Problem 1 (6 marks)

Bob, a retired librarian from SMU, would like to donate some money to his alma mater to endow a $5,000 annual scholarship.  The first scholarship will be awarded at the beginning of year 8.  The University will manage the funds and expects to earn 3.5% per year., with annual compounding.

1. How much will Bob have to donate today to ensure the endowment fund never runs out of money? (3 marks)
2. If Bob wants to increase the amount of the scholarship by 1% per year, how much will he need to deposit today? (3 marks)

Problem 2 (6 marks)

You are an investment advisor and have been referred the following new client.  Rosella is 80 years old and needs to move to an assisted living care facility.  Her health is not great, so you are using a life expectancy of 10 years.  She has investments totalling $300,000 but they are mostly in low yielding savings accounts (her last advisor told her this was the least risky option).  Her pension income amounts to $2,000 per month (this excludes any income from her investments).  Rosella has found several beautiful places to live but the monthly cost is quite high, and she doesn’t know if she can afford any of them.  Rosella wants to know the maximum amount she can afford to spend per month (payment at beginning of month) if she has no other monthly expenses. Assume you can invest her $300,000 and earn 5% compounded monthly.

Problem 3 (9 marks)

Nick Suzuki, 23, newly named captain of the Montreal Canadiens, recently signed an 8-year, $63 million contract ($7,875,000 per year for 8 years, with equal installments paid at the end of each month).  If Nick spends only $20,000 per month over the life of his contract, investing the rest into an investment paying 5% compounded quarterly, how much will he have available to spend every month if he retires at the end of his contract and lives to age 80? (Assume he continues to earn 5% compounded quarterly on his funds).

Problem 4 (6 marks)

After living in residence for a year, Jess has decided to move into an apartment for the remaining 3 years of her degree.  She has found a nice apartment that will cost $1000 per month, payable at the start of each month.  Rent for the first and last month must be paid in advance up front.  How much money will Jess need to have in her account today to be sure she will always have enough for rent. Her bank account pays 4.5% APR with monthly compounding.

Problem 5 (15 marks):

You are considering the following 3 investments, each with an upfront cost of $45,000 today.  Which would you choose?  Show your work to support your answer.

1. $5,000 at the end of each year for 15 years with the first payment one year from today (end of year 1). APR of 6% with semi-annual compounding
2. $5,200 for 16 years with the first payment 2 years from today. APR of 7% with annual compounding
3. $4,400 at the end of each for 17 years with the first payment one year from today (end of year 1). APR of 5% with monthly compounding

Problem 6 (14 marks)

Nineteen-year-old Spanish tennis sensation, Carlos Alcaraz, beat 23-year-old Norwegian Casper Ruud in 4 sets to win the 2022 US Open, collecting a prize of $2.6 million, bringing his total year to date winnings in 2022 to $7.4 million.

5. If Carlos decided to invest half of his US Open winnings, plus $250,000 from his future quarterly earnings (starting next quarter) into an investment earning 5.25% compounded quarterly for the next 10 years, how much would he have at the end of 10 years. (9 marks)
6. If Carlos uses the accumulated funds from (a) to donate to his favourite charities, how much could he donate annually at the end of each year, if he wanted to continue his donations for 20 years? (Assume funds are kept in the same investment) (5 marks)

Problem 7 (9 marks)

You always enjoyed a Starbucks Iced Oat Latte every day (5 days a week) on your way to work at a cost of $5.70 including tax.  At lunch you’d pick up a sandwich and coffee from the bakery at your office building for an all-in cost of $12.50.  You were tired after your long commute so you would order out three nights a week at a cost of about $20 per meal.  You have been trying to save for a trip but never had any extra cash to invest.  Then COVID hit and you had to work from home.   Now that you are back at your office, you are bringing your own coffee, packing your own lunch, and only eating out occasionally.  You estimate you are spending only about 10% weekly of what you were spending pre-covid and saving the rest.  If you invest your weekly savings into a mutual fund with an annual rate of return (APR) of 6.5%, compounded weekly,

1. a) How much will you have accumulated at the end of two years to fund your trip? (7 marks)
2. b) How much would you have to deposit in one lump sum today to have the same amount in your savings at the end of two years? (2 marks)

Problem 8 (19 marks)

You have saved $50,000 to use as a down payment for some property and to build a home. The home is in a prime building location that has trees and a stream running through the property.  The clearing of the land and the building of the house will cost a total $650,000.

1. How much money will you need to borrow through a mortgage for your home? (1 mark)
2. The bank offers to finance your purchase with a 25-year amortized mortgage with a 5-year term at 4.125%. If you want to make monthly payments on this loan (end of each month), how much will each payment be? (5 marks)
3. Prepare an amortization schedule for your first 3 mortgage payments (3 marks)
4. At the end of the 5-year term, the mortgage terms allow you pay down an additional 10% of the original mortgage amount and the terms allow you to change the remaining amortization period. You have saved the additional money to pay down the amount of the loan (additional 10% of the original mortgage amount) and you want to shorten the remaining amortization by 5 years. The bank will fund your mortgage at 4.50% for a 5-year term. If you are to make monthly, what are your new monthly payments for the mortgage after the renegotiation? (9 marks)
5. What would happen to your payment if monthly mortgage payments were made at the beginning of the month instead of the end? (Briefly explain – no calculation required) (1 mark)