MATH1115 MATHEMATICS OF FINANCE WINTER2019 APPLICATION OF TVM: 1. You have borrowed $100,000 for the purchase of a new home. The local bank has offered you a borrowing rate of 6% compounded monthly for a 20 -year loan. s. How much are your monthly payments on this loan? b. How much of the 1st payment is being made towards the payment of interest and how much is being made towards the payment of the principle? c. You have made payments on your mortgage for 5 years ( 60 payments) and it is time to renegotiate your mortgage with the bank. What is the outstanding balance of your mortgage after you have made your 60th payment? d. How much interest was paid over the first 5 years? e. How much of the 61st payment is interest and how much is principal repayment? t. How much interest did you pay over the life of the mortgage? y. Create an amortization table for the first 3 payments. 2. An individual has decided that after retirement, they will require $2,500 per month for the 30 years of life after retirement at 65 . If interest rates are 7.5% compounded monthly, how much will this individual need to save per month if they are currently 25 years old. Assuming the first deposit occurs at the end of the first month. 2. A company is deciding between 2 mutually exclusive projects. Project Alpha will require an initial outflow of $2,000 and will generate $900 in revenue per year (assume end of year) for next 5 years. At the end of the project life the machine purchased for this project can be salvaged for $500. Project Beta will require an initial outflow of $3,000. It will generate annual revenues of $1,200 at the end of each year for the next 5 years. The machine used for project Beta has a salvage value of $100 at the end of 5 years. Which project should the company choose? Assume the discount rate is 12% compounded semiannually. 4. You would like to have $10,000 in your account in five years' time. How much money must you save each month to achieve your goals? Assume you can earn an interest of 6% compounded monthly. MATH1115 MATHEMATICS OF FINANCE WINTER2019 APPLICATION OF TVM: 1. You have borrowed $100,000 for the purchase of a new home. The local bank has offered you a borrowing rate of 6% compounded monthly for a 20 -year loan. s. How much are your monthly payments on this loan? b. How much of the 1st payment is being made towards the payment of interest and how much is being made towards the payment of the principle? c. You have made payments on your mortgage for 5 years ( 60 payments) and it is time to renegotiate your mortgage with the bank. What is the outstanding balance of your mortgage after you have made your 60th payment? d. How much interest was paid over the first 5 years? e. How much of the 61st payment is interest and how much is principal repayment? t. How much interest did you pay over the life of the mortgage? y. Create an amortization table for the first 3 payments. 2. An individual has decided that after retirement, they will require $2,500 per month for the 30 years of life after retirement at 65 . If interest rates are 7.5% compounded monthly, how much will this individual need to save per month if they are currently 25 years old. Assuming the first deposit occurs at the end of the first month. 2. A company is deciding between 2 mutually exclusive projects. Project Alpha will require an initial outflow of $2,000 and will generate $900 in revenue per year (assume end of year) for next 5 years. At the end of the project life the machine purchased for this project can be salvaged for $500. Project Beta will require an initial outflow of $3,000. It will generate annual revenues of $1,200 at the end of each year for the next 5 years. The machine used for project Beta has a salvage value of $100 at the end of 5 years. Which project should the company choose? Assume the discount rate is 12% compounded semiannually. 4. You would like to have $10,000 in your account in five years' time. How much money must you save each month to achieve your goals? Assume you can earn an interest of 6% compounded monthly
