NATIONAL QUIZ BANK "Real Estate Calculations; MATH"
A rectangular lot measures 200 ft. × 300 ft. Property in the area is selling for $150,000 per acre. If the broker charges 8%, how much is she paid?
$16,529 200 ft. × 300 ft. = 60,000 sq. ft. ÷ 43,560 = 1.3774 acres 1.3774 × $150,000 = $206,610 $206,610 × 8% (0.08) = $16,528.80 round to $16,529
After closing expenses of $550 and a 6% commission was paid, the seller received a check for $149,850. What was the sale price of the property?
$160,000 100% - 6% = 94% $149,850 + 550 = $150,400 (needed before commission) $150,400 ÷ 94% (0.94) = $160,000.
Two discount points cost a seller $3,300. What is the amount of the loan?
$165,000 A discount point is 1% of the loan amount. $3,300 (costs of 2 discount points) ÷ 2% (0.02) = $165,000 (loan amount)
A loan officer is paid 45% of the origination fee that her company charges. The loan officer negotiated a reverse mortgage, and her company was paid 2% of the appraised value of $190,000. How much was the loan officer paid?
$1,710 $190,000 × 2% (0.02) = $3,800 total origination fee $3,800 × 45% (0.45) = $1,710
The owners pay $137.81 in monthly property taxes. If the tax rate is $3.50 per $100 and the assessment rate is 35%, what is the value of the property?
$134,997.54 Tax rate= $3.50 ÷ 100 = 0.035 $137.81 × 12 = $1,653.72 annual tax $1,653.72 ÷ 0.035 = $47,249.14 assessed value $47,249.14 ÷ 35% (0.35) = $134,997.54
The semiannual interest paid on a loan was $4,387.50. If the interest rate is 6.5%, what was the loan amount?
$135,000 $4,387.50 × 2 = $8,775 annual interest $8,775 ÷ 6.5% (0.065)= $135,000
A building measures 30 ft. × 80 ft. × 15 ft.. A buyer made an offer of $35 per square foot on the property. The owner made a counteroffer of $2.75 per cubic foot. How much more will it cost the buyer if he accepts the counteroffer?
$15,000 First offer: 30 ft. × 80 ft. = 2,400 sq. ft. × $35 = $84,000. Counteroffer: 30 ft. × 80 ft. × 15 ft. = 36,000 cu. ft. × $2.75 = $99,000. $99,000 - 84,000 = $15,000.
A buyer offer of $295,000 was accepted, and a loan was negotiated for 80% at 7% for 25 years. The closing took place on January 5, and the buyer's first PITI payment is due March 1. Using a 365-day year, with the seller having the day of closing, how much interest would the buyer be debited on the closing statement?
$1,176.77 Step 1, determine the loan amount: $295,000 × 0.80 = $236,000. Step 2, determine the interest: $236,000 × 7% (0.07) $16,520. Step 3, determine what the buyer owes. The buyer will owe 26 days for January (31 - 5 = 26 days) and none for February because the March payment will pay the interest in arrears for February. Total amount due ÷ total days × days owed. $16,520 ÷ 365 × 26 = $1,176.77.
A property is appraised for $125,000. If the assessment rate is 100% and the tax rate is $1 per $100, what are the annual property taxes?
$1,250 $1 ÷ 100 = 0.01 tax rate $125,000 × 0.01= $1,250
An agent who works for XYZ Realty referred a buyer to a broker, who works for ABC Realty. The referring agent is to receive 25% of the buyer's agent's share of the commission when the transaction closes. The buyer purchased a $350,000 home, and the 7% commission was split as follows: listing brokerage, 2%; listing agent, 2%; buyer's brokerage, 1.5%; buyer's agent, 1.5%. How much was the referring agent paid?
$1,312.50 $350,000 × 1.5% (0.015) = $5,250 $5,250 × 25% (0.25) = $1,312.50
A two-story house measures 25 ft. × 50 ft. A one-story family room was added that measures 20 ft. × 20 ft. At a cost of $9.95 per square yard for carpet and $2.50 per square yard for installation, how much will it cost to carpet the house and the family room?
$4,011.67 Step 1, determine the square feet of the house: A = 25 ft. × 50 ft. = 1,250 sq. ft. × 2 = 2,500 total sq. ft. for the two-story house. Step 2, determine the square feet of the addition 20 ft. × 20 ft. = 400 sq. ft. Step 3, determine the total square footage 2,500 + 400= 2,900. Step 4, determine the cost of carpet: Total cost of carpet and install = $12.45 ($9.95 + $2.50) 2,900 ÷ 9 = 322.222 sq. yds. 322.222 × $12.45 = $4,011.67
A sales associate for XYZ Realty listed and sold a $175,000 home. The seller paid a 6% commission of which the sales associate received 2% for listing the property, and 1.5% for selling the property. How much was the brokerage's share of the commission?
$4,375 Total commission = $175,000 × 6% (0.06) = $10,500. Sales associate's share = 3.5% (2% + 1.5%) $175,000 × 3.5% (0.035) = $6,125. $10,500 ‒ $6,125 = $4,375 for the brokerage. Or 6% ‒ 3.5% = 2.5% for the brokerage times the sales price.
If the amount of a loan is $13,500 and the interest rate is 6%, what is the amount of the semiannual interest payment?
$405 A semiannual interest payment is paid twice a year. To find the amount of the payment, divide the annual interest amount by 2: $13,500 × 6% (0.06) (the interest rate) = $810 (annual interest amount) $810 ÷ 2 = $405 (semiannual interest)
An investment property was purchased for $250,000. The owner added a tennis court at a cost of $10,000. Two years later, the property sold for $325,000 and the seller paid a 7% commission plus $250 in attorney fees. If he purchases another property for $350,000, how much capital gains will he exclude?
$42,000 $250,000 + 10,000 = $260,000 $325,000 - 22,750 (7%) = $302,250 - 250 = $302,000 $302,000 - 260,000 = $42,000
The appraised value of a property is $52,350. It is assessed at 38% of the appraised value, and the tax rate is 95 mills. What are the quarterly property taxes?
$472.45 Tax rate = 95 ÷ 1,000 = 0.095 Assessed value = $52,350 × 38% (0.38) = $19,893 $19,893 × 0.095 = $1,889.83 annual taxes $1,889.83 ÷ 4 = $472.45 quarterly taxes
A salesperson lists and sells a home for $825,000 at a 7.5% commission. How much does the salesperson receive after his broker deducts 20% for the company share plus a $500 transaction fee?
$49,000 $825,000 (sales price × 7.5% (0.075)(commission rate) = $61,875 (total commission) ‒ 20% (0.20) (the company share) 20% (0.20) × $61,875 = $12,375 (the company share) $61,875 ‒ $12,375 = $49,500 $49,500 ‒ $500 (the transaction fee) = $49,000 (the salesperson's commission)
A lot contains 9/10 of an acre. What is the depth of the lot if the front measures 150 feet?
261.36 ft. 9 ÷ 10 = 90% 43,560 × 90% (0.90) = 39,204 39,204 ÷ 150 = 261.36 ft.
How many acres are in a lot that is 1/4 of a mile wide by 1/4 of a mile long?
40 acres 1,320 ft. (1/4 [0.25] of 5,280 ft. [1 mi.]) × 1,320 ft. = 1,742,400 sq. ft. ÷ 43,560 (sq. ft. in an acre) = 40 acres.
To secure a $100,000 loan, the buyer paid $3,000 in discount points, and the seller paid $2,000 in discount points. How many points were charged?
5 Knowing each point is 1% of the loan amount and with the total amount of $5,000 being paid, it is easy to see 5 points. $5,000 ÷ $100,000 = 5 points (0.05)
The rooms in Sandy's house measure as follows: living room, 20 ft. × 25 ft.; dining room, 18 ft. × 20 ft.; bedroom, 14 ft. × 26 ft.; bedroom, 15 ft. × 15 ft.; bedroom, 12 ft. × 14 ft.. The carpet she has selected costs $9.95 per square yard. How much will it cost to carpet the entire house?
$1,787.68 To determine the total square footage, see chart. 1,617 ÷ 9 = 179.6667 sq. yds. 179.667 × $9.95 = $1,787.68 for entire house Total house square footage 20 ft. × 25 ft. = 500 sq. ft. 18 ft. × 20 ft. = 360 sq. ft 14 ft. × 26 ft. = 364 sq. ft 5 ft. × 15 ft. = 225 sq. ft. 12 ft. × 14 ft. = 168 sq. ft. Total 1,617 sq. ft
How much monthly PITI payment can a purchaser qualify for if he earns $6,600 gross income monthly and the lender applies 28/36 qualifying ratios?
$1,848 $6,600 income × 28% (0.28) = $1,848 (monthly PITI payment). The lender's 28/36 qualifying ratios mean that the purchaser's total monthly housing expenses should be no more than 28% of his total monthly gross income, and that the purchaser's total monthly obligations must not exceed 36% of his total monthly gross income.
A property was listed for $450,000. A buyer's offer of 95% of the list price was accepted. He had a 20% down payment and secured a 30-year fixed-rate loan at 6.75% interest. How much interest will he pay the first month of the loan?
$1,923.75 Step 1, determine the sales price: $450,000 × 95% (0.95) = $427,500. Step 2, determine the loan amount: $427,500 × 0.80 = $342,000. Step 3, determine the annual interest: $342,000 × 6.75% (0.0675) = $23,085 ÷ 12 = $1,923.75 monthly interest.
What is the sales price of a property whose owner paid a $7,000 commission at a 7% rate?
$100,000 $7,000 (commission) ÷ 7% (0.07) = $100,000 (sales price)
Buyers negotiated a $75,000 loan at 8% interest for 30 years, with the first payment due in arrears on April 1. If the closing takes place on February 24 and using a 360-day year, how much interest must the buyers pay on the day of closing?
$116.67 The buyers will owe interest for the portion of the month they own the home. Total amount due ÷ total days × days owed. The buyers will own the house for 7 days in February (February 24, 25, 26, 27, 28, 29, 30) $75,000 × 8% (0.08) = $6,000 interest for the year. $6,000 ÷ 360 × 7 = $116.67.
If the quarterly interest at 10.5% is $3,150, the principal amount of a loan is
$120,000 To find the principal, divide the annual interest by the percent of interest. In this problem, to find the annual interest multiply the quarterly amount by 4: 4 × $3,150 = $12,500 (annual interest) $12,600 ÷ 10.5% (0.105) = $120,000 (principal amount)
An owner wants to receive a net of $82,000 after selling her home. She has an existing mortgage of $32,500 and will have selling expenses of $444. If the broker is to receive a 7% commission, what is the lowest offer that she can accept for the property?
$123,595.70 $82,000 + $32,500 + $444 = $114,944 $114,944 ÷ 93% (0.93) = $123,595.70
A seller wants to net a 12% profit after paying the brokerage firm a 6.5% commission. If the original purchase price was $104,500, what is the minimum offer they can accept?
$125,176 $104,500 + 12% = $117,040 100% - 6.5% = 93.5% $117,040 ÷ 93.5% (0.935) = $125,176.47 round to $125,176
A broker sold a property for $250,000. He was paid 6% on the first $100,000, 5% on the next $100,000, and 4% on the balance. How much was the broker paid?
$13,000 $100,000 × 6% (0.06) = $6,000 $100,000 × 5% (0.05) = $5,000 $50,000 × 4% (0.04) = $2,000 $6,000 + $5,000 + $2,000 = $13,000
The owners received a semiannual tax bill of $984.38. Property in the jurisdiction is assessed at one-fourth the market value. If the tax rate is $4.50 per $100, what is the estimated market value of the property?
$175,000 Tax rate= $4.50 ÷ 100 = 0.045 $984.38 × 2 = $1,968.76 Annual taxes $1,968.76 ÷ 0.045 = $43,750 Assessed value $43,750 ÷ 25% (0.25) = $175,000
An offer was made for 90% of the $120,900 list price of a property. The offer was accepted, and the lender agreed to negotiate an 80% loan at 8% interest for 30 years. The buyer had placed a $5,000 earnest money deposit in escrow. Additional expenses the buyer would need to pay through escrow included: $350 for title expenses, $250 for attorney fees, and other expenses of $749. How much money does the buyer need to close on the property?
$18,111 $108,810 (sales price) × 90% (0.90) = $120,900 (list price) $87,048 (loan amount) × 80% (0.80) = $108,810 DebitsCredits $108,810$87,048 $350$5,000 $250 $749 $110,159$92,048 $110,159$92,048= $18,111
A broker sold a property and received a 6.5% commission. The broker gave the listing salesperson $3,575, which was 30% of the firm's commission. What was the selling price of the property?
$183,333 The answer requires two steps: (1) find the firm's full commission, and (2) find the selling price using the full commission and the rate. $3,575 (the listing salesperson's commission) = 30% × full commission (1) To find the full commission, divide the listing salesperson's commission by the salesperson's share of 30%: full commission = $3,575 ÷ 30% (0.30) = $11,916.67. (2) To find the sales price, divide the full commission by the brokerage commission rate: full commission ($11,916.67) ÷ brokerage rate (6.5%) = sales price ($183,333).
The buyer had a 20% down payment on a property she purchased for $89,500. She also must pay a 1% origination fee, $350 for title insurance, and one discount point. How much money will the buyer owe at the closing?
$19,682 Step 1, determine the loan amount: $89,500 × 80% (0.80) = $71,600. Step 2, determine the down payment: $89,500 - 71,600 = $17,900. Determine the points and origination fee. $71,600 × 1% (0.01) = $716. Total as shown below: + $17,900 down payment $716 discount points $716 origination fee $350 insurance $19,682 total due at closing
Five years ago, a homeowner bought a home for $250,000. Home values in her area have improved, and the current market value of the house has increased by 15%. If she has $95,875 left to pay on her mortgage loan, what is the current equity in her home?
$191,625 The homeowner's equity is the difference between the market value of her property and the debt that encumbers it. Original cost ($250,000) + increase in value ($250,000 × 15% (0.15) = $37,500) = Current market value ($287,500). Current market value ($287,500) - mortgage debt ($95,875) = the homeowner's equity ($191,625).
A broker received a 6% commission from the sale of a property. The broker gave the salesperson $3,500, which was 30% of the firm's commission. What was the selling price of the property?
$194,450 To find the broker's total commission, divide the salesperson's commission by the percentage of the salesperson's commission: $3,500 ÷ 0.30 (30%) = $11,667. The broker's commission is 6% of the sales price. To find the sales price, divide the broker's commission by the percentage of the broker's commission: $11,667 ÷ 0.06 (6%) = $194,450.
A listing agreement states that the broker will receive a 6% commission. The broker produces a buyer who purchases the home for $210,000. What is the net amount that the seller will receive from the sale?
$197,400 To find the seller's net from the sale, subtract the amount of the broker's commission from the selling price of the home. First, calculate the amount of the commission: 6% (0.06) × $210,000 (selling price) = $12,600. $210,000 ‒ $12,600 = $197,400. Or take $210,000 × 0.94 = $197,400.
Semiannual property taxes of $450 were paid only for the first half of the year. The property sold on July 11 and closed on September 19, with the seller having the day of closing. If the taxes were prorated and paid between the buyer and the seller as of the date of sale, using a 360-day year, what will the seller owe at closing?
$197.50 The seller owes July, August, and 19 days of September for a total of 79 days. The formula is total due ÷ total days × days owed. $450 ÷ 180 × 79 = $197.50.
The listing broker and the buyer's broker agree to split a 7% commission 50-50 on a $196,900 sale. The buyer's brokerage firm gives its salesperson 35% of the commission. How much does the buyer's salesperson earn from the sale?
$2,412.03 196,900 × 7% (0.07) = $13,783 (total commission) $13,783 ÷ 2 (between both brokers) = $6,891.50 $6,891.50 × 35% (0.35) = $2,412.03 (salesperson's commission)
A homeowner received $321,480 after 6% was deducted as the agreed upon brokerage commission. What was the selling price of the property?
$342,000 $321,480 (seller's net) ÷ 94% (0.94) (100% ‒ 6% commission) = $342,000 (the sales price)
A buyer purchased two parcels of land. One parcel was 2 miles square and the other contained 30 acres. If the price of the land was $2,000 an acre, what was the purchase cost?
$2,620,000 One square mile is 640 acres, so 2 square miles is 1,280 acres. The two parcels together contain 1,310 acres (1,280 + 30 = 1,310). To find the cost, multiply the cost per acre by the total acres: 1,310 × $2,000 = $2,620,000.
A salesperson signs a listing agreement with her broker to sell her home. The agreement states that the broker will receive a 7% commission. The home sells for $220,000. What is the net amount that the seller will receive from the sale?
$204,600 The answer requires two steps: (1) find the commission, and (2) subtract the commission from the selling price to find the seller's amount. (1) Brokerage rate (7%) × selling price ($220,000) = commission ($15,400) (2) Selling price ($220,000) - commission ($15,400) = seller's amount ($204,600)
If the market value of a property is $169,000 and it is assessed at 35%, with a tax rate of $4.25 per $100, what are the monthly property taxes?
$209.49 Tax rate = $4.25 ÷ 100 = 0.0425 Assessed value= $169,000 × 35% (0.35) = $59,150 $59,150 × 0.0425 = $2,513.875 annual taxes $2,513.875 ÷ 12 = $209.49 monthly taxes
An owner sold his condo and paid 6% commission to the selling broker. If his net was $200,000, what was the sale price?
$212,765.95 100% - 6% = 94% seller's percentage $200,000 ÷ 94% (0.94) = $212,765.95
If the interest rate on an FHA-insured mortgage loan is 5.5% and the monthly payment is $1,012, the principal sum would be
$220,800 .To find the principal sum, multiply the monthly payment by 12 (12 months in a year) and divide that amount by the interest rate. $1,012 × 12 = $12,144 (annual payments) $12,144 ÷ 5.5% (0.055) (interest rate) = $220,800 (the principal amount)
The buyer assumed a loan of $50,000 at 8.25% interest. Payments are due on the first of the month. The last payment was made on April 1, and the closing took place on April 20, with the seller having the day of closing, and using a 360-day year. Which of these is TRUE?
$229.17 DS, CB Step 1, determine the amount of interest owed: $50,000 × 8.25% (0.0825) = $4,125. Step 2, determine what days the buyer owes: April 1 to April 20 = 20 days. Step 3, determine the amount owed. Total amount due ÷ total days × days owed. $4,125 ÷ 360 × 20= $229.1
A 20-unit commercial office building had a vacancy rate of 5%. Monthly rent for each unit was $975. The office building earned additional monthly income totaling $2,000 from on-site amenities like vending machines, storage facilities, and reserved parking spaces. The property manager calculated the effective gross income from the commercial office building as
$245,100. Here is the formula for calculating effective gross income: gross potential rent + other income - vacancies/collection losses = effective gross income. $975 × 20 = $19,500 × 12 = $234,000 potential gross rent $2,000 × 12 = $24,000 additional income $234,000 + $24,000 = $258,000 $258,000 - $12,900 [5% vacancy] = $245,100
What is the estimated replacement cost of a 65ft. × 30 ft. building at an estimated cost of $128.50 per square foot?
$250,575 65 ft. × 30 ft. = 1,950 sq. ft. × $128.50 per sq. ft. = $250,575. Square footage is found by multiplying the length by the width of the building: 65 ft. × 30 ft.
A lender agreed to a 90% loan-to-value (LTV) ratio with an interest rate of 7%. If the annual interest is $17,640, what was the loan amount?
$252,000 $17,640 ÷ 7% (0.07) = $252,000
A sales associate was paid $2,500, which was half of the 7% that the brokerage collected. What was the sale price of the property?
$71,429 $2,500 × 2 = $5,000 $5,000 ÷ 7% (0.07) = $71,428.57 round to $71, 429
A commercial lease calls for a minimum rent of $1,200 per month plus additional annual rent of 4% of the year's gross business exceeding $150,000. If the total rent paid at the end of one year was $19,200, how much business did the tenant do during the year?
$270,000 There are four steps: (1) minimum rental for the year is 12 times the monthly amount: 12 months × $1,200 per month = $14,400, (2) rental above the minimum is found by subtracting the minimum rent from the total rent paid for the year: $19,200 - $14,400 = $4,800, (3) this overage is 4% of the amount of business that exceeded $150,000. The amount of business that exceeded $150,000 is found by dividing $4,800 by 4%: $4,800 ÷ 4% = $120,000, and (4) total business is the sum of the basic $150,000 and the $120,000 overage: $150,000 + $120,000 = $270,000.
A broker and sales associate split commissions on a 60-40 basis. How much commission will the sales associate earn if he sells a property for $125,000, and a 6% commission is paid?
$3,000 $125,000 × 6% (0.06) = $7,500 $7,500 × 40% (0.40) = $3,000
If a bank wants to earn $3,150 on a loan of $50,000 over 12 months, what interest rate would the bank have to charge?
$3,150 (amount of yearly interest) ÷ $50,000 (loan amount) = 6.3% (0.063) (the interest rate)
A salesperson sells a $150,000 home listed with another brokerage. The listing commission is 6.5% of the selling price, with 35% going to the listing broker, and 60% belonging to the cooperating broker. The salesperson and his broker agreed that she would receive 55% of any commission that she generated for the brokerage firm. For this transaction, the salesperson is entitled to receive
$3,217.50. $150,000 (sales price) × 6.5% (0.065) = $9,750 (listing commission) $9,750 × 60% (0.60) = $5,850 (cooperating broker's commission) $5,850 × 55% (0.55) = $3,217.50 (the salesperson's commission)
A seller is interviewing agents to list her property. She has the following quotes from two different companies: XYZ Realty, 7% commission; and LMN Realty, 5.5% commission. If her house sells for $225,000, how much will she save if she lists her property with LMN Realty?
$3,375 Explanation $225,000 × 7% (0.07) = $15,750 $225,000 × 5.5% (0.055) = $12,375 $15,750 - $12,375 = $3,375 savings
What is the two discount points fee on a $180,000 U.S. Department of Veterans Affairs (VA)-guaranteed loan?
$3,600 $180,000 loan × 2% (0.02) = $3,600 (discount point fee). A point is equal to 1% of the total loan amount. 1% (0.01) × $180,000 = $1,800 × 2 (2 points) = $3,600.
A charge of three discount points on a $120,000 loan equals
$3,600 A discount point is 1% of the amount borrowed (the loan amount). Three points would be 3% of the loan amount of $120,000. 3% (0.03) × $120,000 = $3,600
A couple is applying for a home loan. One spouse has an annual gross income of $102,000, and the other spouse makes $72,000 a year. They have monthly car payments of $875, monthly credit card payments of $620, and their monthly grocery expenses come to $1,200. If the lender uses debt ratios of 28% and 36% to qualify them, what is the maximum monthly housing expense they will qualify for?
$3,725 $102,000 + $72,000 = $174,000 ÷ 12 = $14,500 monthly $14,500 × 28% (0.28) = $4,060 $14,500 × 36% (0.36) = $5,220 $5,220 − $1,495 ($875 + $620) = $3,725 other recurring debt
The market value of a property is $65,000 and is assessed for 45% of its value. If the owner's semiannual tax bill was $511.88, what was the tax rate per $100?
$3.50 $65,000 × 45% (0.45) = $29,250 assessed value $511.88 × 2 = $1,023.75 annual taxes $1,023.75 ÷ $29,250 = 0.035 0.035 × 100 = $3.50
At closing, the seller paid the broker $21,000, which was equivalent to 7% of the selling price. What was the selling price of the property?
$300,000 Commission divided by rate = sales price. $21,000 ÷ 7% (0.07) = $300,000.
Three years ago, the owner paid $165,000 for her investment property. During her period of ownership, she added a family room valued at $16,500 and $10,000 worth of other improvements. If she sells the property for $240,000 and pays a 7% commission, what capital gains may she exclude?
$31,700 $240,000 - $16,800 (7%) = $223,200 $165,000 + $16,500 + $10,000 = $191,500 $223,200 - $191,500 = $31,700
A homeowner sold his property for $99,500. He paid a real estate commission of 6%, paid an attorney $250, paid a transfer tax of $99.50, paid his existing mortgage of $50,140, and agreed to a purchase money mortgage of $10,000. What were his net proceeds at the closing?
$33,040.50 $99,500 × 6% (0.06) = $5,970 DebitsCredits $5,970.00$99,500 $250 $99.50 $50,140 $10,000 $66,459.50$99,500 $99,500‒ $66,459.50= $33,040.50
A purchaser borrowed $85,000, to be repaid in monthly installments of $530.20 at 7% annual interest. How much of the borrower's first month's payment was applied to reducing the principal amount of the loan?
$34.37 There are three steps to solving this problem: (1) find the amount of interest in the first monthly payment by multiplying the annual interest rate by the original amount of the loan (rate × principal = interest) 7% (0.07) × $85,000 = $5,950, (2) divide the annual interest by 12 (12 months in a year) to find the first month's interest $5,950 ÷ 12 = $495.83, and (3) subtract that interest amount from the amount of the regular monthly payment to find the amount available to apply to the principal $530.20 ‒ $495.83 = $34.37.
When the owners sold their property, they paid a 6% commission. Their check after the commission was paid was $470,000. What was the selling price of the property?
$500,000 100% - 6% = 94% seller's percentage $470,000 ÷ 94% (0.94)= $500,000
Federal income tax law excludes gains realized on the sale of a primary residence for couples filing jointly. The amount of this exclusion is
$500,000. Federal tax laws permit a couple filing jointly to exclude up to $500,000 in profits from capital gains taxes on a primary home, not on an investment property.
The lender negotiated a $55,000 loan and charged three discount points. What was the cash outflow of the lender?
$53,350 $55,000 ‒ $1,650 (3%) = $53,350
A property was listed with a broker who belonged to a multiple listing service and was sold by another member broker for $253,500. The total commission was 6% of the sales price. The selling broker received 60% of the commission, and the listing broker received the balance. What was the listing broker's commission?
$6,084 There are two steps to finding the listing broker's commission: (1) Find total commission, and (2) using the total commission, find the listing broker's 40% share of it. (1) Brokerage rate (6%) × selling price($253,500) = total commission ($15,210) (2) Listing broker's share (40%) × total commission ($15,210) = $6,084
A borrower pays $200,000 for a home, makes a down payment of $40,000 and obtains a loan for the balance of the purchase price. The lender charges four discount points for the loan. How much will the borrower pay in discount points?
$6,400 A discount point is 1% of the loan amount. Four discount points is 4% of the loan amount. The loan amount is $160,000 (subtract the down payment of $40,000 from the purchase price of $200,000). To find the amount of the discount points, multiply the loan amount by 4%: 4% (0.04) × $160,000 = $6,400.
Using the dimensions in the following diagram, what is the approximate cost to purchase at $4,000 per acre?
$6,428 [(300 ft. + 400 ft.) ÷ 2)] × 200 ft. 350 ft. (700 ft. ÷ 2) × 200 ft. = 70,000 sq. ft. 70,000 ÷ 43,560 = 1.6070 acres 1.6070 × $4,000 = $6,427.91, round to $6,428
When the seller listed a property, he agreed to pay a 7% commission. The property sold for $190,000. If the listing agent was paid 2%, and the selling agent was paid 1.5%, how much was the broker paid after paying his agents?
$6,650 7% - 2% - 1.5% = 3.5% to the broker. $190,000 × 3.5% (0.035) = $6,650
A first-time buyer paid $135,500 for her property. Taxes in her community are assessed at 80% of the market value. If the tax rate is 700 mills per $100, how much will be escrowed for taxes for her monthly PITI payment?
$63.23 Tax rate = 700 mills ÷ 1,000 = 0.7 ÷ 100 = 0.007 Assessed value $135,500 × 80% (0.80) = $108,400 $108,400 × 0.007 = $758.80 annual taxes $758.80 ÷ 12 = $63.23 monthly tax
A seller wants to net $65,000 on the sale of his house after paying the broker a fee of 6%. How much must the gross selling price be?
$69,149 $65,000 (net price) ÷ 94% (0.94) (100% - 6% (0.06) commission) = $69,148.936 round to $69,149 (sales price rounded up).
One lender charges 6.5% interest and the second lender charges 7%. How much money will the borrower save the first year on a $150,000 loan if he goes with the first lender?
$750 The first lender would charge $150,000 × 6.5% (0.065) = $9,750. The second lender would charge $150,000 × 7% (0.07) = $10,500. $10,500 - $9,750 = $750.
The listing price of a property was $135,000. The buyer made an offer of 90% of the listing price, which was accepted by the sellers. The property appraised for the offer price, and the buyers secured an 85% loan at 9% interest for 30 years. How much interest will be paid in the first payment?
$774.56 $135,000 × 90% (0.90) = $121,500 sales price $121,500 × 85% (0.85) = $103,275 loan amount $103,275 × 9% (0.09) = $9,294.75 annual interest $9,294.75 ÷ 12 = $774.56
The buyers applied for a U.S. Department of Veterans Affairs (VA) loan to purchase a property for $79,500. The property appraised at $79,000. They agreed to pay a 1% loan origination fee. How much did they pay in origination fees?
$790 $79,000 (100% loan) × 1% (0.01) = $790
A small condo sold for $62,250, which was 75% of the list price. What was the list price?
$83,000 $62,250 (sales price) ÷ 75% (0.75) = $83,000 (the list price)
This month's interest payment is $585.70. If the buyer secured a 90% loan at an 8.75% annual rate of interest, what was the sale price?
$89,250 $585.75 × 12 = $7,028.40 annual interest $7,028.40 ÷ 8.75% (0.0875) = $80,324.57 loan amount $80,324.57 ÷ 90% (0.90) = $89,249.52, round to $89,250
Two brokers split the 6% commission equally on the sale of a small commercial tract of land. What was the selling price of the tract if the selling salesperson received $1,074, which was 40% of the portion of the total commission coming to the selling broker?
$89,500 $1,074 (salesperson's commission) ÷ 40% (0.40) = $2,685 (total commission) ÷ 3% (0.03) (1/2 of total 6% commission) = $89,500 (the sales price)
If a lender agrees to make a loan based on an 80% loan-to-value (LTV) ratio, what is the amount of the loan if the property appraises for $114,500 and the sales price is $116,900?
$91,600 The LTV ratio will be based on the relationship of the loan to either the appraisal or the purchase price, whichever is less. In this case, the appraisal is less. Therefore, the loan will be 80% of $114,500, which equals $91,600. $114,500 × 80% (0.80) = $91,600
A building sold for $157,000. The broker charged a 6% commission and gave 10% to the salesperson who took the listing. What was the listing salesperson's commission?
$942 $157,000 (sales price) × 6% (0.06) = $9,420;(listing commission) $9,420 × 10% (0.10) commission percentage) = $942 (listing salesperson's commission)
An apartment building has 20 units and a vacancy rate of 5%. The monthly rent is $1,000. The property manager was paid 5% of the gross monthly rents. How much did the property manager earn for the prior month?
$950 The property manager was paid $950: A 20-unit apartment building with a 5% vacancy rate = 19 occupied units (20 × 5% = 19 occupied units) 19 × $1,000 = $19,000 gross monthly rents $19,000 × 5% = $950
A parcel of vacant land is 80 feet wide on the street side of the property and 200 feet deep. The parcel was sold for $200 per front foot. How much money would a salesperson receive for his 60% share in the 10% commission?
$960 A front foot measures frontage on the front of the property. 80 feet × $200 = $16,000 sale price $16,000 × 10% commission(0.10) = $1,600 (total commission) $1,600 × 60% (0.60) = $960 (the salesperson's commission)
A rectangular lot is 275 ft. deep, and it contains 2/3 of an acre. What is the length of the lot?
105.6 ft. 43,560 ÷ 3 = 14,520 × 2 = 29,040 sq. ft. 29,040 ÷ 275 ft. = 105.60 ft. 43,560 × 0.6667 (2 ÷ 3 = 0.6667) = 29,041.45 sq. ft. 29,041.45 ÷ 275 ft. = 105.6052 ft.
How many square feet of living area are in the following house?
2,087.5 35 ft. × 40 ft. = 1,400 sq. ft. [(15 ft. + 40 ft.) ÷ 2 × 25 ft.] = 687.5 sq. ft. 1,400 + 687.5 = 2,087.5
How many cubic yards of concrete must a builder buy to pour a sidewalk that measures 45 ft. × 3.25 ft. and is 5 inches thick?
2.2571 5 in. ÷ 12 in. = 0.4167 in. 45 ft. × 3.25 ft. × 0.4167 ft. = 60.9423 cu. ft. 60.9423 ÷ 27 = 2.2571 cu. yds.
The following legal description contains how many acres: the S½ of the SE¼ of the NW¼ of the NE¼ of Section 7?
5 acres To calculate acres in a survey system legal description, multiply all the denominators and divide that number into 640 acres. In this problem, multiply all denominators: 2 × 4 × 4 × 4 = 128. Then divide 640 by 128: 640 (acres in a section) ÷ 128 = 5 acres.
A salesperson received a $2,800 commission on his 35% share of the total commission on the sale of a property that sold for $160,000. What was the commission rate?
5% $2,800 (agent's commission) ÷ 35% (0.35)(agent's percentage) = $8,000 (total commission) $8,000 ÷ $160,000 (sales price) = 5% (commission rate)
A broker sold a residence for $210,000 and received $10,500 as commission in accordance with the terms of the listing contract. What was the broker's commission rate?
5% To find the commission rate, divide the commission amount by the selling price: $10,500 ÷ $210,000 = 0.05 (5%).
A broker and sales associate split commissions on a 60/40 basis. If the broker's share of the commission was $3,500, and the sale price was $83,333, what was the commission rate?
7% $3,500 ÷ 60% (0.60) = $5,833.33 $5,833.33 ÷ $83,333 = 7% (0.07)
A property sold for $235,000, and the selling broker's half of the commission was $8,225. What was the commission rate?
7% $8,225 × 2 = $16,450 total commission paid $16,450 ÷ $235,000 = 7% (0.07)
A property was purchased for $175,000. If the loan was $131,250, what was the loan-to-value (LTV) ratio?
75% $131,250 ÷ $175,000 = 75% (0.75)
The area of a rectangle that is 50 ft. × 170 ft. is
8,500 sq. ft. 50 ft. × 170 ft. = 8,500 sq. ft. The area of a rectangle is length × width.
Last month's loan payment included $412.50 interest on a $60,000 loan balance. What is the annual rate of interest?
8.25% To find the annual rate of interest, divide the annual amount of interest by the loan balance. In this problem, to find the annual amount of interest, multiply the monthly amount by 12: $412.50 × 12 = $4,950(annual interest amount) $4,950 ÷ $60,000 (loan balance) = 8.25% (0.0825) interest
A savings and loan agreed to make a $65,000 mortgage at 8% interest for 30 years and charged three points to negotiate the loan. What was the effective yield to the lender?
8.38% The lender yield per point is 1.25% (0.125). 0.125 × 3 = 0.375 8% + 0.38 = 8.38%
A borrower secured an $80,000 loan at 8.25% interest, and the lender's cash outflow was $77,600. What was the effective yield to the lender?
8.63% $80,000 - 77,600 = $2,400 2,400 ÷ $80,000 = 3 points (0.03) 0.125 × 3 = 0.375 8.25% + 0.375 = 8.63%
The N½ of the SW¼ of a section contains how many acres?
80 acres A section has 640 acres. A section is divided into halves (320 acres) and quarters (160 acres). Each of those parts is further divided into halves and quarters. In this problem, a ½ of a ¼ of 640 equals 80 acres. 2 × 4= 8 640 ÷8= 80 acres.
Which of the following properties would a property manager recommend an investor purchase?
A property where the gross monthly rental income was 3% of the purchase price A property manager would recommend an investor purchase the property where the gross monthly rental income was 3% of the purchase price. The higher the percentage number (i.e., the higher the income), the better. This is sometimes referred to as the 1% rule, meaning that the income-producing rental property should produce income that is at least 1% of purchase price.
Which of these would be included in a property manager's accounting as gross profit generated from income-producing rental property?
A) Money generated from an on-site laundry B) Change from an on-site vending machine C) All of these D) Rent C The money generated from all of these would typically be included as gross profit generated from an income-producing property.
All of the following lists contain items typically included in the operating expenses of a rental property EXCEPT
A) pool service, repairs for normal wear and tear, property taxes. B) landscaping, debt service, property taxes. C) water and sewer, property taxes, property insurance. D) property taxes, property management, garbage collection. B Debt service is considered an ownership expense, not an operating expense. Debt service is the money required to cover repayment of a loan (principal and interest) for a particular period of time. These other answer choices are typical operating expenses for rental property.
An investor owns an apartment building, and hires a real estate licensee to serve as the property manager. Which of the following activities performed by the property manager during a market analysis is similar to the market data method of appraising real estate?
Analysis of nearby rental properties comparable to the apartment building An important part of a market analysis is finding properties comparable to the investor's apartment building to determine how the income-producing subject property is performing in relationship to the other properties. The market data approach to appraisals also relies on comparables to determine the market value of the subject property. While debt service might well be considered by the property manager during a market analysis of the subject property, an appraiser appraises each property as if it were free and clear of liens. Finding and signing well-qualified tenants is one of a property manager's responsibilities as an agent of the landlord, but is not in any way related to the market data approach of appraising real estate. Finally, review of environmental law that impacts a property would not typically be a major focus of the appraiser using the market data approach.
An owner of income-producing property asked the property manager to prepare a report showing the cash flow of the property. Which of the following accurately shows the formula for calculating a rental property's cash flow?
Gross income - (expenses and debt service) = cash flow The general formula to calculate a rental property's cash flow is gross income - (expenses and debt service) = cash flow. The formula requires that expenses be subtracted from gross income, not net income. Net income typically refers to income where expenses have already been subtracted. Operation costs (expenses) and debt service (e.g., mortgage payments) would be subtracted from—not added to—income.
When dimensions are stated as 75 × 125, the first measurement given refers to
the foot frontage. Foot frontage is the first measure that appears in a lot size. For example, a measurement of 75 ft. × 125 ft. indicates that 75 ft. is the front footage.
