# 12. Assume that a gallon of milk costs $2.99 today. If the a

12. Assume that a gallon of milk costs $2.99 today. If the average annual inflation rate over the past 30 years was 2.75% p.a., what did a gallon of milk cost 30 years ago?13. What is the future value on the day of the last deposit of 25 annual deposits of $750 per year (first deposit to be made today) given an interest rate of 5.5% p.a.?14. Assume that I deposit $750 into an account exactly 10 years from today. How much will be in my account at the end of year 50, assuming that my account pays interest of 4.5% p.a.?15. What is the future value at the end of year 15 of $10,000 deposited today into an account that pays interest of 4.5% p.a., but with monthly compounding?16. Walt is evaluating an investment that will provide the following returns at the end of each of the following years: year 1, $12,500; year 2, $10,000; year 3, $7,500; year 4, $5,000; year 5, $2,500; year 6, $0; and year 7, $12,500. Walt believes that he should earn an annual rate of 8 percent on this investment. How much should he pay for this investment?17. Assume that Claudia started a paper route on January 1, 1970. Since that day, at the end of every three (3) months (first deposit made on April 1, 1970), she deposited $500.00 into a savings account, which paid her interest of 4 percent annually but with quarterly compounding. On January 1, 1980, she took the balance in her savings account and transferred it to an account that paid 11.5% p.a. Assuming that Claudia did not deposit any additional money into the account after the transfer, how much did she have in her account on January 1, 2014?18. On the day that his first child was born, Ezio Auditore de Firenze deposited $3,000 into an investment account. The only purpose for the account was to pay for his son’s first year of college tuition. Assume that his son, Flavia, started college on his 18th birthday and his first year tuition payment had to be made that day. The amount needed on that day was $26,000. If that was indeed the amount of money in the account on Flavia’s 18th birthday, what annual rate of return did Ezio earn on his investment account?19. Desmond Miles has $1,500 that he will use as a down payment on a car. Assuming that he can afford a payment of $225 per month, how much can Desmond spend on a car (that is, what is the total cost of the car that Desmond can purchase) if the interest rate is 5.75% and if he will finance his purchase with a 5 year, monthly payment loan?20. Suppose you deposit $5,000 into an account earning 4 percent interest, compounded monthly. How many years (rounded to one decimal place – for example, 32.1843 year = 32.2) will it take for your account to be worth $8,500?21. Suppose you deposit $5,000 into an account earning 4 percent interest, compounded monthly and you also make monthly contributions of $50 (first monthly contribution made one month after the initial deposit is made). How many years (rounded to one decimal place – for example, 32.1843 year = 32.2) will it take for the account to grow to $7,500 in this case?22. Assume that I am trying to borrow money from you to finance my business. Assume that I promise to repay you in three installments, one payment of $5,000 to be made exactly 2 years from today, a second payment of $10,000 to be made exactly 5 years from today, and a final payment of $15,000 to be made 8 years from today. If your opportunity cost of funds is 7.5% p.a., (that is, use an interest rate of 7.5% for this question), how much should be willing to lend me today?23. What is the future value at the end of year 25 of depositing $5,000 today, $3,500 at the end of years 1, 2 and 3, $5,000 at the end of years 4, 5, 6 and 7 and $4,250 at the end of years 8, 9, 10, 11 and 12 into an account that pays 9.5% p.a.? (No deposits will be made into the account after year 12).24. If you wanted to fund a scholarship that would pay $12,500 per year forever at GSU, how much would you have to deposit today if you wanted the scholarship to start paying five (5) years from today? Assume the endowment could earn 6.25% p.a. interest forever.25. You currently owe $20,000 on a car loan at 8.25 percent interest. If you make monthly payments of $596.59 per month, how long (i.e., number of months rounded to one decimal place) will it take you to fully repay the loan?26. It is now January 1. You plan to make 5 deposits of $300 each, one every 6 months, with the first payment being made exactly six months from today. If the bank pays a nominal interest rate of 12% but uses semiannual compounding, how much will be in your account exactly 12 years from today?27. You must make a payment of $3,800 exactly 8 years from today. To prepare for this payment, you will make 5 equal deposits into an account that pays a nominal interest rate of 7.6% p.a., with quarterly compounding. If your first deposit is made today (and then you make four additional deposits in each of the next four quarters – that is, a deposit 3 months from today, another 6 months from today and so on), what must each of the 5 payments be for you to exactly achieve your goal?USE THE INFORMATION BELOW TO ANSWER THE FOLLOWING THREE QUESTIONSVito Scaletta just bought his dream car, 2014 Aston Martin DB9 that cost $208,700. He paid $35,000 down and financed the balance over 84 months at 6.25% p.a. (Assume that Vito makes all required payments on time).28. What is the monthly payment on Vito’s loan?29. What will the balance on Vito’s loan be at the end of the fourth year (that is, immediately after Vito makes his 48th payment on the loan)?30. What is the total amount of interest that Vito will pay over the entire term of the loan (that is, the total amount of interest that is paid on payments 1 through 84)?31. Today is your 30th birthday and you have a dream of retiring on your 65th birthday. You want to put aside however much is necessary on your 31st through 65th birthdays (35 annual payments) to have enough to retire. You’ve estimated that you will live until you are 90 and you want the first withdrawal to occur on your 66th birthday, with the last payment occurring on your 90th birthday. You think that you will need $150,000 per year to spend during retirement. You estimate constant interest rates of 11.25%. Assuming that you currently have $7,500 deposited in your retirement account, how much must you put aside each year in order to have sufficient money to retire at age 65?32. John Keene recently invested $5,000 in a project that is promising to return 6.5 percent per year. The cash flows are expected to be as follows:End of CashYear Flow1 $10002 9503 8754 ???5 850Note that the 4th year cash flow is unknown. Assuming the present value of this cash flow stream is $5,000 (that is, CF0 = -5000), what is the missing cash flow value (that is, what is the cash flow at the end of the 4th year)?33. You have a $25,000 balance on your credit card. You plan to make monthly payments of $450 until the balance is paid off. The interest rate on your credit card is 17.5% p.a., compounded monthly. A letter in the mail informs you that you are approved for a new credit card and balance transfers are subject to a 9.5% p.a., compounded monthly. How many months sooner will you pay off your bill?