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1.a) Consider an annuity of 6 cash flows of $5,000 payable annually. If the interest rate is 7 per cent per annum, what is the value of this annuity today if the first cash flow is to be paid immediately? [8 marks]

3.  b) You are considering the purchase of a home for $700,000. You have available a deposit of $100,000. The bank will lend you money at 7 per cent per annum compounded monthly over a period up to 20 years. If you borrow the required funds over 20 years, what are the monthly repayments? After two years, how much do you still ow the bank? What is the interest component of the 25^th repayment? [7 marks]

2. How does private banking intersect with money laundering? How can bankers safe-guard their institutions to avoid becoming involved in shady financial transactions through their private banking operations?

3.A family friend is planning her retirement from work in the U.S. She is 62 years old right now (time () and has the choice of taking her Social Security (a public pension program) according to the following schedule (first payment noted in parentheses): I. Early retirement at age 62 (month 0) $1,300 per month for life II. Regular retirement at age 67 (month 60) $1,800 per month for life III. Delayed retirement at age 70 (month 96) $2,300 per month for life If her expected life expectancy is 92 years old (exactly), what are the present values of the choices? (Assume r = 4% (annual)) 4. (a) If you will be making equal deposits into a retirement account for 20 years (with each payment at the end of the year), how much must you deposit each year if the account earns 8% compounded annually and you wish the account to grow to $5,000,000 after 40 years (in time 40)? (b) How does your answer to part (a) change if the account pays interest compounded monthly at an annual rate of 8%? Note: use monthly compounding for all calculations. 5. (a) You belong to an unusual pension plan because your retirement payments will continue forever (and will go to your descendants after you die). If you will receive $48,000 per year at the end of each year starting 40 years from now (i.e., the first payment is in time 40), what is the present value of your retirement plan if the discount rate is 5%? (b) How does your answer to part (a) change if you will receive $4,000 per month every month forever (in perpetuity) starting 40 years from today (the first payment is in time period 480) and you compound monthly?