RE EXAM (MATH)

Ms. Williams purchased a house in a run-down condition and spent an amount equal to 10% of the purchase to fix it up and bring it to its present value. The house in now worth $18,700. The cost of the house is equal to the existing loan of the property. The amount of the loan is

$17,000 ($18,700 = 100% purchase price + 10% fix-up money. $18,700 divided by 110% = $17,000)

Tom obtains an interest-only purchase money loan for $60,000. The interest rate is 9.5% and the term is 30 years. How much interest will Tom have paid at the end of the 30-year term?

$171,000 ($60,000 x 9.5% = $5,700 interest per year. $5,700 x 30 years = $171,000 total interest)

An owner of a home listed it at a price which would leave him $16,800 after the broker received a 6% commission. If the broker sold the property at the listed price, how much commission would he receive

$1,072 ($16,800 divided by 94% = $17,872 - $16,800 = $1,072 commission)

Frank purchased a home for $80,000. He financed the purchase with a 90% conventional fixed-rate loan. The loan fee charged by the lender was 2%. The private mortgage insurance company charged a .50% first-year premium and a .75% renewal premium. What was the loan fee? The first-year premium? The monthly renewal premium?

$1,440; $360; $45 (Loan fee = $80,000 x 90% x 2% = $1,440. First year premium = $80,000 x 90% x .5% = $360. Monthly renewal = $80,000 x 90% x .75% divided by 12 = $45)

Ted, an intelligent real estate investor wants to purchase a 60-unit apartment building that has an annual net income of $180,000. How much would he be willing to pay for the building if he uses a 12% capitalization rate?

$1,500,000 ($180,000 divided by 12% = $1,500,000)

If an income property is valued at $250,000 using a 6% capitalization rate, how much would an investor pay for the property if he demanded a 10% capitalization rate

$150,000 ($250,000 x 6% = $15,000 annual net income. $15,000 divided by 10% = $150,000. Remember, as capitalization rate goes up, the value goes down)

Inventory in a store costs $8,500 net. It was sold for 20% profit. However, 10% of the gross profit was lost due to bad credit risks over a period of one year. How much profit did the store owner make that year

$1,530 ($8,500 x .20 = $1,700 x .10 = $170. $1,700 - $170 = $1,530)

Under Article 7, if the actual costs are $159 on a $4,000 loan, the maximum costs that can be charged is:

$159.00 (The broker charges the actual costs or the maximum costs, whichever is less. The maximum costs for this loan are $390, therefore the broker may only charge the actual costs of $159)

A lender charged the borrower 2 points for making a loan. The lender then sold the loan immediately to an investor at a discount of 4-1/2 percent and received $35,800. What was the original loan amount?

$37,487 ($35,800 divided by 95.5% = $37,486.91. Note the 2 points have nothing to do with answering this question)

FHA mortgage insurance premium is calculated at a rate of 0.5% annually. How much is the premium for the month in which the remaining principal owed is $92,347

$38.48 (The annual premium on $92,347 would be $461.74 ($92,347 x 0.005). One month's premium is $38.48 ($461.74/12)

A real estate investor purchased a property for $15,000. He paid $5,000 down and executed a non-interest bearing note for $10,000 in favor of the seller. Before the end of the first year and before he had made any principal payments, he sold the property for double what he paid for it. Each $1.00 of his investment is now worth?

$4.00 (The owner's equity is based upon the difference in value and loan amount. $30,000 - $10,000 = $20,000. $20,000 / $5,000 = $4. His $5,000 investment is now worth $20,000 or $4 for each $1 invested)

Jim purchased a home for $85,000, with a $25,000 down payment and financed the balance with a $60,000 straight note. He then sold the property for double the purchase price, paying no principal or interest payments on the loan during his ownership. Each dollar invested is now worth?

$4.40 ($85,000 x 2 = $170,000 new selling price. $170,000 - $60,000 loan = $110,000 profit. $110,000 (profit) divided by $25,000 (invested) = $4.40)

Assume a second trust deed has a face amount of $6,000, payable at $75 a month plus 8.2% interest per year. What would be the amount of the interest due on the first monthly payment?

$41 ($6,000 x .082 equals $492 interest for one year. $492 divided by 12 = $41 first month's interest)

Bob took a listing providing for a 6% commission on the sales price of $210,000. Sue made an offer at the listed price, but did not complete the transaction. The seller declared a forfeiture of the 5% deposit. A provision in the deposit receipt provides that the broker will receive half of the buyer's deposit in the event of the buyer's default. Under these circumstances, the broker is entitled to

$5,250 ($210,000 x 5% = $10,500 divided by 2 = $5,250)

Mary sold her house and took back a second trust deed for $5,400. She immediately sold it for $4,050. What was the rate of discount

25% ($5,400 - $4,050 = $1,350 (amount discounted) divided by $5,400 = .25 (25%)

A lender loans borrower Smith a sum of $1,800 and takes back a note and deed of trust. The note was set up to be fully amortized over a 1-year period, interest at 8% per year, payable at $162 per month. When the note was drawn, it was immediately sold to an investor for a 15% discount. If the loan were fully paid off at the end of the year, what percent return would the investor make on this investment?

27% (12 monthly payments x $162 per month (includes principal and interest) = $1,944 total amount received. $1,800 x 15% (discount) = $270. $1,800 - $270 = $1,530 (cost to investor). $1,944 (amount received) - $1,530 (cost to investor) = $414 profit made. $414 divided by $1,530 x 100 = 27% return)

How many acres are in the S 1/4 of the SE 1/4 of Section 10 and the N 1/2 of the NW 1/2 of Section 3 and the N 1/2 of the NE 1/4 of Section 16?

280 (40 + 160 + 80 = 280 acres. Remember there are 640 acres in a section total)

The estimated remaining economic life of a building is 25 years. What is the annual recapture rate using the straight-line method

4% (100% (total depreciation) divided by 25 years = 4% depreciation per year)

Fred pays $16,240 for a home. If it costs 10% to sell his home before he could sell it at a profit, how much would it have to appreciate

$1,804.44 (100% (sales price) - 10% = 90% or $16,240 purchase price. $16,240 divided by 90% = $18,044.44. $18,044.44 - $16,240 = $1,804.44)

Mr. White sold an apartment building for $139,000. This was 20% more than what he paid for it. His original cost was approximately

$115,833 (Divide $139,000 by 120% to produce an answer of $115,833.33)

Ned just sold his house for 9% less than he paid for it. The selling price was $105,900. What was the original purchase price?

$116,374 ($105,900 represents 91% of the original price. $105,900 divided by 91% = $116,373.63(original purchase price)

Ken, an investor, wants to build a rental property which will have a gross income of $3,200 per month and annual expenses of $6,500. The investors require a 10% capitalization rate on the investment. If the improvements cost $200,000, how much can the investors pay for the land?

$119,000 ($3,200 x 12 = $38,400 gross annual income. $38,400 - $6,500 (expenses) = $31,900 annual net income. $31,900 divided by 10% (cap rate) = $319,000 total property value (land and improvements). $319,000 - $200,000 = $119,000 available to pay for the land

John purchased an income property for $575,000. The land is valued at $200,000. If straight line depreciation is used over a 30 year period, the annual depreciation would be

$12,500 ($575,000 - $200,000 = $375,000 (value of improvements). $375,000 divided by 30 years = $12,500 annual depreciation)

A deposit receipt states, "Buyer to assume existing first trust deed of $8,000 at 6-1/2% paid per quarter." If Mr. Pinkham took possession February 15th and the first interest payment was due on March 15th, how much would Mr. Pinkham pay on the next interest date

$130.00 ($8,000 x 6-1/2% (0.065) = $520.00 interest/year; $520 divided by 12 (months) = $43.33 interest/month; $43.33 x 3 (1/4 of a year) = $130.00/quarter)

A lender has agreed to provide a loan on the following terms: 90% LTV for the first $50,000 of appraised value; 95% LTV of the second $50,000 of appraised value and 97% of the remaining amount. If the property appraised for $140,000, how much will the lender's loan be

$131,300 (To determine the amount of the loan, multiply the level amount times its percent. Get the loan amount for that level and then add the level loan amounts together to get the total loan amount. $50,000 x .90 = $45,000$50,000 x .95 = $47,500$40,000 x .97 = $38,800Total: $131,300)

Frank just sold his house for 6% more than he paid for it. The selling price was $140,450. What was the original purchase price

$132,500 ($140,450 divided by 106% = $132,500)

A seller has $5,000 closing costs, a $93,000 loan balance, and pays 7% commission on a $125,000 sale. What are his net proceeds from the sale

$18,250 ($5,000 + $93,000 = $98,000 total dollar expenses of closing. Convert 7% to a decimal and multiply. $125,000 x .07 = $8,750 commission; $125,000— $98,000— $8,750 = $18,250 net proceeds to seller)

What is 75% of $250,000?

$187,500 (Convert 75% to a decimal and multiply; $250,000 x.75 = $187,500)

Mr. Jones, an owner of a packaging firm, purchased a new machine in 1991 and paid $5,500. It was estimated at the time of the purchase to have a total economic life of 10 years and a salvage value of $550. Using the straight line method of depreciation, the book value at the end of 7 years would be:

$2,035 (Salvage value must be deducted before computing depreciation. $5,500 - $550 = $4,950 divided by 10 = $495 per year x 7 years = $3,465. $5,500 - $3,465 = $2,035 (book value)

Dick purchased a home for $118,600 and arranges to finance the purchase with a 90% loan. The terms of the loan are 10.75% annual interest, a 2% loan fee, and a three point discount. What is the amount of the loan fee and the discount?

$2,135; $3,202 ($118,606 x 90% = $106,740 (amount of loan) x 2% (loan fee) = $2,135. $106,740 x 3% (discount) = $3,202)

The lender's underwriting criteria would accept a housing expense to income ratio of 33% and a ratio of total debt service of up to a maximum of 38% of monthly gross income. The applicant has an outstanding college loan payable at the rate of $150.00 per month and a car payment of $450.00 monthly. Gross annual income is established at $100,000 per annum. What is the maximum PITI the lender will approve?

$2,566.67 ($100,000/12) x 0.38 is $3,166.67 - ($150 + $450) = $2,566.67)

To buy a car, Bob executed a second trust deed and note on his home for $2,600, payable at $66.00 per month, including interest at 8%. When he sold his home, he paid off the entire loan balance of $1,989.50. What was the total face amount of the principal on the loan?

$2,600 (The face amount of the loan is the amount of the original amount on the note)

A man has an investment in a 30-unit rental property which was adjacent to a freeway. Because of its proximity to the freeway, the owner lost $250 per month in rent. If the capitalization rate were set at 15%, the loss in value to the property was

$20,000 ($250 x 12 = $3,000 divided by .15 = $20,000)

How much money would have to be invested at 8% interest to provide an income of $140.00 per month

$21,000 ($140 x 12 = $1,680 per year. $1,680 divided by 8% = $21,000)

Lynn sold a home for $27,000. She made a 15% profit. What did the home cost

$23,478 ($27,000 divided by 115% = $23,478)

The net income of an apartment building went down $200 per month when a freeway was built nearby. If investors demand a 10% capitalization rate for this area, how much has the building lost in value?

$24,000 ($200 x 12 = $2,400. $2,400 divided by 10% = $24,000)

A property sold for $110,000. Buyer Tom financed 90%. Approximately how much will the monthly PMI increase his payment if the renewal rate is .30%?

$24.75 ($110,000 x 90% = $99,000 (amount of loan) x .30% = $297 yearly renewal rate. 297 divided by 12 = 24.75 monthly increase)

When there is an existing assessment lien against a property and the buyer assumes that lien, the cost basis of the property is then the original cost, plus the amount of the lien. If Juan and Rosa bought a home for $240,000, and assumed an existing assessment lien in the amount of $2,000, what is their cost basis

$242,000 (The cost basis of a property is the purchase price plus any liens and capital improvements)

How much money must be loaned to receive $15,000 if the money is loaned for five years at 12% interest

$25,000 ($15,000 (total interest) divided by 5 = $3,000 (interest per year). $3,000 divided by 12% = 25,000 loan amount)

Hector and Maria Hernandez have paid a total of $10,500 in mortgage interest and $1,500 in property taxes in this tax year. If they are in the 28% tax bracket, their tax savings is

$3,360 (The taxpayer is permitted to deduct $12,000 from earned income. At the 28% tax rate, the savings would be $3,360; ($10,500 + $1,500) x 0.28 = $3,360)

Mr. Johnson purchased a home for $79,000 with a $19,000 cash down payment and a $60,000 loan. This loan was interest free and required no payments of principal for five years. One year later he sold the home for double its purchase price. Each dollar of his original cash investment now equals

$5.16 (79,000 x 2 = $158,000. $158,000 - $60,000 = $98,000. $98,000 divided by $19,000 = $5.16)

Ted purchased a building for $250,000. The terms of purchase were $175,000 cash, and a purchase money deed of trust for the balance. If the land is valued at $50,000 what is the adjusted cost basis of the property after it is fully depreciated

$50,000, the value of the land. (Only the improvements are depreciated. Therefore, after the property has been fully depreciated the adjusted cost basis would still be the original value of the land, $50,000)

An apartment has total operating expenses of $75,000 a year and income of $750 a month for each of its 15 units. If an investor wants a 12% return on his money, what is the value of this property to him?

$500,000 ($750 x 15 = $11,250 income per month; $11,250 x 12 = $135,000 income per year; $135,000 income - $75,000 expenses = $60,000 annual net operating income. Convert 12% to a decimal and divide; $60,000 12 = $500,000 value to investor)

Jane purchased a home for $150,000. She received a loan from the bank for 75% of the purchase price, payable at $1,600 per month including 10% interest. She then sold the home for $165,000 before she even made the first payment on the loan. What was her equity at the time of the sale?

$52,500 ($150,000 x 75% = $112,500 loan amount. $165,000 - $112,500 loan = $52,500 equity)

A buyer assumed a note secured by a deed of trust. The balance of the note was $11,000 with an annual interest rate of 6-1/2% payable quarterly. The interest on the note was to be prorated upon possession of the property. If the interest on the note had been paid to March 15, and he took possession February 15, he would owe how much prorated interest

$59.58 (One month's interest from February 15 to March 15. $11,000 x .065 = $715 per year divided by 12 = $59.58 per month)

Mr. Johnson listed his home with Broker Smith for $165,000 with a commission rate of 6%. Broker Smith brought an offer at 10% less than the listed price. Mr. Johnson said he would accept the offer if the broker reduced his commission by 16-2/3%. If they all agreed to these terms, what amount of commission would Broker Smith receive?

$7,425 (16-2/3% is 1/6. 1/6 of 6% is 1% (so total commission is 5%). $165,000 x 90% (100% - 10%) = $148,500 selling price. $148,500 x 5% = $7,425)

A lender is providing 90% of the financing for a new house. If the house appraises for $75,000, what is the buyer's down payment

$7,500 (100% - 90% = 10% down payment. Convert 10% to a decimal and multiply. $75,000 x .10 = $7,500)

The original value of a property was $130,000, with the land valued at $20,000. If the economic life of the improvements were estimated to be 30 years using the straight line approach, what was the book value of the property after 15 years

$75,000 ($130,000 - $20,000 = $110,000. $110,000 divided by 30 years = $3,666.67. $3,666.67 x 15 years = $55,000 depreciation. $130,000 - $55,000 = $75,000 book value)

What is the salesperson's 45% of a 6% commission on a $31,000 sale?

$837.00 ($31,000 x 0.06 = $1,860 x 0.45 = $837)

A buyer wants a 8% return on his investment and he is interested in a retail center that produces a net operating income of $75,000 per year, what would the investor be willing to pay for the center?

$937,500 (Divide the net income, $75,000 by the capitalization rate, 8% to get $937,500)

A house was purchased 5 years ago for $90,000. The area has generally appreciated at an annual rate of 2%. How much should the house sell for now?

$99,000 (5 years 2% per year = 10% appreciation (straight line); 100% + 10% = 110% property is now worth relative to original purchase price; $90,000 x 110% = $99,000 current value)

The principal balance on a loan is currently $58,500. The scheduled monthly payment on the loan, including principal and interest, is $550. All of the payment goes toward interest, except for $46. What is the interest rate

10.34% ($550 - $46 principal payment = $504 interest payment. $504 x 12 months = $6,048 annual interest. $6,048 divided by $58,500 loan balance = .1034 (10.34%)

If building costs increase by 15%, the purchasing power of the investment dollar decreases by

13% ($1.00 divided by $1.15 = .87 (87%). Purchasing power is 87% of what it was, which means it has decreased by 13%)

Steve purchased a note worth $6,000 for $5,500. Interest rate on the note is 5%. What was his percentage of profit made on his investment if the note is paid off in one year?

14.5% ($6,000 x .05 = $300. $6,000 - $5,500 = $500. $300 + $500 = $800 divided by $5,500 = .145 (14.5%)

A house fronts on two roads running at right angles to each other. The house touches one road for 2,660 feet and on the second road for 1,980 feet. Another property line is parallel to the shorter of the two roads and runs for 2,660 feet. The final boundary is a straight line connecting the open ends. How many acres does the property contain

142 (To find the area of a trapezoid, add base 1 and base 2, then divide the total by 2 and multiply by the height)

Ted paid $85,000 for a house, putting up a 15% cash down payment and borrowing the balance at 8.5% interest. The loan is payable over 30 years with monthly payments of $560, including principal and interest. If Ted makes the payments as scheduled, the percentage that the original cost of the house increased because of the use of credit is?

152.2% ($560 x 360 months = $201,600 (loan payments). $85,000 x 15% = $12,750 (down payment). $201,600 + $12,750 = $214,350 (total cost). $214,350 divided by $85,000 x 100 = 252.2%. 252.2% - 100% (original cost) = 152.2% increase)

An individual borrowed $9,000 on a straight note and an interest of 7%. If the total interest paid on the note totaled $840.00, the term of the loan was

16 months (To determine this, you multiply $9,000 times 7%, which equals $630.00 interest per year. Next $630.00 divided by 12 equals $52.50 per month. And finally $840.00 total interest divided by $52.50 equals 16 months)

A $7,000 loan is sold to an investor for $6,500. It is a straight note, due and payable at the end of one year. It bears a 9% interest rate. What percentage return on the principal dollar invested will be made by the investor

17.38% ($7,000 x 9% = $630 interest paid on the loan. $7,000 - $6,500 = $500 made by investor as a result of the discount. $630 + $500 = $1,130 total profit made by investor. $1,130 divided by $6,500 = 17.38)

The S 1/2 of the SE 1/4 of Section 4, the N 1/2 of the NW 1/4 of Section 8, and the N 1/2 of the NE 1/4 of Section 15 contain how many acres?

240 (The S 1/2 (640 acres to a section divided by 2 = 320) of the SE 1/4 (320 divided by 4 = 80) contains 80 acres. The N 1/2 of the NW 1/4 and the N 1/2 of the NE 1/4 both contain 80 acres. 80 x 3 = 240 acres)

John has a loan for $18,000 with interest to be paid at the rate of $225 quarterly. What is the interest rate on the loan?

5% but less than 6% (225 x 4 = 900 divided by 18,000 = .05 (5%)

Assume Mr. Willis owns his home but he borrowed money to buy it with a loan payable at $112.44 per month. The balance on the loan for the last month was $16,000. $32.44 was applied on his principal on his last payment. What was the interest rate on the note in these circumstances?

6% ($112.44 (monthly payment) - $32.44 (principal part of payment) = $80.00 (interest). $80.00 x 12 months = $960 interest per 1 year. $960 divided by $16,000 (loan balance) = 6%)

An apartment building cost $600,000. It brings in a net income of $4,000 per month. The owner is making what percentage of return on the investment

8% ($4,000 per month x 12 months equals $48,000 per year (always convert monthly rent to annual rent in the income approach). Net income $48,000 + $600,000 cost (or value) = 8% return on the investment)

Jim bought a second trust deed and note that had a face amount of $1,800 on which he was allowed a 20% discount. If he received payments of $120 per month, including 8% interest, for 1 year, what was his percentage of return on his investment?

No return was received on the investment ($1,800 x 20% = $360. $1,800 - $360 = $1,440. $120 x 12 = $1,440 - $1,440 = 0. No return on this investment)

What is the indicated value of a home if the others in the neighborhood sold recently for between $160,000 and $167,000, and the subject house has a pool (valued at $8,000 by the appraiser) that the others do not have

between $168,000 and $175,000 (If the value of the pool is $8,000, the adjustment is a direct addition to the range of the current sales in the neighborhood which did not have pools)

Two appraisers, one using a capitalization rate of 10% and the other one 8%, both agree that the net income of a building was $11,200. The higher capitalization rate made the price of the building

lower by 20% ($11,200 divided by 10% = $112,000. $11,200 divided by 8% = $140,000. $140,000 - $112,000 = $28,000 or 20% lower)

Jessie Petersen makes a written offer to buy Sam Lewis's house for $120,000. She confides in Sam's agent, George Smith, that if necessary she'd pay $10,000 more, but she doesn't want Sam to know that. George should:

warn Jessie that he must pass on to Sam anything useful he knows (Jessie is entitled to honest treatment, so Sam should explain that he owes her no confidentiality and that he does owe a duty of notice to Sam)