# 4.7 Review Exercises

## Chapter 4 Review Exercises

- 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].
- What is the purchase price of the bond?
- What is the premium or discount?

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

- 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].
- What did Greg pay to purchase the bond?
- What is the premium or discount?
- At what price did Greg sell the bond?
- 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]

- 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].
- Calculate the flat price on the purchase date.
- Calculate the quoted price as a percentage of face value.

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

- 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]

- 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].
- Calculate the yield to maturity on the purchase date.
- Calculate the yield to maturity on the selling date.
- 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]

- 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].
- Calculate the flat price on the purchase date.
- Calculate the quoted price as a percentage of face value.

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

- 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] - 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] - 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].
- Calculate the flat price on the purchase date.
- Calculate the quoted price.

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

- 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] - 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.
- Calculate sinking fund payment.
- What is the periodic expense of the debt?
- How much interest does the fund earn with the [latex]17^{th}[/latex] payment?
- What is the book value of the fund after the [latex]9^{th}[/latex] payment?
- What is the balance in the fund after three years?
- By how much does the fund increase with the [latex]23^{rd}[/latex] payment?
- On which payment does fund reach the half way point to the [latex]\$300,000[/latex]?
- By how much does the fund increase in the [latex]10^{th}[/latex] year?
- How much interest does the fund earn in the [latex]12^{th}[/latex] year?
- 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]

- 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.
- Calculate sinking fund payment.
- What is the balance in the fund at the half way point?
- How much interest does the fund earn in year five?
- Calculate the amount by which the sinking fund increased in year two.
- What is the book value in the fund at the end of year three?
- What is the final balance in the fund?
- What is the total increase in the fund?
- 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.