# 7.7 Review Exercises

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

**Click to see Answer**a. $107,523.91; b. Premium=$7,523.91

- 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%.
- 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?

**Click to see Answer**a. $4,397.56; b. Discount=$602.44; c. $5,136.32; d. Gain=$738.76

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

**Click to see Answer**a. $61,302.61; b. 119.89%

- 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%

- 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.
- 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.

**Click to see Answer**a. 10.24% b. 2.41%; c. 20.66%

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

**Click to see Answer**a. $16,469.68; b. 96.27%

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

**Click to see Answer**a. $92,021.62; b. $90,899.55

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

- 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.
- 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?

**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.