4.7 Review Exercises

Chapter 4 Review Exercises

  1. A [latex]\$100,000[/latex] face value bond has a [latex]5.03\%[/latex] coupon. The bond is purchased when there were [latex]13.5[/latex] years to maturity and the yield to maturity was [latex]4.29\%[/latex].
    1. What is the purchase price of the bond?
    2. What is the premium or discount?
    Solution

    a. [latex]\$107,523.91[/latex]; b. Premium=[latex]\$7,523.91[/latex]

  2. Greg purchased a [latex]\$5,000[/latex] bond with a [latex]4.3\%[/latex] coupon when there was [latex]12[/latex] years to maturity and the yield to maturity was [latex]5.7\%[/latex]. Four years later, Greg sold the bond when the yield rate was [latex]3.9\%[/latex].
    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?
    Solution

    a. [latex]\$4,397.56[/latex]; b. Discount=[latex]\$602.44[/latex]; c. [latex]\$5,136.32[/latex]; d. Gain=[latex]\$738.76[/latex]

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

    a. [latex]\$61,302.61[/latex]; b. [latex]119.89\%[/latex]

  4. A [latex]\$35,000[/latex] bond with a [latex]7\%[/latex] coupon is purchased for [latex]132.92[/latex] when there was [latex]12[/latex] years to maturity. Calculate the yield rate.
    Solution

    [latex]3.6\%[/latex]

  5. An investor purchases a [latex]\$55,000[/latex] bond with a [latex]4\%[/latex] coupon for [latex]\$33,227.95[/latex] when there was [latex]10.5[/latex] years to maturity. After [latex]4[/latex] years, the investor sold the bond for [latex]\$60,231.63[/latex].
    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.
    Solution

    a. [latex]10.24\%[/latex] b. [latex]2.41\%[/latex]; c. [latex]20.66\%[/latex]

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

    a. [latex]\$16,469.68[/latex]; b. [latex]96.27\%[/latex]

  7. A [latex]\$6,500[/latex] bond with a [latex]6.7\%[/latex] coupon is purchased three years before maturity when the yield rate was [latex]8\%[/latex]. Construct the appropriate bond schedule for the bond.
    Solution
    Payment Number Bond Payment Interest on Book Value at Yield Accumulated Discount Book Value Remaining Discount to be Accumulated
    [latex]0[/latex] [latex]\$6,278.52[/latex] [latex]\$221.48[/latex]
    [latex]1[/latex] [latex]\$217.75[/latex] [latex]\$251.14[/latex] [latex]\$33.39[/latex] [latex]\$6,311.91[/latex] [latex]\$188.09[/latex]
    [latex]2[/latex] [latex]\$217.75[/latex] [latex]\$252.48[/latex] [latex]\$34.73[/latex] [latex]\$6,346.64[/latex] [latex]\$153.36[/latex]
    [latex]3[/latex] [latex]\$217.75[/latex] [latex]\$253.87[/latex] [latex]\$36.12[/latex] [latex]\$6,382.75[/latex] [latex]\$117.25[/latex]
    [latex]4[/latex] [latex]\$217.75[/latex] [latex]\$255.31[/latex] [latex]\$37.56[/latex] [latex]\$6,420.31[/latex] [latex]\$79.69[/latex]
    [latex]5[/latex] [latex]\$217.75[/latex] [latex]\$256.81[/latex] [latex]\$39.06[/latex] [latex]\$6,459.38[/latex] [latex]\$40.62[/latex]
    [latex]6[/latex] [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 [latex]\$4,000[/latex] bond with a [latex]5.2\%[/latex] coupon is purchase two years before maturity when the yield rate was [latex]3.7\%[/latex]. Construct the appropriate bond schedule for the bond.
    Solution
    Payment Number Bond Payment Interest on Book Value at Yield Amortized Premium Book Value Remaining Premium to be Amortized
    [latex]0[/latex] [latex]\$4,114.65[/latex] [latex]\$114.65[/latex]
    [latex]1[/latex] [latex]\$104[/latex] [latex]\$76.12[/latex] [latex]\$27.88[/latex] [latex]\$4,086.77[/latex] [latex]\$86.77[/latex]
    [latex]2[/latex] [latex]\$104[/latex] [latex]\$75.61[/latex] [latex]\$28.39[/latex] [latex]\$4,058.38[/latex] [latex]\$58.38[/latex]
    [latex]3[/latex] [latex]\$104[/latex] [latex]\$75.08[/latex] [latex]\$28.91[/latex] [latex]\$4,029.46[/latex] [latex]\$29.46[/latex]
    [latex]4[/latex] [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 [latex]\$62,000[/latex] face value bond carrying an [latex]8.88\%[/latex] 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 [latex]4.44\%[/latex].
    1. Calculate the flat price on the purchase date.
    2. Calculate the quoted price.
    Solution

    a. [latex]\$92,021.62[/latex]; b. [latex]\$90,899.55[/latex]

  10. A company with a [latex]\$150,000[/latex] debt establishes a sinking fund earning [latex]3.89\%[/latex] 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.
    Solution
    Payment Number Payment Interest Increase Balance Book Value
    [latex]9[/latex] [latex]\$3,085.78[/latex] [latex]\$248.41[/latex] [latex]\$3,334.19[/latex] [latex]\$28,877.23[/latex] [latex]\$121,122.77[/latex]
    [latex]10[/latex] [latex]\$3,085.78[/latex] [latex]\$280.83[/latex] [latex]\$3,366.61[/latex] [latex]\$32,243.84[/latex] [latex]\$117,756.16[/latex]
    [latex]11[/latex] [latex]\$3,085.78[/latex] [latex]\$313.57[/latex] [latex]\$3,399.35[/latex] [latex]\$35,643.19[/latex] [latex]\$114,356.81[/latex]
    [latex]12[/latex] [latex]\$3,085.78[/latex] [latex]\$346.63[/latex] [latex]\$3,432.41[/latex] [latex]\$39,075.60[/latex] [latex]\$110,924.40[/latex]
    [latex]39[/latex] [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]
    [latex]40[/latex] [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 [latex]\$300,000[/latex] face value bond with a [latex]4\%[/latex] coupon is issued with [latex]15[/latex] years to maturity. A sinking fund earning [latex]6.35\%[/latex] 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 [latex]17^{th}[/latex] payment?
    4. What is the book value of the fund after the [latex]9^{th}[/latex] payment?
    5. What is the balance in the fund after three years?
    6. By how much does the fund increase with the [latex]23^{rd}[/latex] payment?
    7. On which payment does fund reach the half way point to the [latex]\$300,000[/latex]?
    8. By how much does the fund increase in the [latex]10^{th}[/latex] year?
    9. How much interest does the fund earn in the [latex]12^{th}[/latex] year?
    10. What is the book value of the fund after the [latex]6^{th}[/latex] year?
    Solution

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

  12. A company borrowed [latex]\$400,000[/latex] and set up a sinking fund earning [latex]3.7\%[/latex] 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?
    Solution

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

Attribution

“7.7 Review Exercises” from Business and Financial Mathematics by Valerie Watts is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License, except where otherwise noted.

“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.

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Financial Math - Math 1175 Copyright © 2023 by Margaret Dancy is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License, except where otherwise noted.

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