4 This assignment covers material from Units 10 to 12 in the Mathematics 244 Study Guide. It is due after Unit 12 in the Study Guide is completed. Total Marks = 100 1. Business Mathematics A debt of $12,000 is to be amortized by equal payments at the end of each month for five years. Interest is charged at 24% compounded monthly. a. What is the size of each payment? b. Construct a partial amortization schedule to show the outstanding principal after the second payment. (4 marks) c. What interest and principal is included in the 35th payment? (4 marks) (2 marks) 1 2. 2 A debt of $25,000 is to be amortized by making payments of $1500 at the end of each month. The interest rate is 12% compounded monthly. a. What is the outstanding principal after the 12th payment? (6 marks) b. What is the size of the final payment? (8 marks) Mathematics 244 / Assignment Manual 3. Business Mathematics A $10,000 loan will be repaid at the end of five years by a sinking fund that earns 12% compounded semi-annually. The interest rate on the loan is 8% compounded semi-annually. a. What is the total cost to the debtor at the end of each six months? (2 marks) b. Find the sinking fund interest income for the 10th period. (4 marks) c. What is the book value of the debt at the end of the 10th period? (2 marks) 3 4 4. A $500, 8% bond is purchased on February 1, 2004, to yield 10% compounded semi-annually. The interest on the bond is payable on February 1 and August 1 each year. Find the purchase price if the bond is redeemable at face value on February 1, 2014. (6 marks) 5. A bond with a face value of $1000 and 15 years remaining until maturity pays a coupon rate of 10% semi-annually. Calculate its yield to maturity if it is priced at $1100. (4 marks) Mathematics 244 / Assignment Manual 6. Business Mathematics A $1000, 9.25% compounded semi-annually coupon bond issued January 6, 1979, matures on January 6, 2004. What was its market price on August 8, 1981 when the required yield to maturity was 17% compounded semi-annually? (4 marks) 5 7. 6 A couple took out a mortgage for $135,000 on a home they are purchasing. The mortgage has an amortization period of 20 years and a term of five years. The interest rate is 8% compounded semi-annually. a. What was the size of the monthly mortgage payments in the first five years of the mortgage? (4 marks) b. At the end of the first five years, the mortgage was renewed at 12% compounded semi-annually. What was the size of the new mortgage payment? (6 marks) Mathematics 244 / Assignment Manual c. Business Mathematics Suppose the couple decide to make weekly payments on their renewed mortgage. What is the size of their weekly payments? (2 marks) 7 8. 8 A company is considering installing a new machine that initially costs $800,000, with a further outlay of $100,000 at the end of each of years three and six for maintenance. The salvage value is $75,000 at the end of 10 years. Expected returns are $125,000 for each of the first three years, and $175,000 for each of the remaining seven years. Should the company install the new machine if money is worth 9% compounded annually? (12 marks) Mathematics 244 / Assignment Manual 9. Business Mathematics A firm is evaluating two machines. The first costs $250,000 and will require annual maintenance of $30,000 per year for 10 years. At the end of 10 years, the salvage value will be $75,000. The second machine costs $400,000, and will require maintenance of $225,000 at the end of the fifth year. The salvage value after 10 years will be $175,000. Which machine should the firm select if interest is 8.5% compounded annually? (10 marks) 9 10. A new product will cost $350,000 to launch. Expected profits are $55,000, $65,000, and $100,000 in years two to four, and $120,000 in each of years five to seven. What is the IRR of the new product launch? Would you recommend that the company proceed, based on their cost of capital of 10%? (20 marks) 10 Mathematics 244 / Assignment Manual a. Assignment 4 This assignment covers material from Units 10 to 12 in the Mathematics 244 Study Guide. It is due after Unit 12 in the Study Guide is completed. Total Marks 100 1. Business Mathematics A debt of $12,000 is to be amortized by equal payments at the end of each month for five years. Interest is charged at 24% compounded monthly. a. What is the size of each payment?(2 marks) b. Construct a partial amortization schedule to show the outstanding principal after the second payment.(4 marks) c. What interest and principal is included in the 35th payment? (4 marks) 1 d. A debt of $25,000 is to be amortized by making payments of $1500 at the end of each month. The interest rate is 12% compounded monthly. 2 a. What is the outstanding principal after the 12th payment? (6 marks) e. What is the size of the final payment?(8 marks) Mathematics 244 / Assignment Manual f. A $10,000 loan will be repaid at the end of five years by a sinking fund that earns 12% compounded semiannually. The interest rate on the loan is 8% compounded semiannually. a. What is the total cost to the debtor at the end of each six months? (2 marks) g. Find the sinking fund interest income for the 10th period. (4 marks) h. What is the book value of the debt at the end of the 10th period? (2 marks) Business Mathematics 3 4 Mathematics 244 / Assignment Manual Business Mathematics i. A $500, 8% bond is purchased on February 1, 2004, to yield 10% compounded semiannually. The interest on the bond is payable on February 1 and August 1 each year. Find the purchase price if the bond is redeemable at face value on February 1, 2014.(6 marks) j. A bond with a face value of $1000 and 15 years remaining until maturity pays a coupon rate of 10% semiannually. Calculate its yield to maturity if it is priced at $1100.(4 marks) 5 k. A $1000, 9.25% compounded semiannually coupon bond issued January 6, 1979, matures on January 6, 2004. What was its market price on August 8, 1981 when the required yield to maturity was 17% compounded semiannually?(4 marks) 6 Mathematics 244 / Assignment Manual l. A couple took out a mortgage for $135,000 on a home they are purchasing. The mortgage has an amortization period of 20 years and a term of five years. The interest rate is 8% compounded semi annually. a. What was the size of the monthly mortgage payments in the first five years of the mortgage?(4 marks) m. At the end of the first five years, the mortgage was renewed at 12% compounded semiannually. What was the size of the new mortgage payment?(6 marks) Business Mathematics 7 n. Suppose the couple decide to make weekly payments on their renewed mortgage. What is the size of their weekly payments? (2 marks) 8 Mathematics 244 / Assignment Manual o. Business Mathematics A company is considering installing a new machine that initially costs $800,000, with a further outlay of $100,000 at the end of each of years three and six for maintenance. The salvage value is $75,000 at the end of 10 years. Expected returns are $125,000 for each of the first three years, and $175,000 for each of the remaining seven years. Should the company install the new machine if money is worth 9% compounded annually?(12 marks) 9 p. A firm is evaluating two machines. The first costs $250,000 and will require annual maintenance of $30,000 per year for 10 years. At the end of 10 years, the salvage value will be $75,000. The second machine costs $400,000, and will require maintenance of $225,000 at the end of the fifth year. The salvage value after 10 years will be $175,000. Which machine should the firm select if interest is 8.5% compounded annually?(10 marks) 10 Mathematics 244 / Assignment Manual q. A new product will cost $350,000 to launch. Expected profits are $55,000, $65,000, and $100,000 in years two to four, and $120,000 in each of years five to seven. What is the IRR of the new product launch? Would you recommend that the company proceed, based on their cost of capital of 10%?(20 marks) Business Mathematics 11