $5,136.32; d. Gain=$738.76

    

3. A 25-year, $50,000 bond with a 5.75% coupon was issued on June 1, 2008. The bond was purchased on November 21, 2019 when the yield to maturity was 3.85%.
   1. Calculate the flat price on the purchase date.
   2. Calculate the quoted price as a percentage of face value.
   Click to see Answer

   a. $61,302.61; b. 119.89%

    

4. A $35,000 bond with a 7% coupon is purchased for 132.92 when there was 12 years to maturity. Calculate the yield rate.
   
   Click to see Answer

   3.6%

    

5. An investor purchases a $55,000 bond with a 4% coupon for $33,227.95 when there was 10.5 years to maturity. After 4 years, the investor sold the bond for $60,231.63.
   1. Calculate the yield to maturity on the purchase date.
   2. Calculate the yield to maturity on the selling date.
   3. Calculate the investor’s rate of return when the bond was sold.
   Click to see Answer

   a. 10.24% b. 2.41%; c. 20.66%

    

6. A $17,000 bond with a 3.8% coupon has a maturity date of October 1, 2035. The bond is purchased on May 30, 2023 when the yield to maturity was 4.19%.
   1. Calculate the flat price on the purchase date.
   2. Calculate the quoted price as a percentage of face value.
   Click to see Answer

   a. $16,469.68; b. 96.27%

    

7. A $6,500 bond with a 6.7% coupon is purchased three years before maturity when the yield rate was 8%. Construct the appropriate bond schedule for the bond.
   
   Click to see Answer

   Payment Number	Bond Payment	Interest on Book Value at Yield	Accumulated Discount	Book Value	Remaining Discount to be Accumulated
   0				[latex]\$6,278.52[/latex]	[latex]\$221.48[/latex]
   1	[latex]\$217.75[/latex]	[latex]\$251.14[/latex]	[latex]\$33.39[/latex]	[latex]\$6,311.91[/latex]	[latex]\$188.09[/latex]
   2	[latex]\$217.75[/latex]	[latex]\$252.48[/latex]	[latex]\$34.73[/latex]	[latex]\$6,346.64[/latex]	[latex]\$153.36[/latex]
   3	[latex]\$217.75[/latex]	[latex]\$253.87[/latex]	[latex]\$36.12[/latex]	[latex]\$6,382.75[/latex]	[latex]\$117.25[/latex]
   4	[latex]\$217.75[/latex]	[latex]\$255.31[/latex]	[latex]\$37.56[/latex]	[latex]\$6,420.31[/latex]	[latex]\$79.69[/latex]
   5	[latex]\$217.75[/latex]	[latex]\$256.81[/latex]	[latex]\$39.06[/latex]	[latex]\$6,459.38[/latex]	[latex]\$40.62[/latex]
   6	[latex]\$217.75[/latex]	[latex]\$258.38[/latex]	[latex]\$40.63[/latex]	[latex]\$6,500[/latex]	[latex]\$0[/latex]
   Totals	[latex]\$1,306.50[/latex]	[latex]\$1,527.98[/latex]	[latex]\$221.48[/latex]

    

8. A $4,000 bond with a 5.2% coupon is purchase two years before maturity when the yield rate was 3.7%. Construct the appropriate bond schedule for the bond.
   
   Click to see Answer

   Payment Number	Bond Payment	Interest on Book Value at Yield	Amortized Premium	Book Value	Remaining Premium to be Amortized
   0				[latex]\$4,114.65[/latex]	[latex]\$114.65[/latex]
   1	[latex]\$104[/latex]	[latex]\$76.12[/latex]	[latex]\$27.88[/latex]	[latex]\$4,086.77[/latex]	[latex]\$86.77[/latex]
   2	[latex]\$104[/latex]	[latex]\$75.61[/latex]	[latex]\$28.39[/latex]	[latex]\$4,058.38[/latex]	[latex]\$58.38[/latex]
   3	[latex]\$104[/latex]	[latex]\$75.08[/latex]	[latex]\$28.91[/latex]	[latex]\$4,029.46[/latex]	[latex]\$29.46[/latex]
   4	[latex]\$104[/latex]	[latex]\$74.54[/latex]	[latex]\$29.46[/latex]	[latex]\$4,000[/latex]	[latex]\$0[/latex]
   Totals	[latex]\$416[/latex]	[latex]\$301.35[/latex]	[latex]\$114.65[/latex]

    

9. A $62,000 face value bond carrying an 8.88% coupon is purchased on July 15, 2023. The bond matures on November 1,2037. At the time of purchase, the market rate on the bond was 4.44%.
   1. Calculate the flat price on the purchase date.
   2. Calculate the quoted price.
   Click to see Answer

   a. $92,021.62; b. $90,899.55

    

10. A company with a $150,000 debt establishes a sinking fund earning 3.89% compounded quarterly to retire the debt in full in ten years. The company makes quarterly payments into the sinking fund. Construct a partial sinking fund schedule showing the details of the payments in year three, the last two payments and the totals.
    
    Click to see Answer

    Payment Number	Payment	Interest	Increase	Balance	Book Value
    9	[latex]\$3,085.78[/latex]	[latex]\$248.41[/latex]	[latex]\$3,334.19[/latex]	[latex]\$28,877.23[/latex]	[latex]\$121,122.77[/latex]
    10	[latex]\$3,085.78[/latex]	[latex]\$280.83[/latex]	[latex]\$3,366.61[/latex]	[latex]\$32,243.84[/latex]	[latex]\$117,756.16[/latex]
    11	[latex]\$3,085.78[/latex]	[latex]\$313.57[/latex]	[latex]\$3,399.35[/latex]	[latex]\$35,643.19[/latex]	[latex]\$114,356.81[/latex]
    12	[latex]\$3,085.78[/latex]	[latex]\$346.63[/latex]	[latex]\$3,432.41[/latex]	[latex]\$39,075.60[/latex]	[latex]\$110,924.40[/latex]
    39	[latex]\$3,085.78[/latex]	[latex]\$1,371.64[/latex]	[latex]\$4,457.42[/latex]	[latex]\$145,499.62[/latex]	[latex]\$4,500.38[/latex]
    40	[latex]\$3,085.78[/latex]	[latex]\$1,414.98[/latex]	[latex]\$4,500.76[/latex]	[latex]\$150,000.38[/latex]	[latex]-\$0.38[/latex]
    Totals	[latex]\$123,431.20[/latex]	[latex]\$26,569.18[/latex]	[latex]\$150,000.38[/latex]

     

11. A $300,000 face value bond with a 4% coupon is issued with 15 years to maturity. A sinking fund earning 6.35% compounded semi-annually is set-up to accumulate the face value of the bonds.
    1. Calculate sinking fund payment.
    2. What is the periodic expense of the debt?
    3. How much interest does the fund earn with the 17th payment?
    4. What is the book value of the fund after the 9th payment?
    5. What is the balance in the fund after three years?
    6. By how much does the fund increase with the 23rd payment?
    7. On which payment does fund reach the half way point to the $300,000?
    8. By how much does the fund increase in the 10th year?
    9. How much interest does the fund earn in the 12th year?
    10. What is the book value of the fund after the 6th year?
    Click to see Answer

    a. $6,129.04; b. $12,129.04; c. $3,977.07; d. $237,288.64; e. $39,819.74; f. $12,190.77; g. 19; h. $21,857.64; i. $12,510.51; j. $212,146.63

     

12. A company borrowed $400,000 and set up a sinking fund earning 3.7% compounded semi-annually to retire the debt in seven years. The company made monthly deposits into the fund and rounded the payment up to the next dollar.
    1. Calculate sinking fund payment.
    2. What is the balance in the fund at the half way point?
    3. How much interest does the fund earn in year five?
    4. Calculate the amount by which the sinking fund increased in year two.
    5. What is the book value in the fund at the end of year three?
    6. What is the final balance in the fund?
    7. What is the total increase in the fund?
    8. What is the total amount of interest accumulated by the fund?
    Click to see Answer

    a. $4,184; b. $187,214.25; c. $8,918.61; d. $52,968.39; e. $241,023.63; f. $400,060.56; g. $400,060.56; i. $48,604.56;

Attribution

“Chapter 14 Summary” from Business Math: A Step-by-Step Handbook (2021B) by J. Olivier and Lyryx Learning Inc. through a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License unless otherwise noted.