Part II: PROBLEMS Compute a final numerical answer for each of the following problems. You should work out your solutions on loose leaf paper, however, I may or may not collect your worked out solutions. To be safe, however, I suggest that you write out a solution for every problem and be ready to turn it in if asked. Unless specifically told in a problem to do otherwise, round all dollar answers to 2 decimal places, round time (years or months) answers to one (1) decimal place and record interest rates as percent values rounded to one (1) decimal place. However, be sure to NOT input a dollar sign, commas, or percent sign on D2L. For example, record $3,284.33965 as 3284.34, record 37.285432 years as 37.3 and record .064358 = 6.4358% as 6.4.

21. In 2020, the total world population was 7.794 billion people. Population experts predict that this number will grow at a compound rate of 0.92% annually over the next 20 years. If that growth rate is correct, what will be the world population (in billions) in 20 years (i.e., in 2040)? Enter your answer in billions, rounded to 3 decimal places; for example, enter 11.12793 billion as 11.128.

22. Over the past 10 years, the average inflation rate in the United States has been 1.8 percent per year. Due to large government deficits related to COVID and projected deficits for new proposed social programs, many economists believe that this rate may triple (to 5.4 percent per year) over the next 10 years. Currently, a price of a gallon of gasoline is about $2.49. If the inflation rate over the next 10 years averages 1.8 percent per year, in 2031, gasoline will cost $2.98 per gallon. If the inflation rate is instead 5.4 percent per year over the next 10 years, what will gasoline cost (per gallon) in 2031?

23. You expect to deposit the following cash flows at the end of years 1 through 5, $1,000; $4,000; $9,000; $5,000; and $2,000 respectively. What is the future account value at the end of year 6 if you can earn 10% compounded annually?

24. You won a contest at a local business that has paid you a single $5,000. At 22, you have decided to invest these funds for 45 years until you retire. During this time your account will earn 13%, compounded annually, every year. As soon as you retire (exactly 45 years from today) you will start withdrawing retirement funds every year for an additional 33 years, but you are investing more conservatively at 8% compounded annually. How much can you withdraw each year in retirement?

25. You have just graduated and have decided to purchase a new sports car to enjoy your newfound freedom. Your local credit union will provide financing for 60 months at a 9 percent annual rate, compounded monthly. You will give 15 percent of the $26,000 purchase price in cash to the dealer. The credit union will be used to finance the remaining 85 percent of the purchase price with the first payment due 1 month from today. What will be your monthly payment?

26. You have just agreed to a new loan and have purchased a $3,000 computer today. The loan has a 19.6% annual interest rate, compounded monthly. The minimum monthly payment is $58, and you do not expect to ever pay more than the minimum payment. Assuming no additional charges or costs will occur with this loan, approximately what will you owe on the loan at the end of 3 years (36 months) when you expect to need another new computer?

27. What is the future value on the day of the last deposit of 35 annual deposits of $750 per year (first deposit to be made today) given an interest rate of 5.5% p.a.?

28. Assume that I will deposit $600 into an account exactly 10 years from today. How much will be in my account at the end of year 75 (i.e., 75 years from today), assuming that my account pays interest of 4.5% p.a.?

29. The ShortHolder bank pays 6.50% p.a., but with daily compounding assume a 360-day year), on a 9-month certificate of deposit. If you deposit $20,000 you would expect to earn __________ in interest (rounded to the nearest dollar).

30. With continuous compounding at 2.4% p.a. for 25 years, what is the approximate future value of a $120,000 initial investment (rounded to the nearest dollar)?

31. For $125,000 Laura Croft can purchase a 15-year ordinary annuity which will pay her a yearly payment of $14,895.00 for 15 years. What is the annual interest rate implicit in this investment? Round your answer to the nearest tenth (for example, record 0.4325 as 43.3% - but do not include the percent sign in iCollege).

32. Nathan Drake is considering borrowing $100,000 for 30 years at a compound annual interest rate of 9% p.a. The loan agreement calls for 30 equal annual payments, to be paid at the end of each of the next 30 years (payments include both principal and interest.) What is the annual payment that will fully amortize Nathans loan?

33. Cloud Strife is going to place $12,500 into a certificate of deposit (CD) at a 6% annual rate (compounded annually) with a maturity of 54 months. How much money will Cloud receive when the CD matures?

34. Clementine and Lee expect to deposit the following cash flows at the end of years 1 through 5, $1,000; $4,000; $9,000; $5,000; and $2,000 respectively. Alternatively, they could deposit a single amount today and have the same amount in your account at the end of year 5. How large does the single deposit need to be today if Clementine and Lee can earn 10% compounded annually on their account?

35. What is the future value at the end of year 18 of $10,000 deposited today into an account that pays interest of 5.4% p.a., but with daily compounding (assume 365 days per year)?

36. Over Dinas objections, Ellie is evaluating an investment that will provide the following returns at the end of each of the following years: year 1, $10,000; year 2, $11,500; year 3, $7,500; year 4, $5,000; year 5, $2,500; year 6, $0; and year 7, $12,500. Ellie believes that she should earn an annual rate of 8 percent on this investment. How much should Ellie pay for this investment?

37. On the day that his first child was born, Ezio Auditore de Firenze deposited $6,200 into an investment account. The only purpose for the account was to pay for his sons 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 $45,000. If that was indeed the amount of money in the account on Flavias 18th birthday, what annual rate of return did Ezio earn on his investment account?

38. Marcus Holloway has $1,500 that he will use as a down payment on a car. Assuming that he can afford a payment of $375 per month, how much can Marcus spend on a car (that is, what is the total cost of the car that Marcus can purchase) if the interest rate is 3.25% and if he will finance his purchase with a 5 year, monthly payment loan?

39. Suppose Link deposits $5,000 into an account earning 5.785 percent interest, compounded monthly. How many years (rounded to one decimal place for example, 32.1843 year = 32.2) will it take for Link s account to be worth $20,000?

40. Suppose Crash Bandicoot deposits $5,000 into an account earning 4 percent interest, compounded monthly and Crash also makes monthly deposits of $250 (first monthly contribution made one month after the initial deposit is made) into this account. How many years (rounded to one decimal place for example, 32.1843 year = 32.2) will it take for the account to grow to $17,500 in this case?

41. Assume that Ratchet and Clank are trying to borrow money from you to finance their new business. Assume that Ratchet and Clank 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 you be willing to lend Ratchet and Clank today?

42. What is the future value at the end of year 28 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).

43. If Lisa Hamilton wants to fund a scholarship that would pay $13,500 per year forever at GSU, how much would Lisa have to deposit today if she wanted the scholarship to start paying six (6) years from today? Assume the endowment could earn 6.25% p.a. interest forever.

44. Kratos currently owes $26,000 on a car loan at 4.25 percent interest. If Kratos makes monthly payments of $696.59 per month, how long (i.e., number of months rounded to one decimal place) will it take him to fully repay the loan?

USE THE INFORMATION BELOW TO ANSWER THE FOLLOWING THREE QUESTIONS

Vito Scaletta just bought his dream car, a 2020 Bugatti Divo, that cost $5,808,215. He paid $500,000 down and financed the balance over 84 months at 4.25% p.a. (Assume that Vito makes all required payments on time).

45. What is the monthly payment on Vitos loan?

46. What will the balance on Vitos loan be at the end of the fourth year (that is, immediately after Vito makes his 48th payment on the loan)?

47. 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)?

48. Today is your 25th 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 $175,000 per year to spend during retirement. You estimate constant interest rates of 10.25%. Assuming that you currently have $10,000 deposited in your retirement account, how much must you put aside each year in order to have sufficient money to retire at age 65?

49. Daigo Dojima recently invested $6250 in a project that is promising to return 2.25 percent per year. The cash flows are expected to be as follows:

End of Year	Cash Flow
1	1000
2	950
3	875
4	???
5	850

Note that the 4th year cash flow is unknown. Assuming the present value of this cash flow stream is $5500 (that is, CF0 = -5500), what is the missing cash flow value (that is, what is the cash flow at the end of the 4th year)?

50. What is the present value of a cash flow of $10,000 per year for 45 years (with the first cash flow received today and the last cash flow received exactly 44 years from today) given an interest rate of 0% p.a.?