The __________ show the number of equal parts in the whole or total and the _____________ shows the number of those parts with which you are working.
-denominator
-numerator
Which number is the numerator and which number is the denominator?
7 is the numerator and 8 is the denominator
What is a proper fraction?
-on in which the numerator is smaller than the denominator--it is less than a whole or one:
What is an improper fraction?
one in which the numerator is larger than the denominator--it is more than one:
A mixed number is what...
a whole number plus a fraction:
Real estate math problems are easily solved when the fractions are turned into decimals. What is the equations to turn proper fractions, improper fractions and mixed numbers into decimals?
a.
b.
c.
a. proper fraction: 7 ÷ 8 = 0.875
b. improper fraction: 11 ÷ 8 = 1.375
c. mixed number: 1 ÷ 2 = 0.5 + 11 = 11.5
Many real estate computations are based on the calculations of percentages. A percent expresses a portion of a whole: percent means "____________". The whole or total always represents what?
What are the parts of:
a. 5%
b. 75%
c. 120%
per hundred
100%
a. 5% is 5 parts of 100
b. 75% is 75 parts of 100
c. 120% is 100 parts of 100 plus 20 parts of another 100
To solve a problem involving percentages, the percentage must be converted to either a decimal or fraction. The formula to convert a percentage to a decimal:
a. move the decimal ____ places to the left and drop the percent sign
b. or divide number by ____.
a. two
b. 100
**TO convert a decimal to a percent, move the decimal in the number two places to the right and add the percent sign or multiply the number by 100.
Convert the percentages into a decimal:
a. 5%
b. 75%
c. 120%
a. 0.05
b. 0.75
c. 1.20
Convert the decimals into percentages:
a. 0.0875
b. 0.05
c. 0.2
d. 1.82
a. 8.75%
b. 5%
c. 20%
d. 182%
What three elements do percent problems contain?
rate (percentage), total and part
What are the three formulas for solving all percentage problems? Hint: total, rate, and part.
Fill out the T bar
________________
/
total x rate = part
part ÷ rate = total
part ÷ total = rate
When working with percentage problems:
Multiply when part is the _______. Divide when part is the _________. When you divide, always enter _______ into the calculator first.
unknown
known
part
There are 200 homes in your prospecting area. If 5% of them sold last year, how many homes sold last year?
200 (total) x 0.05 (rate) = 10 homes (part)
A broker received $10,200 for the sale of a house. If the commission rate was 6%, what was the total sales price?
If a broker received a $7,700 commission on a $110,000 sale, what was the commission rate?
7%
When analyzing word problems it is very important to find out which facts and numbers ____ and _____ be needed in solving the problem
will
will not
Percent problems using commission:
The full commission is a percentage of the sales price unless otherwise stated in the problem. Remember that commission rates charged to clients, and that commission is split. How is commission split?
-commission is split between brokers than it is split between the broker and the salesperson
A seller listed his home for $200,000 and agreed to pay a full commission rate of 5%. The home sold four weeks later for 90% of the list price. The listing broker agreed to give the selling broker 50% of the commission. The listing broker paid the listing salesperson 50% of her share of commission, and the selling broker paid the selling salesperson 60% of his share of commission. How much commission did the selling salesperson receive?
$2,700
refer to T bar
After deducting $5,850 in closing costs and a 5% broker's commission, the sellers received their original cost of $175,000 plus a $4,400 profit. What was the sales price of the property?
$195,000
STEP 1: Calculate the seller's net after commission:
$175,000 (original cost) + $4,400 (profit) + $5,850 (closing costs) = $182,250 net after commission
STEP 3: Calculate the total sales price using the formula for total: part ÷ rate = total
$185,250 net after commission (part) ÷ 95% rate after commission = sales price (total)
185,250 ÷ 0.95 = $195,000
To check, take 5% of the sales price, or,
$195,000 x 0.05 = $9,750, which is subtracted from the sales price of $195,000, leaves the seller's desired net after commission of $185,250
A profit is made when an item is sold for more than the purchase price. If an item is sold for less than the purchase price, there is a loss on the sale.
Not that in the case of solving problems, profit is the part and is larger than the total
true
A home was listed for $125,000. It sold for $123,200, which resulted in a 10% profit over the original cost. What was the original cost?
$112,000
STEP 1: Calculate the rate that the sale price represents.
100% original cost + 10% profit = 110% sales price.
STEP 2: Calculate the original cost using the formula for total: part ÷ rate = total.
Interest is the cost of using money. The amount of interest paid is determined by the agreed annual interest rate, the amount of money borrowed (loan amount) or amount of money still owned (loan balance), and the period of time the money is held.
When interest is calculated for ONE YEAR: The formulas for percentage calculations also are used for interest computations.
When interest is NOT calculated for a FULL YEAR, the formula must have a "time" factor. What is the formula
Principal (total) x rate x time (in months) = interest (part)
1. What is the annual interest on a $10,000 loan on which the interest rate is 12%?
2. How much interest would be charged if the loan could be paid off in seven months?
1. $1,200
$10,000 (total) x 12% (rate) = interest (part)
$10,000 x 0.12 = $1,200 interest
or
2. $700 interest
$10,000 x 0.12 x = interest
$10,000 x 0.12 x 0.583333 = $700
or
The process of paying off a loan in equal installments of principal and interest is known as what? The interest is calculated each month on the remaining loan balance, and "time" is 1 month or . The payment is first applied to the accrued interest with the remaining balance applied to reduce the principal.
amortization
What is the balance after two payments on a loan in the original amount of $150,000 with monthly payments of $1,449.00 at 10% over a 20-year period?
First month:
$150,000 loan (total) x 10% (rate) x (time) = $1,250 interest first month (part)
$1,449.00 total payment
-1,250.00 interest first month
$ 199.00 principal reduction first month
Second Month:
$150,000.00 original loan
- 199.00 first month's reduction
$149,801.00 second month balance
$149,801.00 loan balance (total) x 10% (rate) x (time) = $1,248.34
$1,449.00 total payment
-1,248.34 interest second month
$ 200.66 principal reduction second month
$149,801.00 second month balance
- 200.66 second month's reduction
$149,600.34 balance after 2nd month payment beginning of third month (answer)
The loan discount is a method of increasing the lender's yield on a loan without increasing the interest rate. One point equals what percent of the loan amount?
When using the T bar formula to solve a loan discount problem, where do you plug in the discount point on the T?
1%
-Where part is
The lender will charge a 1-point origination fee and loan discout points. What will be the total due for points on an $98,000 loan?
$98,000 (total) x % (1% + % rate) = total points (part)
= (1 ÷ 2) + 3 = 3.5% = 0.035
$98,000 x 0.035 = $3,430 total due for points (answer)
Property taxes and insurance premiums usually are expressed as rate per unit of value. When solving problems with taxes or insurance premiums, plug these numbers in the _____ section of the T bar formula.
part
A house has been appraised at $90,000 and is taxed at an annual rate of $2.50 per $100 of appraised valuation. What is the yearly tax?
$90,000 (total) x 0.025 (rate) = $2,250 (part) total annual tax
Linear measurement is measurement of a _____. When the term per foot, per linear foot, per running foot, or per front foot are used, determine the total length of the object. To measure front footage of a lot, use the ______ footage. To measure linear feet for a fence, measure the sides to be fenced. If two dimensions are given for a tract of land, the first dimension is the __________ if they are not labeled.
-line
-street
-frontage
A rectangular lot is 50 feet x 150 feet. The cost to fence this lot is priced per linear/running foot. How many linear/running feet will be used to calculate the price of the fence, assuming the entire lot is to be enclosed in the fence?
50 ft + 150 ft + 50 ft +150ft = 400linear/running feet (answer)
A parcel of land that fronts on I-45 in Houston is for sale at $5,000 per front foot. What would it cost to purchase this parcel of land if the dimensions are 150' by 100'?
150 front feet x $5,000 per front foot = $750,000 cost to purchase (answer)
Area is the two-dimensional surface of an object. Area is quoted in square units (such as feet, yards, or acres). A real estate agent would use this formula to compute the area of a parcel of land or figure the square footage of living area in a house. What formula do you use when computing the area of a square or rectangular parcel?
area = length x width
How many square feet are in a room 15'6"5 x 30'9"?
STEP 1: Convert "inches" to a decimal figure by dividing by 12 inches per foot.
6" ÷ 12 = 0.5' 9" ÷ 12 = 0.75'
STEP 2: Calculate the area.
15.5' x 30.75' = 476.625 sqft (answer)
Important to remember with area problems, area is always expressed in....
square units.
If carpet costs $63 per square yard to install, what would it cost to carpet the room that is 15.5' x 30.75'?
15.5 x 30.75 = 476.625 sqft
there are 9sqft per square yard
479.625 ÷ 9 = 52.958333 square yards
52.958333 sqyd x $63 per sqyd = $3,336.37 carpet cost (answer)
How many square feet are in a square yard?
9
To compute the amount of surface in a triangular-shaped area, use the formula:
area of a triangle = (base x height)
or
area of a triangle = (base x height) ÷ 2
The base of a triangle is the _________, the side on which the triangle rests. The ______ is an imaginary straight line extending from the point of the uppermost angle straight down to the base.
bottom
height
How many square feet are contained in a triangular parcel of land that is 400 ft on the base and 200 feet high?
(400' x 200') ÷ 2 = 40,000 sqft (answer)
How may acres are in a three-sided tract of land that is 300' on the base and 400' high?
/ this kind of triangle 400' split top down to base middle.
To compute the area of an irregular room, a house, or parcel of land, divide the shape into... next, compute the area of each regular figure and add the areas together to obtain the total area.
regular rectangles, squares, or triangles.
What is the total square foot of the office building below?
A = 40' x 40' = 1600 sqft
B = (20' X 40') ÷ 2 = 400 sqft
C = (20' x 40') ÷2 = 400 sqft
1,600 +400 +400 = 2,400 sqft (answer)
Volume is the space inside a three-dimensional object. It is used, for example, in measuring the interior airspace of a room to determine the required capacity for a heating unit or to calculate the amount of concrete needed on a construction project. Volume is always expressed in ______. What is the formula for computing volume?
-cubic unit
volume = length x width x height
A building is 500 ft long, 400 ft wide, and 25 ft high. How many cubic feet of space are in this building?
500' x 400' x 25' = 5,000,000 cubic ft
How many cubic yards of concrete would it take to build a sidewalk measuring 120' long, 2'6" wide, and 3" thick?
STEP 1: Convert inches into feet
6" = 6/12 = 0.5' 3" = 3/12 = 0.25"
STEP 2: Calculate cubic feet and convert to cubic yards.
To compute the volume of a triangular prism, such as the airspace under a gable roof or in an A-frame cabin, what is the formula?
Volume = 1/2 (length x width x height)
A building is 40 feet by 25 feet with a 10-foot high ceiling. The building has a gable roof that is 8 feet high at the tallest point. How many cubic feet are in this structure, including the roof?
STEP 1: Divide the structure into two parts: the rectangular dwelling unit and the trigangular prism roof unit.
Dwelling unit : 40' (L) by 25' (W) by 10' (H)
Roof unit: 40' (L) by 25' (W) by 8' (H)
STEP 2: Calculate the area of each portion and combine the totals.
40' x 25' x 10' = 10,000 cubic ft
1/2 (40' x 25' x 8') = 4,000 cubic ft
10,000 cubic ft + 4,000 cubic ft = 14,000 total cubic ft (answer)
Prorations ensure that expenses are divided fairly between the seller and the buyer.
____________ items are items to be prorated that are owed by the seller but eventually will be paid by the buyers. The seller pays the buyer for these expenses at closing
______________ are items to be prorated that have been prepaid by the seller but not fully used up. The buyer owes the seller for these expenses.
____________, such as rental income, would be prorated and the income for the unused days transferred to the buyer from the seller at closing.
-Accrued expense items
-Prepaid expense items
-Prepaid income items
Prorated items that have not been used up by the seller, such as prepaid insurance policy, is what? And paid by who?
prepaid expense items
-paid by buyer
Prorated items that are owned by the seller but eventually will be paid by the buyer such as interest on an assumed loan or accrued ad valorem property taxes are what...
accrued expense items
What are three important key factors when computing prorations?
-The seller owns the property on the day of closing; the seller is charged expenses for that day and gets income for that day. This is called prorating through the day of closing, which is a requirement of the Texas promulgated sales contract.
-Prorations are based on either a statutory year or a calendar year.
-The buyer pays the seller for prepaid expense items; the seller pays the buyer for accrued expense items. The party receiving the money "gets the credit"; the party paying the money is "debited".
The seller owns the property on the day of closing, is charged expenses and receives income that day. This is required by the Texas promulgated sales contract.
true: called prorating through the day
What is the difference between a statutory year (aka banker's year) and a calendar year?
-statutory year (banker's year) based on a 360-day year, using 30 days in each month.
-A calendar year based on a 365-day year, using the actual number of days in each month.
When prorating, the buyer pays the seller for ___________ items and the seller pays the buyer for __________ items.
-prepaid expense items
-accrued expense items
What are the three steps in prorating an item?
1. The charge must first be broken down into yearly, monthly, and daily amounts, depending on the type of charge. Decide when type of year to use: statutory; a total monthly charge will be divided by 30, or calendar; the total monthly charge would be divided by the actual number of days in the month of closing.
2. The prorated period is calculated using the actual number of months and days, using a calendar year or 30 days per month, using a statutory year.
3. The monthly and daily amounts are then multiplied by the number of years, months and days in the prorated period to determine the accrued or unearned amount to be credited or debited at closing
Interest on a mortgage loan is collected in arrears; each month's payment includes interest for the prior month. Therefore, it a seller's loan is assumed by the buyer, the seller owes interest for the portion of the month that he owned the property. The interest proration would be a _____ to the seller and a ____ to the buyer.
-debit
-credit
A buyer purchases a home for $175,000 and plans to assume the seller's existing loan for $146,750 with monthly payments of $1449 at 10%. The closing date is set for August 18. Because interest on a mortgage loan is collected in arrears, the August 1 payments covered July's interest. Therefore, the seller has not yet made a payment to cover August's interest, and the seller will owe a portion of the interest to the buyer for the next house payment, how much would that be for a calendar year and a statutory year?
Statutory
Step 1: Find the dollars per day for interest: Calculate the amount of interest in the monthly payment, then divide that amount by 30 days.
$149,750 x 10% x 1/12= $1222.916 interest for the month
$1222.916 ÷ 30 days = $40.763 daily interest
Step 2: Calculate the period for which the seller owes the buyer:
18 days through the day of closing
Step 3: Finally, multiply the daily interest amount by the number of days to be charged to the seller:
$40.763 x 18 days = $733.73 prorated interest using a statutory year; a debit to the seller and a credit to the buyer.
Calendar: same steps just different days in month.
Step 1: Calculate the charge per day (31 days in August)
$1222.916 ÷ 31 days = $39.448 daily interest.
Step 2: Calculate period: 18 days
Step 3: multiply the daily charge by the number of days:
$39.448 x 18 days = $710.06 prorated interest, using a calendar year
taxes are paid at the end of the year
true; arrears; bank pays; we pay monthly to bank; then bank pays at end of year
The seller will owe the buyer for accrued taxes from when to when?
From January 1 through the day of closing.
**If the current tax bill has not been issued, the proration is generally computed on the previous year's bill
A sale is to be closed on September 17, and current real estate taxes of $1,200 are to be prorated accordingly. How much will the seller credit to the buyer with a statutory year and a calendar year?
Statutory year
Step 1: Determine the prorated cost of the real estate tax per month and day for the statutory year;
$1,200 annual taxes ÷ 12 mo = $100 taxes/mo
$100 mo taxes ÷ 30 days = $3.333 taxes/day
Step 2: The accrued period is 8 mo 17 days
Step 3: Multiply the monthly and daily charges by the accrued period and add the totals to determine the prorated real estate tax;
$100 taxes/mo x 8 mo = $800
$3.333 taxes/day x 17 days = %56.661
$800 + 56.661 = $856.661 prorated taxes, using a statutory year.
Calendar year
Step 1: A tax bill of $1,200 ÷ 365 days = $3.287/day
Step 2: The accrued period from January 1 to September 17 runs 260 days (Jan 31 days, Feb 28 days)
Step 3: $3.287 x 260 days = $854.62
If the bank gave John a 90% loan on a house valued at $88,500, how much additional cash must he produce as a down payment if he already had paid $4,500 in earnest money?
$4,350 due at closing
$88,500 (total) x 0.1 (rate) = $8,850 down payment
$8,850 - $4,500 earnest money = $4,350 due at closing
What did the owners originally pay for their home if they sold it for $98,672, which gave them a 12% profit over their original cost?
$88,100 original cost
100% total original cost + 12% profit = 112% sales price
$98,672 (part) ÷ 1.12 (rate) = $88,100 (total)
For women pooled their savings and purchased a six-unit apartment building for $350,000. If one person invested $80,000 and two contributed $87,500 each, what percent of ownership was left for the forth investor?
27%
$80,000 + $87,500 + $87,500 = $255,000
350,000 - $255,000 = $95,000 4th investor
$95,000 ÷ $350,000 = 0.2714 = 27%
Jacob wants to determine the principal amount still owed on this mortgage loan. He knows that the interest portion of his last monthly payment was $391.42. If he is paying interest at the rate of 11½%, what was the outstanding balance of the loan before that last payment was made?
$40,843.83 principal balance
$391.42 mo interest x 12 = $4,697.04 annual interest.
$4,697.04 (part) ÷ [0.115 (rate) x 1 (time] = $40,843.83
The home at 1358 DeKalb Street is valued at $95,000. The local tax is $1.71 per $100. What is the amount of the monthly taxes?
$135.38 mo taxes
$95,000 x $0.0171 = $1,624.50 annual taxes
$1,624.50 ÷ 12 = $135. 38 monthly taxes
What is the total cost of a driveway 15 feet wide, 40 feet long, and 4 inches thick if the concrete costs $60 per cubic yard and the labor costs $1.25 per square foot?
$1,194.00 total cost
Concrete:
4" ÷ 12 = 0.333'
15' x 40' x 0.333' = 199.8 cubic feet
199.8 cubic feet ÷ 27 = 7.4 cubic yards
7.4 cubic yards x $60/cubic yard = $444 concrete cost
Labor:
15' x 40' = 600 square feet
600 x $1.25/square foot = $750 labor cost
$444 concrete + $750 labor = $1,194 cost
An owner agrees to list his property if he can receive at least $47,300 after paying a 5% broker's commission and paying $1,150 in closing costs. At what price must it sell?
$51,000 sales price
$47,300 + $1,150 = $48,450 net after commission
100% (total rate) - 5% (rate) = 95% net after commission
The Loving Gift Shop pays rent of $600 per month plus 2.5% of gross annual sales in excess of $50,000. What was the average monthly rent last year if gross annual sales were $75,000?
Two brokers split the 6% commission equally on a $73,000 home. The selling salesperson, Saul, was paid 70% of his broker's share. The listing salesperson, Elisha, was paid 30% of her broker's share. How much did Elisha receive?
$675
$73,000 x 0.06 = $4,380 total commission
$4,360 ÷ 2 = $2,190 broker's share
$2,190 x 0.3 = $657
A 100-acre farm is divided into lots for homes. The street require one-eight of the whole farm. If there are 140 lots, how many square feet are in each lot?
27,225 square feet per lot
1/8 =0.125 (1 ÷ 8)
100 acres x 0.125 = 12.5 acres for streets
100 total acres - 12.5 acres for streets = 87.5 acres for lots
87.5 acres for lots x 43,560 = 3,811,500 square feet
How much interest will the seller owe the buyer for a closing date of August 10 if the outstanding loan balance is $43,580? The interest rate on this assumable loan is 10½% and the last payment was paid on August 1. Prorations are to be done through the day of closing, using a statutory year.
$48,580(total) x 10½% (rate) x 1/12 (time) = $381.325 month's interest
$381.325 ÷ 30 = $12.711 day's interest
Step 2: Calculate time.
August 1 through August 10 = 10 days
Step 3: Multiply the daily amount by the number of days.
$12.711 x 10 = $127.11 interest proration
The buyer has agreed to pay $175,000 for a property. If she makes a 10% down payment, how much will she owe at closing for points if there are 2.5 loan discount points and a 1-point origination fee?
$175,000 (total) x 0.9 (rate) = $157,500 loan amount (part)
$157,500 (total) x 0.035 (rate) = $5,512.50 for points
Calculate eight months' interest on a $5,000 interest-only loan at 9%.
$316.67
$5,000 (total) x 0.095 (rate) x 8 months ÷ 12 = $316.67 interest
**When the "time fraction" would convert to a "repeating decimal" (ex: 8/12=0.66666), don't convert the fraction to a decimal. Multiply the total by the rate and then by the fraction's numerator; then, divide by the denominator
The Fernandez family has sold their home and closing is set for May 23. If last year's tax bill totaled $1,282 and was paid, how much will the tax proration be? Prorate through the day of closing using a calendar year.
$502.22 tax proration
Step 1: Calculate monthly and daily rates:
$1,282 annual tax ÷ 365 = $3.512 daily tax
Step 2: Calculate time.
Seller owes the buyer for January 1 through May 23 = (J=31)+(F=28)+(M=31)+(A=30)+(M=23)=143 days
Step 3: Multiply daily rates by the number of days.
$3.512 x 143 days = $502.22 tax proration
What is the monthly net operating income on an investment of $115,000 if the rate of return is 12½%?
$1,197.92 monthly net operating income
$115,000(total) x 0.125(rate) = $14,375 annual net operating income
$14,357 ÷ 12 = $1,197.92 monthly net operating income
What is the interest rate on a $10,000 loan with semiannual interest of $450?
9% annual interest rate
$450 ÷ ($10,000 x 0.5) = 0.09 = 9%
An office building produces $68,580 annual net operating income. What price would you pay for this property to show a minimum return of 12% on your investment?
$571,500 price
$68,580(part) ÷ 0.12(rate) = $517,500 price
If a broker received a 6.5% commission that was $5,200, what was the sales price?
$80,000 sales price
$5,200(part) ÷ 0.065 = $80,000 sales price
Duc Van earns an annual income of $60,000; Lan earns $2,400 per month. How much can Duc Van and Lan pay monthly for their mortgage payment if the lender uses a 28% qualifying ratio?
$2,072 monthly PITI payment
$60,000 annual salary ÷ 12 = $5,000 Duc Van monthly salary + Lan's monthly salary = $7,400 total monthly salary
$7,400 x 0.28 = 2,072
What percentage of profit would you make if you paid $10,500 for a lot, built a home on the lot at a cost of $93,000, and then sold the house and lot for $134,550?
30% rate of profit
$10,500 + $93,000 = $103,500 cost of the home
$134,550 sales price - 103,500 = $31,050 profit
$31,050(part) ÷ $103,500(total) = 0.3 =30% rate of profit
**Profit and loss are based on cost or a prior year's figure. Ex: to calculate the profit from year 2009 to 2010, total will be the year 2009 figure.
A fence is being built to enclose a lot 125 feet by 350 feet. How many running feet of fence will it take to enclose the lot?