1. a) You are planning to buy a car worth $20,000. Which of the two deals described below would you choose, both with a 48-month term?
• the dealer offers to take 10% off the price, and lend you the balance at an APR of 9%, monthly compounding.
• the dealer offers to lend you $20,000 (with no discount) at an APR of 3%, monthly compounding.
b) You have just taken a 25-year mortgage loan for $200,000. The annual percentage rate on the loan is 8%, compounded semi-annually, and payments will be made monthly.
• Estimate your monthly payments.
• Suppose that exactly 4 years from now you renegotiate your mortgage loan. If rates at that time on the remaining life of your mortgage are 6%, what will be your new monthly payment? How much have you paid in interest to this point, and how much in principal?
2. a) You are 35 years old today and are considering your retirement needs. You expect to retire at age 65 (in 30 years) and you plan to live to 99. You want to buy a house costing $300,000 on your 65th birthday and your living expenses will be $30,000 a year after that (starting at the end of year 65 and continuing through the end of year 99, 35 years), assume an annual interest rate of 8%, annual compounding:
• How much will you need to have saved by your retirement date to be able to afford this course of action?
• Alternatively, suppose you already have $50,000 in savings today. If you can invest money at 8% a year, how much would you need to save at the end of each year for the next 30 years to be able to afford this retirement plan?
b) In 30 years, you plan to set up a fellowship fund for Carleton university that pays out $100,000 per year in perpetuity with an annually compounded discount rate of 5%. In order to set up the fund in 30 years, how much do you need to save each year (starting this year) assuming you can get a semi-annually compounded return of 10% on your savings for the next 30 years?
3. You have been hired to run a pension fund for Mackay Inc, a small manufacturing firm.
The firm currently has Gh¢5 million in the fund and expects to have cash inflows of $2 million a year for the first 5 years followed by cash outflows of $ 3 million a year for the next 5 years. Assume that interest rates are at 8%.
a) How much money will be left in the fund at the end of the tenth year?
b) If you were required to pay a perpetuity after the tenth year (starting in year 11 and going through infinity) out of the balance left in the pension fund, how much could you afford to pay?
4. a) You would like to purchase a house that costs $250,000 and you make a 10% down payment. You borrow the remaining at an APR of 12%, semi-annually compounded, to be repaid in monthly installments for the next 25 years. How much do you pay every month?
Suppose you decide to increase your monthly payment by an additional 1/12th of the present payment (i.e., you divide an additional monthly mortgage payment equally over the 12 months), what is the time required to repay the loan if you make that additional monthly payment every year?
b) Your child was just born and you are planning for his/her college education. Based on your wonderful experience in Finance at Carleton, you decide to send your child to Carleton University as well. You anticipate the annual tuition at that time to be $50,000 per year for the four years of college. You plan on making equal deposits on your child's birthdays for age one through seventeen inclusive to fund their education. Assume the first tuition payment is due exactly 18 years from today and the expected return is 10% APR with quarterly compounding over this period. Calculate the annual deposit.
c) Suppose you are analyzing the following possible cash flows: Year 1 CF = $100; Years 2 and 3 CFs = $200; Years 4 and 5 CFs = $300. The required discount rate is 7%.
i) What is the value of the cash flows at year 5?
ii) What is the value of the cash flows today?
iii) What is the value of the cash flows at year 3?
5. Suppose your parents wish to buy a house whose current market value is $150,000. They have approached a loan officer at the Bank of Nova Scotia who offers them 25-year mortgage financing for 75% of the purchase price at a rate of 6.75%. Payments are to be made on a monthly basis even though the bank is required by Canadian laws to compound the interest semiannually.
(a) What are the effective annual and monthly rates of interest on the loan?
(b) Assuming the loan payments are due at the end of each month:
(i) determine the size of the monthly loan payments
(ii) determine the amortization schedule for the first 3 months
(iii) determine the principal outstanding at the end of the 5th year.