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Finance 301 HW216 questions About: Perpetuities and Annuities  Interest Rate Concepts: APR/EAR  Solving application problems using TVM exam_1_formula_sheet.pdf quiz__homework_2.pdf Unformatted Attachment Preview Formula Sheet =( = ) PV(perpetuity) = PMT r PMT  1  PV(annuity)  = r    ( ∗ (1 + ) = = ln( )/ln(1 + ) PV(constant growing perpetuity)  1  (1  r )t  FV(annuity)  )× ( −1 = ) ( ( PMT r  g  PMT   1  r t  1  r  ) )× Periodic Rate: r = APR/N, where “N” stands for the # of periods in a year. APR   With monthly compoundin g : EAR  1   1 12   12 PV ( Benefits)  CF0  CF1 CF2 CFN   1 2 (1  r ) (1  r ) (1  r ) N or EAR = (1 + periodic rate)# of periods - 1 Homework 2 Started: May 26 at 3:13pm Quiz Instructions Question 1 1 pts Question #1 and #2 use the following setup: You have just received a windfall from an investment project. It will be paying you $15,000 at the end of the first year, $25,000 at the end of the second year, and $35,000 three years from today. The interest rate is 3.5\% per year. What is the present value of your windfall? Question 2 What is the future value of your windfall in three years (on the date of the last payment)? 1 pts Question 3 2 pts You have a loan outstanding. It requires making three annual payments of $1000 each at the end of the next three years. Your bank has offered to allow you to skip making the next two payments and instead to make one large payment at the end of the loan’s term in three years. The interest rate on the loan is 5\%. What final payment will the bank require you to make so that the bank is indifferent between the two forms of payment? Question 4 1 pts Question #4 and #5 use the following setup: You want to endow a scholarship that will pay $10,000 per year forever, starting one year from now. The school’s endowment discount rate is 7\%. What amount must you donate to endow the scholarship? Question 5 1 pts If you endow it today, but it makes the first award to a student 6 years from today. Under this circumstance, what amount must you donate to endow the scholarship? Question 6 2 pts When Alfred Nobel died, he left the majority of his estate to fund five prizes, each to be awarded annually in perpetuity starting one year after he died. If he wanted the cash award of each of the five prizes to be $45,000 and his estate could earn 7\% per year. And, suppose the cash award will grow by 4\% per year. How much would he need to set up the prizes today? A. $1.5 millions B. $2 millions C. $5 millions D. $7.5 millions Question 7 1 pts You are thinking of building a new machine that will save you $1000 in the first year. The machine will then begin to wear out so that the savings decline at a rate of 2\% per year forever. What is the present value of the savings if the interest rate is 6\% per year? Question 8 1 pts What is the present value of $1000 paid at the end of each of the next 50 years if the interest rate is 6\% per year? Question 9 1 pts Assume that your parents wanted to have $120,000 saved for college by your eighteenth birthday and they started saving on your first birthday (that is, when you turned one). They saved the same amount each year on your birthday and earned 8\% per year on their investments. How much would they have to save each year to reach their goal? Question 10 2 pts You are thinking of purchasing a house. The house costs $350,000. You have $50,000 in cash that you can use as a down payment on the house, but you need to borrow the rest of the purchase price. The bank is offering a 30-year mortgage that requires monthly payments and has an APR of 6\% per year. What will your monthly payment be if you take this mortgage? Question 11 1 pts From Question #10, how much interest is paid off in your first mortgage payment? Question 12 1 pts Victor would like to subscribe to Netflix for the next 60 months (the first payment is due one month from today). The monthly charge of Netflix is $8. On the other hand, Victor can use Amys Netflix account if he is willing to pay her a one-time fee today. Suppose the monthly interest rate is 1\%. Under which of the following fees would Victor pay Amy and use her account rather than buying his own account? A. $400 B. $350 C. $300 D. Victor would pay Amy and use her account under both (B) and (C). Question 13 1 pts You want to borrow $89,000 from your local bank to buy a new sailboat. You can afford to make monthly payments of $1850, but no more. Assuming monthly compounding, what is the highest rate you can afford on a 60-month APR loan? Please express the interest rate in the form of APR. A. 8.56\% B. 9.05\% C. 9.58\% D. 10.23\% Question 14 1 pts What is the Effective Annual Rate (EAR) of the interest rate in Question 13? A. 9.44\% B. 9.85\% C. 10.32\% D. 10.87\% Question 15 2 pts You have just turned 22 years old, and have accepted your first job. Now you will decide how much money to put into your retirement plan. The plan works as follows: You expect to live to 100 and work until you turn 65. You estimate that you will need $100,000 per year, starting at the end of the first year of your retirement (i.e. when you turn 66) and ending on your one-hundredth birthday. You will contribute the same amount to the retirement plan at the end of every year when you work (i.e., from your age of 23 to your age of 65). Every dollar in the plan earns 7\% per year. How much do you need to contribute each year to fund your retirement? Question 16 1 pts A benefactor proposes to endow a professorship at Iowa State University with a gift that will provide a salary of $150,000 a year plus an annual growth rate of 2\% forever. It will take a larger donation for the benefactor to set it up today if ...... A. the starting salary is lower B. the interest rate earned by endowments is lower C. the faculty member is an accountant D. the annual growth rate is 1\% Quiz saved at 3:14pm Submit Quiz ... Purchase answer to see full attachment