## Final Exam

1. Tony had his 22nd birthday this week, and he has decided he'd like to be a millionaire by the time he retires at age 65. If Tony can set aside equal amounts each month until he retires in a 10% account, how large would his monthly payments have to be to have $1 million by the time he retires? a. $8,450.05

2. I want to be a millionaire when I retire at 65 and I've just had my 57th birthday. How much do I have to set aside each month until I retire in my 10% account to have my $1 million?

3. If you borrow $120,000 in the form of a 25-year mortgage amortized monthly at the 7% annual rate, what is your monthly payment?

4. What is the principal balance after two years on the mortgage described in question 3?

5. If I deposit $4,000 today in an investment paying 10% annual interest and I withdraw $800 per year, how many withdrawals will I be able to make, if those withdrawals are made at the end of the year?

6. You've decided to go to graduate school, and you've calculated that you will need $8,500 per year for each of the three years you expect to be there. If you intend to enroll five years from today, given an interest rate of 9%, how much money should you set aside today?

7. Your driveway is 30 feet by 42 feet. If you cover it with a three-inch layer of concrete, how many cubic feet of concrete will you need?

a. 630 cubic feet b. 1,260 cubic feet c. 415 cubic feet d. 315 cubic feet

8. Sylvia purchased a home earlier this year for $167,750 and took out a mortgage for $142,375 at 8% for 30 years. What was the loan-to-value ratio on the mortgage, and what is her down payment as a percentage of the purchase price?

9. Your cousin Kara recently purchased a new home for $179,500. The lot is worth $36,000 according to the appraiser. The lot size is 75 feet x 140 feet. What is the cost per square foot of the lot?

10. Ghulam purchased his home a year ago for $275,000 and has been told by an appraiser that it is currently worth $297,000. What has been the rate of appreciation the home has experienced over the last year?

11. Dennis has an opportunity to purchase a duplex for $325,000. He intends to finance the purchase with an 80% loan-to-value mortgage amortized over 30 years at a 7% rate of interest. If he buys the duplex and the value remains at $325,000 for one year, how much equity will Dennis have in the duplex at the end of the first year?

12. When Adrienne sold her home, she paid a 6% commission of $14,700. What was the sale price of Adrienne's home?

13. Dennis, from question 11, sold his duplex three years after he purchased it for $382,550. What was the compound annual appreciation that Dennis earned during his three-year holding period?

14. Karen asked a local real estate broker to come out and do a market analysis on her house because she was thinking of selling. The broker told her that the home should be listed for $235,900 and that he would be charging a 5% commission on the sale. If the home sells for 95% of the listing price, how much will Karen have to pay the broker for the commission?

15. Jason just signed a purchase agreement to sell his condo for $215,000. He bought it three years ago for $185,000. What was his annual average rate of appreciation over the three years?

16. Frances is selling her home after being transferred to another city for her job. She would like to net $175,000 from the sale of her home after paying a 6% commission to the broker. What sale price does the home have to sell for in order for Frances to receive her desired net proceeds?

17. Partha is selling a manufacturing building that has been in his family for years. The broker informed him that the commission would be 5% on the first $500,000 in sale price, 4% on the second $500,000 in sale price, and 2% on anything in excess of $1,000,000. If the building sells for a sale price of $1,250,000 how much commission does Partha have to pay?

18. The service station located two blocks from your home is installing a new fuel tank. The tank is 15 feet long and has a diameter of 6 feet. How many cubic feet of fuel does the tank hold?

a. 282.6 cubic feet b. 423.9 cubic feet c. 141.3 cubic feet d. 372.6 cubic feet

19. Elise recently purchased the NW 1/4 of section 12 to house her horses and set up a training ring. She paid $475,000 for the land. How much did Elise pay per acre?

20. A half-acre lot on the outskirts of the city is listed for $8 per square foot. The commission on the listing contract is 7% of the sale price. If the lot sells for 85% of the listing price, what is the amount of the gross commission on the sale?

21. Denny took a listing on a four-unit apartment building with a list price of $425,000. The property sold for 95% of the list price. The net proceeds to the seller were $375,487 after the commission was paid. What was the commission rate charged on the sale of the four-unit building?

22. Tim is hoping to purchase a condo for $225,000, and he intends to get a mortgage of $157,500 at a 7% interest rate amortized over 25 years. What is the loan-to-value ratio on the mortgage?

23. A sum of $50,000 is invested today to provide a man with an annual income for 20 years; the first payment is to be received in one year. Given an interest rate of 5%, how much will the annual payments be?

24. How much money do you have to invest today in order to be able to spend $500 in two years and $700 in four years if you can earn 10% on your investment?

25. If your starting salary is $37,000 and you receive a 5% raise each year for the next 20 years, what will your salary be in year 20?

26. Kate is buying a condo; the purchase price is $315,000, and she is taking out a 90% loan-to-value mortgage to finance the purchase. The interest rate on the loan will be 7.25%, and it will be amortized over 30 years. What are Kate's monthly principal and interest payments on the mortgage going to be if it is a fixed-rate mortgage?

27. Five years from now Kate decides to sell her condo from question 26. If the property has gone up in value by 3% per year compounded annually, what is the expected sale price of the condo?

28. What is the mortgage balance when Kate sells her condo in question 27?

29. What is Kate's total equity in her condo when she sells it in question 27?

30. Pat bought a new house and closed on it last week for the price of $345,000. He took out a 75% loan-to-value 30-year mortgage to finance the purchase. He will be making payments of $1,635.48 for principal and interest each month on the loan. What is the rate of interest Pat is paying on the mortgage?

31. If Pat decides to sell the house in question 30 after 10 years, what will be the amount of his mortgage payoff?

32. The home that Maxine bought a couple of years ago cost $169,500 at the time of her purchase. She obtained a mortgage of $135,600 amortized over 25 years at a 5.5% rate of interest. What is the amount of her monthly mortgage payment?

33. What is the loan-to-value ratio on Maxine's mortgage in question 32?

34. Four years ago the country club took out a mortgage to finance the construction of a new club house. The total amount financed came to $2,500,000, and it had a 20-year term and an interest rate of 7%. What is the current principal balance on the mortgage?

35. What portion of the country club's (question 34) next payment, payment 49, will go toward principal reduction?

36. Dale took out an ARM three years ago for $179,500 at a 6% rate of interest with a 30-year amortization. His interest rate readjustment is coming up later this month, when the mortgage will be exactly three years old. He has been told that the treasury bond index, which is the index against which his mortgage is benchmarked, will be 4.5%. The margin on his loan is 2%. What will the new mortgage payment on his loan be after the interest rate is readjusted assuming that there are no payment caps on the mortgage?

37. Mary Jo recently bought a townhouse in a new development in town. When she went to the bank to apply for a mortgage, she found out that the bank had recently introduced biweekly mortgages. She thought that sounded interesting, so she asked what the payment would be on such a mortgage for $180,000 at 6% interest with a 30-year amortization. What will the biweekly payment be?

38. Gina has just finished her first year in the real estate brokerage business. She has sold $3,750,000 worth of real estate. Her broker told her at the beginning of the year that she would get 50% of the commission on her first $1,500,000 in real estate sales and 60% on all sales thereafter. If her sales were at an average commission rate of 3% of the sale prices, how much did Gina make in her first year?

39. Which of the following is not an equation?

40. Your cousin Kara recently purchased a home for $179,500. The lot is worth $36,000 according to the appraiser. The lot size is 75 feet x 150 feet. What is the square footage of the lot?

a. 75 square feet b. 11,250 square feet c. 150 square feet d. 15.96 square feet

41. Laura is paying her broker a 7% commission to sell her house. How would you express Laura's expected net proceeds after her commission is paid?

42. Sharon purchased a new home for the price of $322,500 and took out a 25-year 6.5% interest rate mortgage for $258,000 to finance the purchase. She will have to pay loan costs that total $5,000 to take out the mortgage. What is the APR that the lender will have to disclose to Sharon at the closing?

43. What is the loan-to-value ratio of the mortgage in question 42?

44. Equity is equal to_- mortgage balance.

a. Principal balance b. Market value c. Down payment d. Total interest

45. The mortgage you took out this morning to purchase a new home required you to make a down payment of $45,000. If you took out an 80% loan-to-value mortgage, what was the purchase price of your home?

46. What was the amount of your mortgage in question 45?

47. The type of mortgage that starts at a certain rate of interest but can have the interest rate and the payments increase at different points in time is referred to as:

a. A shared appreciation mortgage b. An adjustable rate mortgage c. A constant payment mortgage d. A reverse annuity mortgage

48. Your sister purchased a home five years ago for the price of $199,500. Today the assessor told her that the property was worth $254,618. What has been her annual compound rate of appreciation on the home?

49. When Kent took out his shared appreciation mortgage, the bank reduced his interest rate by 25% in exchange for 25% of the appreciation that would take place over the next five years. If Kent paid $275,500 for the home and after five years its value has increased to $325,000, how much must Kent pay to the lender to meet the terms of the mortgage?

50. If the market rate of interest when the loan was originated in question 49 was 12% and the mortgage had a loan-to-value ratio of 80% amortized over 30 years, what was Kent's monthly payment during the first year of the loan?

51. Kristi's mortgage was originated five years ago for $176,600 to be amortized over 30 years at 5.75% interest. If Kristi makes regular payments on the loan until it is satisfied, how much total interest will Kristi pay on the loan?

52. Given the mortgage in question 51, what portion of payment number 3 is principal?

53. Given the mortgage in question 51, how much principal will Kristi pay over the life of the loan?

54. If you take out a mortgage for $217,900 amortized over 25 years at a 6% rate of interest and the lender charges you 2 points plus a 1% origination fee, what is the lender's effective rate of return?

55. What is the APR that must be disclosed to the borrower in the mortgage described in question 54?

56. In the cost approach to determining value, the depreciated cost of the improvements is added to the value of the ___________ in order to obtain the value estimate.

a. The total construction cost of the improvements b. The historical construction cost of the improvements c. The depreciated cost of the improvements d. The cost of the land

57. Betty is appraising a 2,000-square-foot colonial style house that has four bedrooms. One of the comparables that Betty chose to use in her sales comparison approach was another colonial with similar square footage, four bedrooms. The property was otherwise very similar to the subject property, but it had a swimming pool in the backyard, and the subject did not have a pool. The comparable sold for $245,000, and the appraiser thinks the market value of the pool is about $25,000. What is the indicated value of the subject property?

58. Ben, your boss at the appraisal firm, has just given you an assignment to appraise a single-family home, and he wants you to use the gross rent multiplier to get its value. The subject should bring in about $1,450 per month if it were to be rented out. The very best comparable you can find was rented for $1,350 when it sold earlier this month for a price of $165,000. What is the indicated value of the subject property using the GRM form of the income approach and the given comparable?

59. Which of the following is critical in the value estimate using the income approach and IRV?

a. Net investment income b. Investment value c. Discount rate d. Capitalization rate

60. The appraiser is going to use the band of investment method of estimating a cap rate. He is going to use the mortgage constant for a 75% loan-to-value mortgage amortized for 25 years at a 6% interest rate and a required return on equity for the investor of 13%. What is the annual mortgage constant that should be used in the formula for estimating the cap rate?

61. The potential gross income minus the vacancy and rent loss allowance is called what?

c. BTCF

62. The amount of cash flow that the investor earns in a year after all operating expenses, debt service, and income taxes have been paid is called what?

b. BTCF

c. ATCF

63. Amanda has invested $150,000 in a small office building, and it is generating after-tax cash flows of $5,000 in year 1, $6,000 in year 2, $7,000 in year 3, $8,000 in year 4, and $9,000 in year 5 plus a $225,000 reversion, or sale price, at the end of year 5. Given Amanda's required rate of return of 10%, what is the net present value of the cash flows of the building?

64. You are analyzing a potential investment in an office building, and you notice that the before-tax cash flow is positive. What does that tell you about the debt coverage ratio?

a. It is greater than 1

b. It is less than 1

d. Nothing

65. If the one-year spot rate for treasuries is 4.5% and the two-year spot rate is 4.25%, what is the indicated forward rate from the end of period one to the end of period two?

66. An investment opportunity has three potential outcomes. It could earn a return of 22% if the economy does really well, and you think there is a 25% probability of that happening. If the economy is just average, the return should be 15%, and the probability of that is 40%. If the economy does very poorly, you will earn only a 4% return, and there is a 35% probability of that taking place. What is your expected return?

67. Given the expected return you calculated from the information in question 66, what is the standard deviation of the returns from the same question?

68. You were talking about this book around the office, and your boss suggested that you help her solve a problem she had been working on. A property your company is considering investing in has an IRR of 18%. The cash flows from operations have a present value of $425,000, and the cash flow from the sale of the property will be $975,000. What percentage of the IRR comes from operations, and what percentage comes from the sale?

a. 30.3% from the sale and 69.7% from operations b. 43.6% from the sale and 56.4% from operations c. 69.7% from the sale and 30.3% from operations d. 56.4% from the sale and 43.6% from operations

69. Fred purchased a small office building that has a potential gross income of $145,500, a 6% vacancy rate, and net income of $24,700. What are the operating expenses in year 1?

70. Blair just took a listing on a 4,000-square-foot retail building and is putting together a cash flow analysis. The lease states that the store has a base rent of $8 per square foot and a percentage rent of 4% of annual sales revenue. If the store has sales revenue of $1 million, what is the total rent for the next year?

71. Lauren's company is looking for new office space. She is looking at a building that is in a good location for her needs, and the lease terms include rent for the first five years of $10.50, $10.50, $12.00, $13.75, and $14.25, respectively, per square foot. What is the average rent per square foot per year?

72. What is the effective rent on the building that Lauren is considering in question 71, given a 10% discount rate?

73. How much overage rent is there in the lease in question 70?

74. You are measuring a home for a listing, and the main body of the house is a rectangle that is 35 feet x 45 feet, and there is a year-round porch off the back that is 10 feet x 14 feet. What is the square footage of the main floor?

a. 1,575 square feet b. 140 square feet c. 1,435 square feet d. 1,715 square feet

75. The state deed transfer tax rate in your state is $3.30 per $1,000 of sale price, and you just closed on the purchase of your first home, for which you paid $265,900. You paid $53,180 in cash and the balance with a 30-year mortgage at 6%. What amount of state deed tax did you pay at closing?

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