Downside #1 (eight marks)Quicken Loans, the Detroit based mostly mortgage lender, with the backing of Warren Buffetâs Berkshire Hathaway has supplied $1 billion to anybody who fills out an ideal 2014 NCAA menâs basketball match bracket(guesses the winners for every of 64 video games). The $1 billion is paid in 40 annual funds or you possibly can take a lump sum of $500 million. What annual rate of interest was used to find out the current worth of the $1 billion prize?Downside #2 (20 marks)Michael needs to avoid wasting so as to purchase a home in four years which he estimates will price $225,000. He has a number of sources of funds:.His mother and father will give him $1,000 per quarter beginning in three months, which will likely be deposited into an account paying 5% compounded quarterly..He’ll obtain $5,000 from his Auntâs property in a single yearâs time which will likely be deposited into the identical account as above..He presently has $15,000 money in a checking account (similar as above)..He’ll take out a mortgage on the time of buy on which heâll make month-to-month funds of $1,000 over a 20 yr amortization. He expects the rate of interest on the mortgage on the time to be four%.a)Calculate how rather more Michael might want to have in four years so as to have the ability to buy the home.b)To make up the shortfall, Michael will make month-to-month contributions to his funding account which earns 6percentcompounded yearly. How a lot should he save every month to have sufficient to purchase the home in four yearsâ time?Downside #three (9 marks)Dawson borrows $75,000 for 3 years from the financial institution to buy asailboat. That is an amortized mortgage with equal funds every month. The mortgage is absolutely paid off with the ultimate cost. The quoted rate of interest (APR) is 9% per yr with month-to-month compounding. Assuming you make your entire funds on time:a)What’s the excellent steadiness on the mortgage proper after you’ve made your 30th cost?b)What portion of the 31st cost is principal?Downside #four (12 marks)Ben and Cassie are shopping for their first home. They will afford to pay $1,000 per thirty days for the cost. The financial institution will lend them 75% of the acquisition worth of the home they buy, at an annual price of 5% for a 4 yr time period. The mortgage will likely be amortized over 25 years. a)?What’s the most they will pay for a brand new home?b) ?Ben remembers from finance class that the shorter the amortization interval, the much less complete curiosity you’ll pay. Calculate how a lot curiosity they’d save in the event that they made month-to-month funds over a 20 yr amortization fairly than a 25 yr amortization.Downside #5 (12 marks)You might be presently 25 years previous and need to begin saving to your retirement. You begin off very decided and put apart $5,000 yearly, beginning one yr from now, for 10 years. Lastly, you get sick of saving and spend all of your wage however go away your financial savings (steadiness plus earned curiosity) untouched for one more 20 years while you retire. Assume rates of interest are 7% compounded semi-annually while you’re saving,however drop to six% compounded quarterly after that.a) ?How a lot will you be capable to draw a yr while you retire at 55 assuming your first withdrawal happens on the finish of your retirement yr when you estimate you’ll dwell for 25 years after retirement?b) ?How will your reply change when you begin receiving funds firstly of the yr as a substitute of the top of the yr?Downside #6 (four marks)A wealthy relative has bequeathed you a cost of $1,000 one yr from now. Annually after that, you’ll obtain a cost on the anniversary of the final cost that’s eight% bigger than the earlier cost. This sample of funds will go on without end. If the rate of interest is 12% per yr:a)What’s todayâs worth of the bequest?b)What’s the worth of the bequest instantly after the primary cost is made?Downside #7 (6 marks)You simply settled an insurance coverage declare. The settlement requires rising funds over a 6-year interval. The primary cost will likely be paid one yr from now within the quantity of $40,000. The next funds will improve by 5 p.c yearly. What’s the worth of this settlement to you as we speak when you can earn 7.5 p.c (compounded yearly) in your investments?Downside #eight (four marks)Archieâs Aeronautics wish to purchase some extra land and construct a brand new coaching facility. The anticipated complete price is $12.four million. The CEO of the agency is sort of conservative and can solely do that when the corporate has adequate funds to pay money for the complete building undertaking. Administration has determined to avoid wasting $235,000 a month for this goal. The agency earns 7% compounded month-to-month on the funds it saves. How lengthy does the corporate have to attend earlier than increasing its operations?