a) You have just joined the investment banking firm of H-O & Co. They have offered you two different salary arrangements. You can have $75,000 per year at the end of each the next two years, or you can have $55,000 per year at the end of each of the next two years along with a $30,000 signing bonus today. If the interest rate is 12% annual, compounded monthly, which is a better offer?

b) 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 lends 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. Question 2:

You have been hired to run a pension fund for 2018 MBA Cohort Inc., a small manufacturing firm based in Ottawa. The firm currently has $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, all at the end of each year. Assume that interest rates are 8% per annum, annually compounded.

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 (i.e., ordinary perpetuity starting in year 11 and going through to infinity) out of the amount left in the pension fund, how much could you afford to pay?

Question 3:

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 age 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, i.e. for 35 years). Assume an annual interest rate of 8%, annual compounding:

i) How much will you need to have saved by your retirement date to be able to afford this course of action?

ii) 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) You bought a house a year ago for $250,000, borrowing $200,000 at quoted rate of 12% annual from TD bank, with semi-annual compounding, on a 25-year loan. Interest rates have since come down to 9%. You can refinance your mortgage at this new rate. i) How much are your monthly payments on your current loan (at 12%)?

ii) How would your monthly payments change if you could refinance your mortgage at 9% (with a 24-year term loan)?

iii) Suppose you kept your monthly payments at the original amount found above at 12%, but refinanced at 9%, how long would it take you to pay off your mortgage?

Question 4:

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 an annual 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 semi-annually.

(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 amount 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. How much interest has been paid over the 5 years?