Problem #1 (8 marks)Quicken Loans, the Detroit based mortgage lender, with the backing of Warren Buffet’s Berkshire Hathaway has offered $1 billion to anyone who fills out a perfect 2014 NCAA men’s basketball tournament bracket(guesses the winners for each of 64 games). The $1 billion is paid in 40 annual payments or you can take a lump sum of $500 million. What annual interest rate was used to determine the present value of the $1 billion prize?Problem #2 (20 marks)Michael wants to save in order to buy a house in 4 years which he estimates will cost $225,000. He has several sources of funds:.His parents will give him $1,000 per quarter starting in 3 months, which will be deposited into an account paying 5% compounded quarterly..He will receive $5,000 from his Aunt’s estate in one year’s time which will be deposited into the same account as above..He currently has $15,000 cash in a bank account (same as above)..He will take out a mortgage at the time of purchase on which he’ll make monthly payments of $1,000 over a 20 year amortization. He expects the interest rate on the mortgage at the time to be 4%.a)Calculate how much more Michael will need to have in 4 years in order to be able to purchase the house.b)To make up the shortfall, Michael will make monthly contributions to his investment account which earns 6%compounded annually. How much must he save each month to have enough to buy the house in 4 years’ time?Problem #3 (9 marks)Dawson borrows $75,000 for three years from the bank to purchase asailboat. This is an amortized loan with equal payments each month. The loan is fully paid off with the final payment. The quoted interest rate (APR) is 9% per year with monthly compounding. Assuming you make all of your payments on time:a)What is the outstanding balance on the loan right after you have made your 30th payment?b)What portion of the 31st payment is principal?Problem #4 (12 marks)Ben and Cassie are buying their first house. They can afford to pay $1,000 per month for the payment. The bank will lend them 75% of the purchase price of the house they purchase, at an annual rate of 5% for a four year term. The mortgage will be amortized over 25 years. a)?What is the most they can pay for a new house?b) ?Ben remembers from finance class that the shorter the amortization period, the less total interest you will pay. Calculate how much interest they would save if they made monthly payments over a 20 year amortization rather than a 25 year amortization.Problem #5 (12 marks)You are currently 25 years old and want to start saving for your retirement. You start off very determined and put aside $5,000 every year, starting one year from now, for 10 years. Finally, you get sick of saving and spend all your salary but leave your savings (balance plus earned interest) untouched for another 20 years when you retire. Assume interest rates are 7% compounded semi-annually while you are saving,but drop to 6% compounded quarterly after that.a) ?How much will you be able to draw a year when you retire at 55 assuming your first withdrawal occurs at the end of your retirement year if you estimate you will live for 25 years after retirement?b) ?How will your answer change if you start receiving funds at the beginning of the year instead of the end of the year?Problem #6 (4 marks)A rich relative has bequeathed you a payment of $1,000 one year from now. Each year after that, you will receive a payment on the anniversary of the last payment that is 8% larger than the previous payment. This pattern of payments will go on forever. If the interest rate is 12% per year:a)What is today’s value of the bequest?b)What is the value of the bequest immediately after the first payment is made?Problem #7 (6 marks)You just settled an insurance claim. The settlement calls for increasing payments over a 6-year period. The first payment will be paid one year from now in the amount of $40,000. The following payments will increase by 5 percent annually. What is the value of this settlement to you today if you can earn 7.5 percent (compounded annually) on your investments?Problem #8 (4 marks)Archie’s Aeronautics would like to buy some additional land and build a new training facility. The anticipated total cost is $12.4 million. The CEO of the firm is quite conservative and will only do this when the company has sufficient funds to pay cash for the entire construction project. Management has decided to save $235,000 a month for this purpose. The firm earns 7% compounded monthly on the funds it saves. How long does the company have to wait before expanding its operations?
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