Chapter 8 Exam Math
The property is sold for $350,000. The total commission is 5% of the gross sales price. As listing agent, you are entitled to a 2.75% commission, which you must divide your share with your company, 60% going to you and 40% to your company. How of the commission will go to you?
$350,000 x .0275 =$9,625.00= your gross commission $ 9,625 x .60 (60%) = $5,775.00= your share of the commission
If John receives $1,000 per quarter from an investment that earns 8 percent interest. How much is John's investment?
$1,000 x 4 quarters = $4,000 annual yield$4,000 (part) / .08 = $50,000 $50,000
A $200,000. loan can be amortized with monthly payments of $1,688 over 15 years or $1,432 on a 20 year basis. The 20 year loan would result in total payments of what percent of the 15 year loans total payments?
$1,688 X 12 x 15 = $303,840.00 $1,432 X 12 X 20 = $343,680. $343,680 divided by $303,840. + 1.13 or 113% 113%
John needs to receive $122,200 from the sale of his home after paying a 6% commission in order to payoff his loan. What must the minimum list price be?
$122,200 / .94 = $130,000 $130,000
Joe Green purchased a lot for $15,000 and listed it a year later for 30% more than he originally paid. There was little interest at that price so he reduced the price 20%. He soon found a buyer at the reduced price and paid a sales commission of 6%. What was Joe's profit or loss?
$15,000 * .30 = $4,500; $15,000 + $4,500 = $19,500 listed price; $19,500 * .20 = $3,900; $19,500 − $3,900 = $15,600 sales price; $15,600 * .06 = $936; $15,600 − $936 = $14,664; $15,000 − $14,664 = $336 loss
Scott purchased a home for $175,000 which has appreciated 6% each year for the four years he has owned it. What is the current value? (Use compound appreciation method)
$175,000 + (175,000 * .06) = $185,500; $185,500 + (185,000 * .06) = $196,630; $196,630 + ($196,630 * .06) = $208,427.80; $208,427.80 + ($208,427.80 * .06) = $220,933.47 OR $175,000 + 6% 4 times $220,934
$2,500.00 was earned in 3 months on an investment yielding 10%. The principal was ____.
$2,500. X 4 = $10,000.00 for 1 year., $10,000.00 divided by .10 = $100,000. $100,000
What percentage profit is made on a sale if the selling price is $225,000 and the purchase price is $190,000?
$225,000 − $190,000 = $35,000 profit: $35,000 / $190,000 = .18 or 18% profit 18%
Joe Green sold six acres of vacant land for $2.30 per square foot. What was the selling price?
$3,000 − $1,500 = $1,500; $1,500 / .05 = $30,000
A broker's assistant was paid a base salary of $1,500 per month plus five percent of the broker's gross commissions. If she earned $3,000 last month, how much did the broker earn?
$3,000 − $1,500 = $1,500; $1,500 / .05 = $30,000 $30,000
Nancy and Joan bought a small farm for $300,000 under an installment land contract with a $50,000 down payment. They will pay interest only at 6% for five years when the remaining principal balance becomes due. How much interest will they pay over the life of the contract?
$300,000 - $50,000 = remaining balance: $250,000 * .06 (6%) = $15,000 * 5 = $75,000, Unit 3 $75,000
The property is sold for $350,000. The total commission is 5% of the gross sales price. As listing agent, you are entitled to a 2.75% commission, which you must divide your share with your company, 60% going to you and 40% to your company. How of the commission will go to you?
$350,000 x .0275 =$9,625.00= your gross commission $ 9,625 x .60 (60%) = $5,775.00= your share of the commission $5,775
On a $350,000 30-year mortgage at 8 percent, the monthly PI payment is $2,568.18. On the first payment, how much is applied to reduce the principal?
$350000 * .08 = $28,000 / 12 = $2333.33 first month interest: $2,568.18 minus $2333.33 = $234.85 $234.85
Andy wishes to break even on the sale of his home. He paid $375,000. His closing costs are estimated at $8,200.00 and he will pay a 5% real estate commission. The home must sell for ____.
$375,000. + 8,200. = $383,200. divided by 0.95 = $403,368. rounded You have to add in Andy's costs which are $375,000. + $8,200. Then you have to divide by .95 to factor in the commission to get what Andy's break even point is. $403,368
Using the following figures, calculate the taxable gain on the sale of the family mansion you have just received an offer for on behalf of your client. Your client is married at the time of the sale: The information presented includes the date which the action is accounted for. Original purchase price 1-10-47: $1,250,000, including all closing costs. Tennis courts and fencing added 6-6-47: $25,500. Add pool/fencing 6-15-50: $45,500. Add guest wing 4-10-65: $225,000. Sales price 6-10-95: $3,676,000. Commission and costs of sale: $225,000. ----------------------- What is the taxable gain due from your seller client upon closing?
$500,00 exclusion of taxable gain for married couples (lived in the home as principal residence for two out of the last five years). $1,250,000 + $25,500 + $45,500 + $225,000 + $225,000 = $1,771,000 in total ownership expenses $3,676,000 - $1,771,000 = $1,905,000 - $500,000 = $1,405,000 in taxable gain $1,405,000
A property has an appraised value of $60,000. A loan is granted on the property for 75% of its appraised value. The loan is spread over 25 years at an interest rate of 1/2% per month. If the amount paid toward the principal is to remain constant throughout the life of the loan, what is the first monthly payment?
$60,000 x .75 = $45,000, Loan of $45,000. Fraction to decimal = ½% = .005 .005 x 12 = .06 Loan of $45,000 x .06 = $2,700 / 12 = $225;$45,000 / 300 pymts = $150; $225 (I) + $150 (P) = $375 payment $375
Marc bought 9 adjacent unimproved lots for $8,500 each and plans to divide them into 14 lots and sell them for $7,000 each. He paid $5,200 to install water and sewer lines and miscellaneous improvements. What will Marc's profit be?
$8,500 * 9 = 76,500; 76,500 + $5,200 = $81,700; 14 * $7,000 = $98,000; $98,000 − $81,700 = $16,300; $16,300 / $81,700 = .1995 or 20% 20%
The last monthly interest payment on a mortgage was $825.77. If the interest rate was 7.2%, what was the balance due on the principal?
$825.77 x 12 = Interest for 1 year. Interest for 1 yr. divided by 7.2% = $137,628
10% is also written as ____.
.10
3/4 x 1 7/8 x 6.25 x 4 3/8 = ____.
.75 x 1.875 x 6.25 x 4.375 = 38.45
Which of the following will result in the greatest net for the seller?
1. $125,000 x .07 = 8750, $125,000 - $8,750 - $2,508 = $113,742*** Sale price of $125,000, with commission of 7%, and closing costs of $2,508
The formula to determine the area of a right triangle is ____.
1/2 base x height
A next monthly interest payment on a loan with a principal balance of $19,531 is $109.86. What is the interest rate on the loan?
109.86 * 12 = $1,318.32 annual interest;$1,318.32 (P) / $19,531 (T) = .067499 or 6.75%
Based on the following information, calculate the gain on the sale of a home: 6-6-95 Buy home at $125,000, $600 closing costs. 6-6-96 Add fence and pool at $7,500.
125000 + 600 + 7500 + 15,000 = $148,100, 225000 - 15000 = 210,000, 210000 - 148,100 = $61,900.
John and Joann own a lot that is 75 feet wide and 150 feet deep. The front setback is 25 feet, the rear setback is 20 feet, and the side setbacks are 15 feet. What is the largest possible home that can be built on the lot?
150 - 25 - 20 = 105 feet deep; 75 - 15 - 15 = 45 feet wide; 105 * 45 = 4,725 4,725 sq ft
85% = ____.
17/20
Janet purchased a property several years ago for $250,000 and has decided to sell it. The sales commission and other closing costs will be 10% of the sales price. How much must the home have appreciated in value for Janet to break even?
250,000 / .90 = $277,778; $277,778 - $250,000 = $27,778
The new runway your client is pouring on the east side of the estate is to the ranch house is 3.75 miles long, and covers a total of 5.6 acres, which means the runway is feet wide.
3.75 miles x 5,280 feet = 19,800 feet in length 5.6 x 43560= 243,936 square feet 243,936 divided by 19,800 = 12.32 feet in width. They must be landing very narrow aircraft.
The new runway your client is pouring on the east side of the estate is to the ranch house is 3.75 miles long, and covers a total of 5.6 acres, which means the runway is ____ feet wide.
3.75 miles x 5,280 feet = 19,800 feet in length 5.6 x 43560= 243,936 square feet 243,936 divided by 19,800 = 12.32 feet in width. They must be landing very narrow aircraft. 12.32
The back patio of your client's home must be replaced before you close on the house. It is 35 feet long, 10 feet wide, and the concrete will be poured to a depth of 4 inches. To the nearest yard (be sure to round up whenever estimating concrete), how many cubic yards will your client need for this job?
35' x 10' x .333' = 116.55 cubic feet, 116.55 cubic feet divided by 27 (the number of cubic feet in a cubic yard) = 4.32 cubic yards. Round up to 5 cubic yards. Formula for Cubic Yards: 27 cubic feet in one cubic yard. Convert the dimension in inches to feet (4" divide by 12" = .333 feet) Multiply the 3 dimensions together to find the number of cubic feet (35' x10' x .333' = 116.55) Divide the number of feet in a cubic yard, 27. 116.55 cubic feet divided by 27= 4.32 cubic yards. 5
A person pays $425.00 each year for fire and home insurance. The rate is $4.00 per $1,000 of insured value for a one-year period. If the policyholder's house is worth $150,000, what percent of that value is covered by insurance?
425 divided by 4 = 106.25: 1000 x 106.25= 106,250: 106,250 divided by 150,000 = 0.71 or 71%
A one-acre parcel was listed for sale based on a price of $1.95 per square foot. What was the asking price of the parcel?
43,560 * 1.95 = $84,942 $84,942
An acre consists of ____ square ____.
43,560; feet
You want to build a barn with feed storage on the second floor. The dimensions are 45 feet wide, 60 feet deep, and 30 feet high, with a flat roof. Builder A offers to build it for $7.50 per square foot. Builder B offers to build at $.475 per cubic foot. Which bid is lower, and by what amount?
45 x 60 = 2,700 square feet.2,700 x 7.5 = $20,250 45 x 60 x 30 is 81,000 cubic feet. 81,000 x .475 = $38,475 $38,475 - 20,250 = 18,225 A's bid by $18,225
A rectangular parcel of land is 50 acres. One side is 1,000 feet and faces County Line Road. How deep is the parcel?
50 X 43,560 = 2,178,000; 2,178,000 / 1000 = 2,178 2,178 feet
The S 1/2 of the NE 1/4 of the SW 1/4 of the NE 1/4 of the NW 1/4 of a section is to be paved for a parking lot at $.752 per square foot. The cost is ____.
640 acres x .5 x .25 x .25 x .25 x .25 = 1.25 acres. 1.25 acres x 43,560 = 54,450 square feet. 54,450 x $.752/square feet = $40,946.40 $40,946.40
An investor wants to build a small shopping center and build 72,000 square feet of retail space. If he purchases 3 acres of commercial land, what percentage of the site will the building occupy?
72,000 / (3 * 43,560) = 55% 55%
In 2004 the rent at a 10-unit apartment building was $650 a month per unit. The management company was paid a fee of 10% of gross rent collected plus a bonus of one- half of one month's rent each time a new tenant signed a one-year lease. One apartment remained vacant for three months and four new leases were signed. How much did the property management company earn last year?
9 units x $650 x 12 months ($70,200), 1 unit x $650 x 9 months ($5850)= 76,050 (gross rent). $76,050 x .10 (10%) = $7,605 plus 4 new leases x $325 (half month rent) = $1,300 bonus = $8,905 $8,905
The lot is 90 feet by 110 feet. The fence is to be 6 feet tall. cost for the fence is $3.00 per linear foot, plus $.40 per square foot for labor. What is the total cost of the fence?
90 + 90 + 110 + 110 = 400 linear feet 400 x $3 = $1,200. 6 feet x 400 feet = 2,400 square feet. 2,400 square feet x $.40 = $960 $960 + $1,200 = $2,160 $2,160
A property valued at $250,000 earns $950 per month. What is the annual percentage return?
950 X 12 = 11,400: 11,400 / 250,000 = 0.0456 4.6%
A broker associate is listing a home with 1,000 square feet of living area on an improved building site. The owner insists that the listing price reflect a value of $85.00 per square foot of living area, $32,000.00 for the building site, and include a 4% sales commission. The broker should list the real property for .
? x .96 = 117000, $117,000 / .96 = $121,875 Commission as a Ratio: T-Bar Method List price = 100% − 4% Commission = 96% net to seller.
A broker associate is listing a home with 1,000 square feet of living area on an improved building site. The owner insists that the listing price reflect a value of $85.00 per square foot of living area, $32,000.00 for the building site, and include a 4% sales commission. The broker should list the real property for ____.
? x .96 = 117000, $117,000 / .96 = $121,875 Commission as a Ratio: T-Bar MethodList price = 100% − 4% Commission = 96% net to seller. Part Total | Rateor;117,000 ? | .96 $121,875
The interest portion of a monthly loan payment is $427.93. If the interest rate is 6.875%, what is the current principal balance?
Annual interest = $427.93 * 12 = $5,135.16;P / R = T $5,135.16 / .06875 = $74,693.24 $74,693.24
A trust was established by your grandfather who owns 2,500 acres of prime development ground, but allows the sale of no more than 12.5% of the original amount of land each year. How much land can be sold for development each year? Express the answer as both a decimal fraction and an ordinary fraction.
Convert the percentage to a decimal by moving the decimal point two places to the left. 12.5% becomes .125 Multiply the acreage by the decimal .125 x 2500= 312.50 acres . 50 = 50/100, so convert 50/100 to the lowest common denominator and the answer is ½ Therefore, the trust can sell 312.50 or 312 ½ acres each year 312.5
Your client has decided to purchase four different buildings (an apartment building, a retail location, a self-storage project, and a small warehouse) in different areas of the city, each costing around $125,000. You are trying to sell him a single building, larger and closer to his residence. Your client tells you he would prefer separate investments. This is an example of ____.
Diversification
To solve a percentage problem you have three possible questions: 1).What is the Total Amount if you know the percentage rate and the part of the total amount; 2) What is the Percentage Rate if you know the Total Amount and the Part of the Total Amount; 3) what is the Part of the Total if you know the Percentage Rate. For number two what must you do to get the percentage rate?
Divide the Part by the Total
A homeowner owes $70,000 on a home worth $100,000. The $30,000 difference is known as the homeowner's ____.
Equity
To convert a decimal to a percent, ____.
Move the decimal two places to the right and add the % sign
The ABC Realty Co. sold an in-house listing for $179,000. The seller had agreed to pay the brokerage firm a 6% commission if Helen sold it on her own or split the commission 3.2%/2.8% to pay a co-operating fee of 2.8% to the selling brokerage. Kay procured the buyer. Helen is on a 60% commission split plan, and Kay gets 50%. How much more money did Helen get?
Helen will get 60% of (179,000 * 3.2%) = $3,436.80; Kay will get 50% of (179,000 * 2.8%) = $2,506.00; $3,436.80 - $2,506.00 = $930.80 $930.80
How many acres are contained in a parcel described as the NW ¼ of the NW ¼ AND the N ½ of the NE ¼, NW ¼, Section 10?
How many acres are contained in a parcel described as the NW ¼ of the NW ¼ AND the N ½ of the NE ¼, NW ¼, Section 10?
The purchaser is paying $350,000 for a property with a loan of $150,000. What is the down payment percentage?
If you know the total and the part and want to find the percentage, divide the part by the total. Down Payment = $200,000 ($350,000 - $150,000 ) Down Payment Percentage = $200,000 / $350,000 57.14%
The current market rate is 5.75% with an amortized monthly payment on $1000 to be $5.84. Your buyer want to get a loan for $150,000. What would his payment be.
If you know what a payment would be on $1000, to figure the payment on a loan just divide the loan amount by $1000 and then multiply the answer times the payment. $876.00
Mary bought a home for $150,000, which was 20% less than the asking price. What was the asking price?
Mary bought a home for $150,000, which was 20% less than the asking price. What was the asking price? 20% less means 80% of sales price. We are looking for 80% of the sales price so, ? x .80 = $150,000, Divide 150,000 by .8 = $187,500 $187,500
The ____ is the number of tax dollars per thousand dollars of assessed value.
Mill rate
To convert a percent to a decimal, ____.
Move the decimal point two places to the left and drop the % sign
In order to solve a percentage problem, you have three possible questions: What is the Total Amount if you know the percentage rate and the part of the total amount? What is the Percentage Rate if you know the Total Amount and the Part of the Total Amount? What is the Part of the Total if you know the Percentage Rate? For number three, what must you do to get the Part of the total?
Multiply Total by Rate
Sandy bought a note for $6,750 that was discounted by 25%. What was the original balance on the note?
The discounted note represents 75% of the original note amount. $6,750 / .75 = $9,000
A 40-acre commercial building site sold for $3,500 per acre. The lot is 900 feet deep. What is the price per front foot?
The site sold for 40 * $3,500 = $140,000; The dimensions are 900 x 1,936 (43,560 x 40 = 1,742,400 sq ft. / 900 = 1,936);$140,000 / 1,936 = $72.31 per front foot
If a purchaser borrows $150,000 at 6% and has a monthly payment of $850, what is the principal reduction after the first year?
To figure the principal reduction in a loan for one year, when there is a fixed payment, you determine the interest for a year and the total payments made for one year. You then subtract the total interest from the total payments. $850 x 12 = $10,200 (yearly payment) - $9,000 (yearly interest) = $1,200 (yearly principal reduction)
A salesperson received $3,000 for selling a house. This was 40 percent of the total commission on the sale of a $200,000 house. What was the commission rate on the sale?
Total commission = 3,000 / .4 = 7,500:7,500 divided by 200,000 = 3.75%
The buyer agreed to pay 55% of the closing costs, and the seller agreed to pay the other 45%. Closing costs were $500 for title insurance and $366 for other costs. How much more in dollars did the buyer pay than the seller? (Round to nearest dollar)
Total costs of $866 x 55% = $476.30. The seller pays 866 x 45% = $389.70;The difference is $86.60, rounded to $87. $87
To solve a percentage problem, you have three possible questions: What is the Total Amount if you know the percentage rate and the part of the total amount? What is the Percentage Rate if you know the Total Amount and the Part of the Total Amount? What is the Part of the Total if you know the Percentage Rate and the total? For number one, what must you do to get the total amount?
What is the Total Amount if you know the percentage rate and the part of the total?amount; PART / RATE = TOTAL 6/.06 = 100 What is the Percentage Rate if you know the Total Amount and the Part of the Total Amount?PART / TOTAL = RATE 6/100 = .06 What is the Part of the Total if you know the Percentage Rate?TOTAL * RATE = PART 100 x .06 = 6 Divide the Part by the Rate
The formula to determine cubic yards is ____.
Width (in feet) x length (in feet) x height (in feet), divided by 27
If you have an ARM amortized loan of $80,000 with a PI payment of $560, what could happen to your payment if you gave the lender an additional $10,000?
Your payment could go down
Janet purchased a property several years ago for $250,000 and has decided to sell it. The sales commission and other closing costs will be 20% of the sales price. If Janet sold the home for no profit, what percentage of the sale price does $250,000 represent.
the question tells you that -The sales commission and other closing costs will be 20% of the sales price. $250000 is what she wants, this is 100%. Her cost is 20%, this leaves 80% for her. 100% - 20% is 80% 80%
A 40 x 45 ft. house is on a ½-acre of land. What approximate percentage is NOT taken up by the house?
½ acre = 21,780 sq. ft.: 40 ft. * 45 ft. = 1,800 sq. ft.: 1,800 / 21,780 = .083 = 8% house: Therefore, 92% is the remaining land
