Real Estate Math #18

A The first step is to subtract the rate of depreciation from 100%.100% - 25% = 75%This shows that the property is worth 75% of what it was originally worth. Now we can use the basic percentage formula to solve the problem. We know the "part," i.e., its recently appraised value, and the percentage, so we need to isolate the "whole," which is its original value.P = % × WP ÷ % = W$257,000 ÷ .75 = W$342,666.67 = W

A 10-year-old property was recently appraised for $257,000. It has depreciated 25% since it was new. What was it originally worth? A. $342,667 B. $355,886 C. $356,925 D. $392,125

C First, calculate the year's base rent, by multiplying the square footage by the rental rate (3,000 square feet × $20 per square ft. = $60,000). Next, subtract the amount attributable to the square footage from the total rent, to find the rent attributable to gross sales ($120,000 - $60,000 = $60,000). Finally, divide that portion of the rent by 8% to find the property's gross sales ($60,000 ÷ .08 = $750,000).

A 3,000 square foot retail property rents annually for $20 per square foot, plus 8% of the tenant's gross sales. The building's tenant pays $120,000 rent in one year. What were that year's gross sales? A.$75,000 B.$150,000 C.$750,000 D.$1,500,000

C Each discount point is 1% of the loan amount, so 3 discount points is 3% of $150,000. $150,000 × .03 = $4,500.

A borrower agrees to pay 3 discount points on a $150,000 loan. How much do the discount points cost? A.$1,500 B.$3,000 C.$4,500 D.$9,000

C An interest problem can be solved using the basic percentage formula. However, there's one small twist to this problem: instead of being given the annual amount of interest, we're told the value of the semi-annual payment (meaning there are two per year). Simply multiply $43,312.50 by 2, to find that the annual interest payment is $86,625.Next, plug the numbers into the percentage formula. We know the "part," i.e. the interest, and the "whole," i.e. the principal, so we need to isolate the rate.P = % × WP ÷ W = %$86,625 ÷ $990,000 = %.0875 = %Expressed as a percentage, that's 8.75%.

A borrower obtains a mortgage loan in the amount of $990,000, with semi-annual interest payments of $43,312.50. What is the loan's interest rate? A. 8.50% B. 9.0% C. 8.75% D. 9.25%

C One discount point is the equivalent of one percent of the loan amount. Multiply the loan amount by 1% to find the cost of the discount point ($88,000 × .01 = $880). The other numbers given can and should be ignored.

A borrower takes out an $88,000 loan at 6% interest. The monthly principal and interest payment, amortized over 30 years, is $585. He also makes a $12,000 downpayment. The borrower will need to pay one discount point to the lender. How much is the cost of one discount point? Select your answer below: A.$5.85 B.$88 C.$880 D.$1,000

B The first step is to find out how much the brokerage made as a commission for the first $1,000,000 of the sales price. This can be calculated using the basic percentage formula.P = % × WP = .07 × $1,000,000P = $70,000Now subtract that $70,000 from the total $122,500, and you'll find that the remaining portion of the firm's commission was $52,500. Subtract the $1,000,000 from the total $2,500,000 sales price of the building, and you'll determine that the $52,500 portion of the commission was earned for the remaining $1,500,000 of the sales price.Now you have enough information to use the percentage formula to find the rate. You have the "part," i.e. the commission, and the "whole," i.e. the sales price, so you have to isolate the percentage.P = % × WP ÷ W = %$52,500 ÷ $1,500,000 = %.035 = %Expressed as a percentage, that's 3.5%.

A brokerage sells an apartment building for $2,500,000. The brokerage earns a commission of $122,500. If the firm was paid a 7% commission on the first $1,000,000 of the sales price, what was its rate of commission on the remaining part of the sales price? A. 3% B. 3.5% C. 4% D. 6%

A This question asks for square footage, not cubic footage, so we can disregard the fact that the building has nine-foot ceilings. Instead, simply apply the area formula.A = B × HA = 35 × 60A = 2,100 square feet

A building's dimensions are 35' × 60' × 9'. How many square feet does it contain? A. 2,100 B. 3,450 C. 18,900 D. 21,355

B Subtract the operating expenses from the gross income to find the net income: $1,100,000 - 80% = $220,000. Then divide the net income by the capitalization rate to find the value: $220,000 ÷ 11.5% = $1,913,043.

A building's gross annual income is $1,100,000. Its operating expense ratio is 80%. The capitalization rate is 11.5%. What is the building's value using the capitalization approach? A. $1,585,000 B. $1,913,043 C. $1,688,230 D. $1,934,424

C First, calculate the amount of the downpayment ($380,000 × .5 = $190,000). The balance of the purchase price is the loan amount ($380,000 - $190,000 = $190,000), which is used to calculate the interest paid over the course of the year ($190,000 × .11 = $20,900). Add these elements, plus the prepaid $19,000 to find that the seller receives $229,900 during the first year ($190,000 + $20,900 + $19,000 = $229,900).

A buyer purchases a home for $380,000 using a seller-financed straight loan. If he pays 50% down, makes monthly payments on the balance at 11% interest, and pays an extra $19,000 towards the principal before the end of each year, how much does the seller receive during the first year? A. $39,900 B. $60,800 C. $229,900 D. $250,800

B The first step is to determine the per diem amount of $133.33 ($4,000 divided by 30 equals $133.33). The buyer is entitled to receive the rental income from the 17th through the 30th, for a total of 14 days. Multiply $133.33 by 14 days to find that the prorated amount of rent is $1,866.67, or $1,867.

A buyer purchases an apartment complex that generates $4,000 per month in rental income. Rent is paid at the beginning of each month. The closing date will be the 16th, and the deed will be recorded on the 20th. The seller receives rent for the closing date. In a 30-day month, what portion of rent for the month of the sale is prorated to the buyer? Select your answer below: A.$1,200 B.$1,867 C.$2,000 D.$2,133

C First, calculate the annual net income using the capitalization formula ($1,600,000 x .2 = $320,000). Now you need to use the percentage formula to calculate the gross income, but don't use the percentage of the gross income that is taken up by the operating expenses (which is 40% or .4); instead use the percentage of the gross income that is not taken up by the operating expenses. Since the operating expenses are 40% or .4, that leaves .6 or 60% as the percent of annual income that is net income. You can use this percentage by division to find the larger amount: gross income.Calculate the gross income ($320,000 ÷ .6 = $533,333.33). You can double-check your math by calculating what is 40% of the gross income ($533,333.33 x .4 = $213,333.33), and subtracting that amount (which represents the operating expenses) from the gross income to verify the net income ($533,333.33 - $213,333.33 = $320,000).

A commercial building is valued at $1,600,000 if its annual net income is capitalized at a rate of 20%. If the operating expenses total 40% of the gross income, what is the approximate annual gross income? A.$128,000 B.$192,000 C.$533,333.33 D.$800,000

A The first step is to calculate the property's annual net income. If the operating expense ratio is 83%, that means that the remaining 17% of the gross income is the owner's net income (100% - 83% = 17%). Now plug that information into the basic percentage formula.P = % × WP = .17 × $555,000P = $94,350Now that we know the net income, we have enough information to use the capitalization formula. We know the income and the capitalization rate, so we need to isolate the property's market value.I = R × VI ÷ R = V$94,350 ÷ .11 = V$857,727.27 = V

A convenience store grosses $555,000 annually. Its operating expense ratio is 83%. If the appraiser assigns an 11% capitalization rate, what is the estimated value of the property? A. $857,727 B. $892,345 C. $901,211 D. $950,445

A The first step is to find the total square footage of the lot. Use the area formula.A = B × HA = 150 × 200A = 30,000 square feetNext, we need to find what percentage of the lot can be used for parking. The store occupies 30% of the lot, and the easement occupies another 10%, for a total of 40%. Therefore, 60% of the lot remains for parking. Now we can use the percentage formula to find out how many square feet that represents.P = % × WP = .6 × 30,000P = 18,000 square feet

A convenience store occupied 30% of a 150' × 200' lot. Ten percent of the lot was condemned for a public easement. How many square feet was left for parking after the easement was established? A. 18,000 B. 18,460 C. 19,759 D. 21,346

B This problem involves depreciation, which can be tricky. Remember that the house isn't worth 16% of what it was worth four years ago. Instead, we have to subtract that 16% from 100%. In other words, the house is now worth 84% of what it used to be worth. Now we can apply the Then and Now (Value After) formula, which is just a variation on the basic percentage formula. We know the "part" (its current value, which is only part of the original value) and the percentage of depreciation, and we need to isolate the "whole" value of the home (in other words, the "then" value, or the value before).P = % × WP ÷ % = W$600,000 ÷ .84 = W$714,285.71 = W

A home is presently appraised at $600,000. Calvin bought it new four years ago. Since then it has depreciated 16%. What was the home originally worth? A. $657,800 B. $714,286 C. $734,044 D. $747,900

C Calculate the loan amount ($500,000 - $50,000 = $450,000).Then calculate the amount of the discount points and loan origination fee (which together are 4% of the loan amount, with 3% for discount points and 1% for the loan origination fee).P = % × WP = .04 × $450,000P = $18,000Calculate the brokerage fee.P = % × WP = .06 × $500,000P = $30,000Add the points and the brokerage fee together for the final amount of expenses ($18,000 + $30,000 = $48,000).

A house is sold for $500,000 with a $50,000 downpayment. The seller will pay 3 discount points and a 1% loan origination fee. The brokerage fee is 6%. What are the seller's expenses? A. $43,500 B. $45,000 C. $48,000 D. $50,000

A The first step is to find the value of the loan. We know that the percentage of the downpayment is 20%, so subtract that from 100% and you'll find that the loan value is 80% of the property's sales price. Now we can use the percentage formula to find the loan value.P = % × WP = .80 × $725,000P = $580,000Remember that a point is equivalent to one percent of the loan amount. Therefore, three points is 3% of the loan amount. We can find the value of those points using the percentage formula.P = % × WP = .03 × $580,000P = $17,400However, we still need to find the value of the downpayment. We know it's 20% of the sales price, so we can find that using the percentage formula too.P = % × WP = .20 × $725,000 = $145,000Finally, add the downpayment and the points together to find the amount of cash required at closing.$17,400 + $145,000 = $162,400

A lender charges a borrower 3 points. How much money will the borrower have to have at closing if the sales price is $725,000 and the lender is requiring a 20% downpayment? A. $162,400 B. $21,750 C. $17,400 D. $166,750

320,000

A listing agreement provides that Smith Realty's commission will be 6% of the first $200,000 of the sales price, plus 3.5% of any amount in excess of $200,000. Smith Realty sells the property, and its commission totals $16,200. How much did the property sell for?

B First, multiply the length and width to find the square footage (18 ft. × 15 ft. = 270 sq. ft.). Then, because there are 9 square feet in a square yard, divide by 9 to convert to square yards (270 ÷ 9 = 30 square yards).

A living room needs to be re-carpeted. It measures 18 feet long by 15 feet wide. How many square yards of carpet will need to be purchased? A.10 B.30 C.90 D.270

C Add the settlement costs to the seller's net: $112,000 + $3,686 (settlement costs of $2,450 + $1,236) = $115,686. This amount is 94% of the sales price (100% - 6% commission = 94%). $115,686 ÷ 94% = $123,070.21 (sales price).

A property with no outstanding liens sold. The seller paid $2,450 in discount points, $1,236 in other closing costs, and a 6% commission. She received a closing check for $112,000. What was the selling price? A.$118,720 B.$122,405 C.$123,070 D.$125,250

B Use the capitalization formula (Income ÷ Capitalization Rate = Value) to find the property's value: $12,000 net income ÷ 0.12 rate of return = $100,000 value.

A property's net operating income is $12,000 per year. If an investor wants a 12% rate of return, how much is the property worth to him? / A.$1,440 B.$100,000 C.$144,000 D.$1,000,000

D The seller is responsible for the taxes for the first four and a half months of the year (January, February, March, April, and half of May). $250 × 4.5 = $1,125.

A property's real estate taxes are $250 per month, paid at the end of the year. The property is sold and the closing date is May 15. Which of the following options is closest to what the seller's share of the taxes would be? A.$750 B.$875 C.$1,000 D.$1,125

C The first step is to calculate by how much the February 1st mortgage payment would reduce the principal balance. Start with the balance after the January payment and calculate how much annual interest the borrower would owe on that ($44,731.15 × .05 = $2,236.56 annual interest). Then divide that by 12, since this is a monthly payment ($2,236.56 ÷ 12 = $186.38 monthly interest).Subtract that interest from the total payment amount to find how much that payment will reduce the loan's principal ($1,484.40 - $186.38 = $1,298.02); this is important—otherwise, you are calculating the penalty on interest that hasn't accrued yet (interest on a real estate loan isn't due till the end of a payment period). Subtract that amount from the previous balance to find what the balance will be after making the February payment ($44,731.15 - $1,298.02 = $43,433.13). Multiply that balance by 3% to find the amount of the prepayment penalty ($43,433.13 × .03 = $1,302.99). [Note: alternatively, the interest rate itself may be divided by 12 and the result multiplied by the balance after the January payment and then proceed from there.]

A mortgage includes a prepayment penalty of 3% of the loan's balance at the time of payoff, if the owner pays off the entire balance before a specified date. Monthly amortized principal and interest payments are $1,484.40, with a 5% annual interest rate. The borrower's balance after making the January 1st payment was $44,731.15. On February 1st, he made the next payment as scheduled, and then after that, paid off the entire remaining balance. What would the prepayment penalty be? A.$290.30 B.$1,257.20 C.$1,302.99 D.$1,319.37

C The first step is to figure out what the annual interest payment is. The question only gives semi-annual interest payments, meaning there are two per year. Simply multiply the payment ($6,750) by 2 to determine that the annual interest on the loan is $13,500.Next, plug this information into the basic percentage formula. We know the "part," i.e. the interest, and the rate, so we need to isolate the value of the "whole," i.e. the principal.P = % × WP ÷ % = W$13,500 ÷ .09 = W$150,000 = WFinally, we need to calculate the value of the house. Again, we can use the percentage formula. And again, we know the "part," i.e., the value of the loan, and the percentage, so we need to isolate the "whole," i.e., the value of the house.P = % × WP ÷ % = W$150,000 ÷ .80 = W$187,500 = W

A mortgage loan is 80% of the sales price. The loan's interest rate is 9%, and the borrower makes semi-annual interest payments of $6,750. What is the sales price? A. $176,000 B. $181,250 C. $187,500 D. $191,450

B The first step would be to find the square footage of the lot (198 ft. x 330 ft. = 65,340 square feet). Convert that to acreage (65,340 square feet ÷ 43,560 square feet per acre = 1.5 acres). Divide the cost by the acreage to find the cost per acre ($30,000 ÷ 1.5 acres = $20,000 per acre).

A parcel measures 198 feet by 330 feet. It sold for $30,000. What was the price per acre? Select your answer below: A.$294 B.$20,000 C.$45,000 D.$2,500,000

D First, calculate the square footage of the land.A = B × HA = 940 × 1,660A = 1,560,400Now calculate what 22% of the square footage is.P = % × WP = .22 × 1,560,400P = 343,288Subtract that percentage that reflects the dedication (1,560,400 - 343,288 = 1,217,112).Now divide the square footage by the number of square feet in an acre, in order to determine how many acres are present (1,217,112 ÷ 43,560 = 27.94).Finally, since each lot is a quarter of an acre, multiply the number of acres by 4 to find the number of lots (27.94 × 4 = 111.76 lots).

A parcel of land has dimensions of 940 feet by 1,660 feet. Twenty-two percent of the parcel is to be dedicated to the public for schools and roads. The remaining land is subdivided into one-quarter acre lots. How many lots would there be? A. 94 B. 101 C. 108 D. 111

A First, calculate the amount of the commission ($400,000 × .06 = $24,000). Subtract the outstanding mortgage balance, commission, and other costs from the selling price ($400,000 - $200,000 - $24,000 - $4,000 = $172,000).

A property is listed for $400,000. The sellers owe $200,000 to the bank on the mortgage, and have agreed to pay a 6% commission. They will also owe $4,000 in other closing costs. If the property sells for full price, what will their net proceeds be? A.$172,000 B.$184,000 C.$193,600 D.$200,000

B This is a seller's net problem, except backwards, starting with the sales price. Start by finding the amount of the commission ($340,000 × 0.065 = $22,100) and then subtract the commission from the price paid ($340,000 - $22,100 = $317,900). Subtract the other costs ($68,000 mortgage + $6,400 other closing costs = $74,400) that must be paid to find the seller's net ($317,900 - $74,400 = $243,500).

A property is sold for $340,000. There is a remaining mortgage balance of $68,000, and other closing costs will be $6,400. The seller also must pay a brokerage fee of 6.5%. What will the seller net? A.$237,100 B.$243,500 C.$243,916 D.$254,320

B The first step is to determine the annual income ($10,500 per month × 12 = $126,000 per year). Divide that by the capitalization rate to find the property's value ($126,000 ÷ 0.12 = $1,050,000).

A property produces a 12% rate of return. The property's net income is $10,500 per month. Using the capitalization method, what is the property's market value? A.$875,000 B.$1,050,000 C.$1,512,000 D.$2,000,000

D The first step is to calculate the assessed value, which is only a portion of the property's market value. Calculate this as a basic percentage problem.P = % × WP = .25 × $90,000P = $22,500The formula for calculating an assessment is Assessed Value × Tax Rate = Tax. However, before we can do that, we have to convert the tax rate into decimal form. Divide 5.50 by 100, and the tax rate expressed as a decimal is .055. Now, we can plug that into the assessment formula in order to find out how much tax will be paid.AV × Rate = Tax$22,500 × .055 = $1237.50

A property recently sold for $90,000. It is assessed at 25% of its value. What will the tax be if the tax rate is $5.50 per $100 of assessed valuation? A. $837.45 B. $994.67 C. $1,045.32 D. $1,237.50

A The total commission amount is $6,000 ($100,000 × .06 = $6,000). If the brokerages split it 60/40 in the order stated, the selling brokerage will receive $3,600 ($6,000 × .6 = $3,600) and the listing brokerage will receive $2,400 ($6,000 × .4 = $2,400). The individual listing agent's share will be $1,200 ($2,400 ÷ 2 = $1,200).

A property sells for $100,000. The commission is 6%. The selling brokerage and listing brokerage split the commission 60/40 respectively. Each of the brokerages then splits its share of the commission evenly with its affiliated licensee. How much is the individual listing agent's share of the commission? A.$1,200 B.$2,400 C.$3,600 D.$6,000

C $104,000 (desired net) + $2,400 + $1,500 = $107,900 (required net after commission but before settlement costs). $107,900 ÷ 93% (100% - 7% commission rate) = $116,021.51.

A real estate agent takes a listing in which the seller says she wants to net $104,000. The agent charges a 7% commission. There are expenses of $2,400 in discount points and $1,500 in repairs that will be paid out of the sale price. In order for the seller to net $104,000, the property must sell for at least: A.$112,500 B.$113,750 C.$116,022 D.$119,950

B The first step is to find the square footage of the lot (215 feet × 154 feet = 33,110 square feet). Convert this to acreage (33,110 square feet ÷ 43,560 square feet per acre = 0.76 acres). $40,000 × 0.76 is $30,400, closest to $30,000.

A rectangular lot measures 215 feet by 154 feet. If comparable land sells for $40,000 per acre, how much is this lot likely to sell for? A.$20,000 B.$30,000 C.$40,000 D.$50,000

B Multiply the monthly income by 12 to find the annual net income. $1,100 × 12 = $13,200. Then divide the net income by the rate of return (10%) to find the value. $13,200 ÷ .10 = $132,000.

A rental property produces a 10% rate of return. The net income on the property is $1,100 per month. Using the income approach to value, what is the property's market value? A.$99,500 B.$132,000 C.$155,000 D.$187,500

B To determine the seller's proceeds, start with the selling price ($128,000), subtract the existing loan balance payoff ($43,000), subtract the closing costs ($3,000), and subtract the brokerage fee ($128,000 × .055 = $7,040). The result is $74,960 ($128,000 - $43,000 - $3,000 - $7,040 = $74,960). Click Here for the Next Question

A seller sells his house for $128,000. He pays off the $43,000 balance on the existing loan, and his closing costs are $3,000. What should the seller net if the brokerage fee is 5.5%? A.$14,600 B.$74,960 C.$77,960 D.$140,960

B To determine the seller's proceeds, start with the selling price ($128,000), subtract the seller financing ($63,000), subtract the existing loan balance payoff ($43,000), and subtract the brokerage fee ($128,000 × .055 = $7,040). The result is $14,960 ($128,000 - $63,000 - $43,000 - $7,040 = $14,960). Note: 'Proceeds' is generally understood to mean money actually taken away at closing. Money received over the years for the seller-financed mortgage isn't part of the check the seller gets on closing day, so it's not considered proceeds.

A seller sells his house for $128,000. He takes back a mortgage from the buyer for $63,000. He pays off the $43,000 balance on the existing loan, and pays a 5.5% brokerage fee. What are his proceeds from the sale? A. $14,600 B. $14,960 C. $77,960 D. $140,960

C Start by adding the desired net and the other costs, including the mortgage ($60,000 + $181,800 = $241,800). Subtract the commission percentage from 100% (100% - 7% = 93%), and then divide the total by that percentage ($241,800 ÷ 0.93 = $260,000).Since the agent bases her commission on the total selling price, you can't simply add 7% of the costs and profit to the selling price or you won't quite have her full commission. You need a price that the agent can take 7% from and still satisfy the seller's goals. A fuller explanation is found in the section on seller's net problems in ch. 18 of Fundamentals.

A seller wants to net $60,000 from a transaction, but will have to pay off a mortgage and other fees, at a total cost of $181,800. The seller will also need to pay a 7% commission. What will the property need to sell for? A.$241,800 B.$258,726 C.$260,000 D.$276,060

A Multiply 110 feet by 90 feet to get 9,900 square feet. Multiply 9,900 square feet by $11, which is the cost per square foot. 9,900 × $11 = $108,900 (annual rent). Multiply $108,900 by 9 years to determine the total amount of rent paid over ten years. $108,900 × 9 = $980,100. Divide the total rent paid by 120 (months), the actual term of the lease, and the average monthly rent comes to $8,167.50.

A small office building with measurements of 110' x 90' rents for $11 per square foot annually. Smith signs a 10-year lease, with the first year's rent waived by the landlord. If Smith makes monthly payments, what will the payments average over the ten-year period? A. $8,167.50 B. $9,075 C. $9,345.11 D. $9,875

A One-eighth of a mile is equivalent to 660 feet (5,280 feet ÷ 8 = 660 feet). Multiply to find its square footage (660 feet × 660 feet = 435,600 square feet), and then divide to find the number of acres (435,600 square feet ÷ 43,560 square feet per acre = 10 acres).

A square parcel measures 1/8 of a mile by 1/8 of a mile. How many acres is this property? A.10 B.20 C.40 D.80

A First, multiply the property's boundaries to find its square footage (1,320 feet × 1,320 feet = 1,742,400 square feet). Convert it to acreage (1,742,400 square feet ÷ 43,560 square feet per acre = 40 acres), subtract the unusable portion (40 acres - 8 acres = 32 acres), and multiply by the price per acre (32 acres × $2,000 = $64,000).

A square parcel of farmland measures 1,320 feet from north to south. In the center of the parcel is eight acres of swampland that is not tillable. If the property sells for $2,000 per acre of tillable land, what is the selling price? A.$64,000 B.$80,000 C.$96,000 D.$2,624,000

C Only the building itself is depreciated, rather than the land, which cannot lose value due to depreciation. Multiply 1.5% by 10 years (since the question says "an average of" 1.5% per year, rather than saying it depreciated 1.5% each year), which is 15%. 15% of $120,000 is $18,000.

A ten-year-old home cost $120,000 to build and the land it's on cost $20,000. If an appraiser finds that depreciation has averaged 1.5% per year, what is the total amount of depreciation on the property? A.$1,800 B.$2,100 C.$18,000 D.$21,000

A Use the capitalization formula to solve this problem. (Note, however, that the capitalization formula is just a variation on the basic percentage formula.)Income = Rate × Market ValueWe know the income and the rate, so we need to isolate the value.I ÷ R = V$257,500 ÷ .115 = V$2,239,130 = V

An appraiser determines the property's net operating income is $257,500. If she applies a capitalization rate of 11.5%, what is the market value of the property? A. $2,239,130 B. $2,256,740 C. $2,295,800 D. $2,587,480

B The rent has already been paid to the seller, so the seller will need to give some of that rent to the buyer. The buyer's prorated share will be a debit for the seller and a credit for the buyer on the settlement statement. The seller's share is for the 1st through the 15th (15 days), and the buyer's share is for the 16th through the 30th (also 15 days), so the $1,200 can be divided in half. The settlement statement will show a $600 debit for the seller and a $600 credit for the buyer.

A tenant has already paid his $1,200 rent for the month for a single-family property. The property's owner sells it to a new buyer, with closing occurring on the 15th of June. The parties decide the seller is entitled to rent for the closing date. On the settlement statement, the prorated rent will appear as a: A.$600 debit for the buyer and a $600 credit for the seller B.$600 debit for the seller and a $600 credit for the buyer C.$1,200 credit for the buyer D.$1,200 credit for the seller

B Because the problem gives quarterly interest payments, the first step is to convert that to one annual interest payment. Because there are four quarters in a year, multiply the quarterly amount by 4.$1,200 × 4 = $4,800Now we have enough information to solve the problem, using the basic percentage formula. We know the "part" (i.e., the interest payment) and the rate, so we need to isolate the total loan amount.P = % × WP ÷ % = W$4,800 ÷ .095 = W$50,526.32 = W

Able makes $1,200 quarterly interest payments on a term loan. If the interest rate is 9.5%, what is the amount of the loan? A. $45,060 B. $50,526 C. $52,221 D. $59,788

D The first step is to calculate the value of the loan. If Able puts 20% down, then the value of the loan is 80% of the property's value.P = % × WP = .80 × $550,000P = $440,000Note that the interest is expressed in terms of monthly payments. We'll need to multiply by 12 to find the annual interest.$3,755 × 12 = $45,060Now we have enough information to calculate the annual rate of interest. We know the "part" (i.e., the value of the interest), and the "whole" (i.e., the principal), so we need to isolate the percentage rate.P = % × WP ÷ W = %$45,060 ÷ $440,000 = .102409Expressed as a percentage, that's 10.24%.

Able purchases a property for $550,000 and puts 20% down. The monthly interest payments are $3,755. What is the annual rate of interest? A. 9.50% B. 9.90% C. 10.10% D. 10.24%

A Determine the commission on the first $2,000,000.P = % × WP = .07 × $2,000,000P = $140,000Subtract $140,000 from the total commissions ($185,000 - $140,000 = $45,000).$45,000 is the amount paid on the additional $1,500,000 in sales. Divide this by $1,500,000 to find the commission rate on the excess ($45,000 ÷ $1,500,000 = .03).

Agent J sold $3,500,000 worth of real estate. Her commissions totaled $185,000. She was paid 7% of the first $2,000,000. What is the rate of commission on the remainder of the sales? A. 3% B. 3.5% C. 4% D. 6%

D Under the terms of the listing agreement, the seller will pay the listing firm (Ajax) 8% of the sales price ($300,000 × .08 = $24,000). The seller is not a party to the MLS commission split agreement. It's up to Ajax to share half of the money with Baron Realty in fulfillment of the commission split agreement; the seller owes Ajax the full commission amount, not half.

Ajax Realty lists a property for a seller at a commission rate of 8%. The multiple listing service provides that a listing brokerage will split commissions at a 50-50 rate. Baron Realty, a cooperating brokerage, finds a buyer for the property, at a price of $300,000. How much will the seller owe Ajax Realty at closing? A.$0 B.$12,000 C.$18,000 D.$24,000

C Calculate the size of the pet deposit by determining what one-quarter of a month's rent is ($1,000 × 0.25 = $250). Add that to the ordinary security deposit to find the total amount ($1,000 + $250 = $1,250).

An apartment rents for $1,000 per month. At move-in, a security deposit equal to one month's rent is due. In addition, if the tenant owns a cat or dog, a pet deposit of one-quarter of a month's rent is required. How large a deposit (the term "deposit" refers to refundable money, not rent) would a tenant with a dog need to make? A.$750 B.$1,000 C.$1,250 D.$2,250

A First, calculate the investor's original investment ($88,000 × 4 = $352,000). Calculate the amount he grossed from the sale of the lots ($72,000 × 5 = $360,000). Use the Now and Then formula to find the percentage of profit ($360,000 ÷ $352,000 = 1.0227, of which 2.27% is gross profit). (Alternatively, you could find the difference between the purchase and sale prices ($360,000 - $352,000 = $8,000) and divide that by the cost of the initial investment ($8,000 ÷ $352,000 = 0.0227).)

An investor bought four adjacent lots for $88,000 each, and then combined them and divided them into five lots of equal size. These five lots were then sold for $72,000 each. What is the investor's percentage of gross profit? Select your answer below: A.2.27% B.18.18% C.34.55% D.97.78%

B The purchase price was $62,500. This question is simply two separate percentage problems. First, find the loan amount. Two discount points is 2% of the loan amount, so divide the value of the discount points by 2% to determine that this was a $50,000 loan ($1,000 ÷ .02 = $50,000). The 20% downpayment means this is an 80% loan. Now you can use the loan amount and the loan-to-value ratio to find the purchase price. To calculate the purchase price, divide the loan amount by 80% ($50,000 ÷ .80 = $62,500).

An owner sells a property, and the buyer is going to make a 20% downpayment. The lender requires the buyer to pay two discount points, which turn out to total $1,000. What was the purchase price? Select your answer below: A.$50,000 B.$62,500 C.$75,000 D.$200,000

C The house sold for $372,316 plus whatever was subtracted from the sales proceeds at closing (that is, the seller's selling expenses). Thus, to get the sales price (so we can determine the commission), you first add the selling costs to the sale proceeds. $5,264 + $372,316 = $377,580. Then use the seller's net formula. That is, divide the sales price by the commission rate subtracted from 100 (100% - 7% = 93%). $377,580 ÷ 0.93 = $406,000.

Art sold his house, which was not encumbered with a mortgage. Closing expenses were $5,264, and he paid a commission of 7% of the selling price. He received a check at closing for $372,316. What did the house sell for? A.$398,000 B.$404,260 C.$406,000 D.$411,100

B The first step in calculating a tax problem is to find the property's assessed value ($190,000 × 0.5 = $95,000). Divide the assessed value by $1,000 to find the number of increments ($95,000 ÷ $1,000 = 95) and then multiply by the tax rate to find the annual tax bill (95 × $55 = $5,225).

Bob's property has a fair market value of $190,000. It is in a county where properties are assessed at 50% of value, and the tax rate is $55 per $1,000 of assessed value. What's Bob's annual property tax? A.$2,612.50 B.$5,225.00 C.$7,837.50 D.$10,450.00

D One square mile equals 640 acres. Add those to find the total acreage (640 acres + 5 acres = 645 acres). Multiply the acreage by the price per acre to find the total price (645 × $2,000 = $1,290,000).

Brian purchases two parcels of land, one measuring one square mile and the other containing five acres. If he paid $2,000 an acre, what was his total purchase price? A.$1,208,000 B.$1,209,000 C.$1,280,000 D.$1,290,000

B Since the buyer is taking title on August 1, she's responsible for the property taxes for the remaining five months of the year (August, September, October, November, and December). Divide the annual taxes by 12 to find the monthly amount: $6,000 ÷ 12 = $500. Multiply that figure by 5 to determine the buyer's share of the taxes: 5 x $500 = $2,500. (Generally, the state will tell you when to treat all months as equal, but here the even set of dollar amounts in the answers lets you know that.)

Closing is set for August 1. The seller has already paid the property taxes for the year, totaling $6,000. How much of that amount is the buyer's responsibility? A.$2,000 B.$2,500 C.$3,000 D.$3,500

A It's helpful to draw a picture of this property. The resulting odd shape, however, will have to be broken down into two separate shapes to solve the problem. There should be a large triangle, running 600 feet along its west side and 1,250 feet along its south side, sitting above a long, narrow rectangle, 300 feet long along its western and eastern sides and 1,250 feet along its northern and southern sides.Calculate the area of the rectangle first, by multiplying its length by its width.A = B × HA = 1,250 × 300A = 375,000Now calculate the area of the triangle, by multiplying its length by its width by one-half.A = 1/2 × B × HA = 1/2 × 600 × 1,250A = 375,000Finally, add the two areas together (375,000 + 375,000 = 750,000).

From the point of beginning, a property's boundaries run 900 feet in a southerly direction; then due east for 1,250 feet; then in a northerly direction 300 feet; then back to the point of beginning. How many square feet are in the described parcel? A. 750,000 B. 775,000 C. 800,000 D. 805,000

B Multiply the number of square feet in an acre (43,560) by 3.5 (43,560 × 3.5 = 152,460).

How many square feet are in 3.5 acres? A. 2,240 B. 152,460 C. 158,760 D. 97,574,400

B There are nine square feet in a square yard (3 feet per yard × 3 feet per yard = 9 square feet).

How many square feet are in a square yard? Select your answer below: A.3 B.9 C.27 D.81

B The first step is to calculate the total value of the commission. Use the basic percentage formula.P = % × WP = .06 × $832,000P = $49,920Next, we need to find the value of ABC Realty's 50% share of the commission.P = % × WP = .5 × $49,920P = $24,960Finally, we need to find the value of Johnson's 40% share of ABC Realty's share.P = % × WP = .4 × $24,960P = $9,984

Johnson, a broker for ABC Realty, sold a home listed by ACME Realty for $832,000. The companies split the 6% commission 50/50, and Johnson's share of her company's commission was 40%. What was the amount of Johnson's commission? A. $8,920 B. $9,984 C. $24,960 D. $25,800

C The first step is to calculate how much the annual interest payment is. We know the amount of the principal and the interest rate, so plug those into the basic percentage formula.P = % × WP = .095 × $45,000P = $4,275Now that we know the annual interest, we need to find out how much the monthly interest is. Since there are 12 months per year, divide the annual interest by 12.$4,275 ÷ 12 = $356.25Multiply that amount by 20, since interest accrues for 20 months.$356.25 × 20 = $7,125Add the total amount of interest to the amount of the principal to arrive at the total repayment amount.$7,125 + $45,000 = $52,125

Jones borrowed $45,000 to purchase some office furniture. He agreed to pay 9.5% annual interest plus the amount borrowed at the conclusion of 20 months. What was the amount of the payment? A. $42,550 B. $47,650 C. $52,125 D. $54,675

A 110' × 297' = 32,670 square feet. Divide 32,670 by 43,560 (the number of square feet in an acre) to get .75 acres. Multiply .75 acres by $20,000 to get $15,000.

Mac is interested in selling a parcel of land that measures 110' × 297'. Similar property recently sold for $20,000 per acre. What is Mac likely to get for his land? A.$15,000 B.$20,000 C.$32,670 D.$35,000

C Mavis will need to make a $50,000 downpayment ($500,000 sales price x .90 = $450,000 loan amount; $500,000 sales price - $450,000 loan = $50,000 downpayment). She will also need to pay discount points ($450,000 loan x .02 = $9,000 discount points). The interest rate is not necessary for answering this problem. Add the downpayment and discount points for the total amount due at closing ($50,000 + $9,000 = $59,000).

Mavis buys a home with a $500,000 sales price. She will be obtaining a loan for 90% of the property's value. She is paying two discount points, in order to bring the interest rate down from 5% to 4.75%. What is the total amount of cash that she will owe at closing? A.$9,000 B.$10,000 C.$59,000 D.$60,000

C First determine the fixed monthly rent total: $500 × 12 = $6,000. Next, determine by how much the sales exceeded $200,000. $230,000 - $200,000 = $30,000. Multiply that amount by 5%. $30,000 × .05 = $1,500 (additional commission). Add $1,500 to $6,000 for a total of $7,500.

PQR Store enters into a lease agreement in which it agrees to pay a fixed $500 monthly rent, plus 5% commission on all of its sales over $200,000. If its gross sales for the year total $230,000, what is PQR's total annual rent? A.$6,000 B.$6,500 C.$7,500 D.$15,000

A To calculate the discount points, first find the loan amount ($200,000 × .8 = $160,000). Then multiply that by the percentage of the loan represented by the discount points ($160,000 × .03 = $4,800). Since the question only specified discount points, you would not include the origination fee in your calculations (and you certainly wouldn't need to know the cost of the appraisal or the commission).

Rudiger purchases a home for $200,000, and receives an 80% loan from his bank. He has to pay three discount points to receive the loan. He is also responsible for a 1% origination fee and a $300 appraisal. The seller paid a 6% commission to the listing brokerage. What is the amount of the discount points that he paid? Select your answer below: A.$4,800 B.$6,000 C.$6,400 D.$7,500

C The first step in a seller's net problem like this one is to calculate what the seller's desired net is. Here, the seller's desired net is 25% more than the home's original price, or 125% of the original price.P = % × WP = 1.25 × $110,000P = $137,500 (desired net)However, we still need to factor in the other costs. The second step is to add all costs other than the commission.$137,500 + $750 settlement costs = $138,250The next step is to subtract the commission rate from 100%. The reasoning is that if Smith wants to net $137,500, that is only a portion of what he will actually have to sell the home for if he also wants to pay for the agent's commission.100% - 7% = 93%Finally, we use the percentage formula to calculate the entire sales price for the home if we're to include the agent's commission. We already know the "part," (in other words, the portion of the total sales price that Smith keeps) and the rate, so we need to isolate the "whole" sales price.P = % × WP ÷ % = W$138,250 ÷ .93 = W$148,655.91 = W

Smith bought a home six years ago for $110,000. He wants to sell the property for a 25% profit after paying a 7% commission and $750 in settlement costs. What would he have to sell the home for? A. $134,500 B. $141,216 C. $148,656 D. $150,090

A This problem has to be broken into two segments. The first step is to calculate the value of the part of the commission that was earned at the 6% rate. Use the percentage formula.P = % × WP = .06 × $300,000P = $18,000Now we know that $18,000 of the $21,150 was earned at the 6% rate. Subtract $18,000 from $21,150; the remaining $3,150 of the commission was earned at the 3% rate. Use the percentage formula again, this time switching it around to isolate the unknown quantity, which now is the remaining portion of the sales price.P ÷ % = W$3,150 ÷ .03 = W$105,000 = WFinally, add the $105,000 to the $300,000, for a total sales price of $405,000.

The agent earns a 6% commission on the first $300,000 of the sales price and 3% of that portion of the sales price that exceeds $300,000. The commission is $21,150. What is the sales price? A. $405,000 B. $423,000 C. $459,000 D. $463,500

C This is a percentage question that must be solved in two steps. First, calculate what the total commission was, by finding 6% of the $130,000 sales price.P = % × WP = .06 × $130,000P = $7,800Next, calculate what the salesperson's share of the commission was, by finding 40% of the total commission.P = % × WP = .4 × $7,800P = $3,120

The asking price is $145,000. The property sells for $130,000. The commission is 6%. 60% of the commission goes to the brokerage and 40% goes to the broker. How much did the broker receive? A. $2,190 B. $2,850 C. $3,120 D. $3,335

C The first step is to calculate the area of the property. Use the area formula.A = B × HA = 200 × 175A = 35,000Now multiply 35,000 square feet by $30.50 per square foot to find the sales price.35,000 × $30.50 = $1,067,500Finally, use the percentage formula to calculate the amount of the commission.P = % × WP = .07 × $1,067,500P = $74,725

The brokerage's commission is 7% of the sales price. What is the commission if the property sells for $30.50 per square foot and its dimensions are 200' × 175'? A. $65,118 B. $73,500 C. $74,725 D. $15,250,000

B Multiply the property value by the capitalization rate to get the net income ($280,000 × 10% = $28,000). If the operating expenses are 76% of the gross income, then the net income ($28,000) is the remaining 24% of the gross. Divide $28,000 by 24% to get the gross income ($28,000 ÷ 24% = $116,667).If you're having trouble with this problem, consider it practically (a good idea with any tricky math problem). You know the net income is 24% of the gross. The only figure you have is the net income, however. The question is essentially asking, "For what number is 28,000 equal to 24%?" The number has to be about 4X larger than 28,000, since 24 is almost .25. So that's a practical check on your answer. The only operation with percentages that will give you an answer that sounds about right is division by the percentage. Multiplication clearly doesn't work, so division is the correct choice.

The capitalized value of a property is $280,000, the capitalization rate is 10%, and the operating expenses are 76% of the annual gross income. What is the gross income? Select your answer below: A.$110,544 B.$116,667 C.$121,503 D.$128,888

B This problem requires two steps: finding the annual property taxes, and then prorating them. Begin with the tax assessment problem. The assessed value is 50% of the market value ($180,000 × .5 = $90,000). The tax is calculated using mills, which are equivalent to one-tenth of a cent, so 55 mills equals 5.5 cents on the dollar ($90,000 × .055 = $4,950). Next, prorate the annual tax amount. First, find the per diem amount using a 365-day year ($4,950 ÷ 365 = $13.56). Calculate the number of days for which the buyer is responsible (16 in August, including the closing date, 30 in September, 31 in October, 30 in November, and 31 in December = 138 days). Multiply the number of days by the per diem rate to find the amount the buyer must pay at closing, to cover the remainder of the year's taxes ($13.56 × 138 = $1,871.28).

The closing date is August 16. The property's fair market value is $180,000. In this community, property is assessed at 50% of its market value, and taxes are applied at 55 mills per dollar of assessed value. Using a 365-day calendar year and assuming the buyer is responsible for the closing day, what would the buyer's prorated share of the annual property taxes be? A.$1,856.25 B.$1,871.28 C.$3,078.72 D.$3,743.01

D Using a 360-day year, the per diem rate for the taxes is $5.90 ($2,124 ÷ 360 = $5.90). Since the seller hasn't paid any of the taxes yet, the buyer will have to pay them. Thus, the seller will owe the buyer the property taxes for the period from January 1 through January 24 (the day before closing), which is 24 days. Multiply the per diem rate by the number of days the seller is responsible for to determine the seller's share: $5.90 × 24 days = $141.60.

The closing date is January 25. The annual property tax bill is $2,124, and the seller hasn't paid any part of it yet. The parties agree the buyer will be responsible for taxes on closing day. At closing, using a 360-day year: A. the buyer will owe the seller $1,062 as a prorated share of the taxes B. the buyer will owe the seller $1,982.40 as a prorated share of the taxes C. the seller will owe the buyer $1,062 as a prorated share of the taxes D. the seller will owe the buyer $141.60 as a prorated share of the taxes

B

The maximum amount that a bank will lend to a borrower is twice the borrower's annual income. If a borrower's annual income is $76,200, and she wants to buy a house for $247,000, how large a downpayment will she need to come up with? A.$47,300 B.$94,600 C.$170,800 D.She will be ineligible to purchase this house

A First, find the square footage of the lot (99 feet × 110 feet = 10,890 square feet). Convert that to acreage (10,890 square feet ÷ 43,560 square feet per acre = 0.25, or one-quarter of an acre). Multiply that by the price per acre to find the selling price ($180,000 × 0.25 = $45,000).

The owner of a lot that is 99' by 110' would like to sell it. Similar properties sell for $180,000 per acre. What is the likely selling price for this property? A.$45,000 B.$54,450 C.$60,000 D.$90,000

B The first step is to calculate how much the seller will owe XYZ Realty ($300,000 x .06 = $18,000). ABC Realty receives 50% of the commission ($18,000 x .5 = $9,000). And Suzy will receive 50% of ABC Realty's share ($9,000 x .5 = $4,500).

The seller lists her property with XYZ Realty and agrees to pay a commission rate of 6%. The MLS provides that a listing brokerage will split commissions at a 50-50 rate with the selling brokerage. Suzy, a licensee for ABC Realty, finds a buyer and the property sells for $300,000. If Suzy is entitled to a 50/50 split with her brokerage, how much commission will she receive? A.$2,250 B.$4,500 C.$9,000 D.$18,000

C $520,000 (desired net) + $12,000 + $7,500 = $539,500 (required net after commission but before settlement costs). $539,500 ÷ 93% (100% - 7% commission rate) = $580,107.52.

The seller wants to net $520,000. He pays a 7% commission, $12,000 in discount points, and $7,500 in repairs. Approximately how much should the seller ask for the property? A. $562,500 B. $568,750 C. $580,107 D. $599,750

C One way to solve the problem is to calculate the value before the increase ($3,000 x 12 = $36,000; $36,000 ÷ .08 = $450,000), calculate the value after the increase ($3,500 x 12 = $42,000; $42,000 ÷ .08 = $525,000), and then calculate the difference ($525,000 - $450,000 = $75,000). Another way would be simply to multiply $500 x 12 ($6,000) and then factor in the capitalization rate ($6,000 ÷ .08 = $75,000).

Through careful management, a property manager increases an apartment building's monthly income of $3,000 by an additional $500/month. Assuming a cap rate of 8%, what is the increase in the building's value? A.$37,500 B.$43,750 C.$75,000 D.$525,000

B Multiply the building size by four to find the minimum square footage of the lot (20,000 square feet x 4 = 80,000 square feet). There are 43,560 square feet per acre, so in order to exceed the required 80,000 square feet, you would need a two-acre lot (43,560 square feet x 2 = 87,120 square feet).

Zoning requirements state that a lot must be at least four times the size of the building located on the lot. An architect draws up plans for a building that is 20,000 square feet. At least how many acres does the lot need to be? A.1 B.2 C.3 D.4

B Each lot is worth $10,000. One way to solve this problem is to find the area of one of the triangular lots. Use the triangle area formula, Area = 1/2 Base × Height (900 feet × 484 feet × 0.5 = 217,800 square feet). Convert this to acreage (217,800 square feet ÷ 43,560 square feet per acre = 5 acres), and then multiply by the cost per acre (5 acres × $2,000 = $10,000). Alternatively, you can use the rectangle area formula (Area = Length × Width) to find the area of the entire corn field (900 feet × 484 feet = 435,600 square feet), divide to convert the square footage to acreage (435,600 square feet ÷ 43,560 square feet per acre = 10 acres), multiply by the cost (10 acres × $2,000 = $20,000), and divide by 2 to find the cost of one of the lots ($20,000 ÷ 2 = $10,000).

corn field with a depth of 900 feet and a frontage of 484 feet is bisected by an access road, leaving two triangular lots. If the land sells for $2,000 per acre, how much is each lot worth? A.$2,000 B.$10,000 C.$20,000 D.$100,000