Section 27: Math Basics for Delaware
A property sells for $200,599, which is 15% more than the owner paid eight years ago. What did the owner originally pay for the property (round to the nearest cent)?
$174,433.91 Take the sale price of the property divided by the total profit: 100% + 15% = 115%, then $200,599 ÷ 1.15.
A buyer has a 30-year, $400,000 loan with a 7% interest rate. How much of the first month's mortgage payment is interest?
$2,333.33 $400,000 x 0.07 = $28,000; then $28,000 ÷ 12 = $2,333.33
You were the seller for Margie, who bought a bungalow retreat last year. Your commission earned was $18,000, and your commission rate is 8%. What was the sale price for the home?
$225,000 $18,000/0.08
Marten and Molly bought a home downtown on the main street of a historic small town. Their home has a patio that's adjacent to main street, facing a shop that spans 180 feet. If the value per foot for the location is $1,260, what is the front foot value for their home?
$226,800
A buyer has a 30-year, $750,000 loan with a 5.75% interest rate. How much of the first monthly payment is interest?
$3,593.75 Multiply the principal balance by the interest rate: $750,000 x .0575 = $43,125;. Then find the monthly rate by dividing $43,125 by 12 to get $3,593.75. Since the principal balance is less the next month, the interest amount will change too.
A buyer with a 15-year, $250,000 loan at a 5.5% interest rate has a monthly principal and interest payment totaling $2,042.71. What's the total amount the borrower will pay back over the life of the loan?
$367,687.80 To find the total amount paid back, multiply the monthly payment ($2,042.71) by the total number of payments (180 = 12 payments/year x 15 years). The total paid back is $367,687.80.
Calculate eight months' interest on a $7,500 loan at 7.5%. Round to the nearest dollar.
$375 Figure out the annual interest by multiplying the loan amount by the rate. Once you have the annual interest, divide by 12 months to determine the monthly interest. From there, multiply the monthly interest by the number of months.
Barry has been getting pressure from the Millers about their home, which has been listed for quite some time. They are in a financial bind and need the money. He is finally able to sell their home for $600,000. What will the Millers net after the 7% commission is deducted?
$558,000
A borrower has a 30-year, $500,000 loan with an interest rate of 6.25%. His monthly principal and interest payment is $3,078.59. What's the total amount of interest he'll pay over the course of the loan?
$608,292.40 First, multiply the monthly payment by the total number of payments. Then subtract the original loan value: $3,078.59 x 360 = $1,108,292.40 ‒ $500,000 = $608,292.40.
Calculate 10 months' interest on a $12,500 loan at 6.5%. Round to the nearest dollar.
$677
On a $100,000 sale at a 7% commission rate, what would your commission be?
$7,000
Gary has an 80% LTVR on his new $318,000 townhome with an annual interest rate of 4.125%. What's his interest payment the first month?
$874.50 loan amount = 80% of $318,000 loan amount = $254,400 now we get here interest amount for 1st month that is interest amount = loan amount × interest rate × time period put here value interest amount = $254,400 × 0.04125 / 12 interest amount = $874.50
A home on a triangle-shaped lot sells to your clients, resulting in a net of $85,000 net to the seller. This is $10,000 more than the original sale price from five years prior. If your commission rate was $4,005.24, what was the home's sales price?
$89,005.24
Juan secures a fixed rate amortized 30-year loan for $295,000 at 4.25%. If his monthly P&I payment is $1,750, how much interest does he pay in the second month of the loan?
$1,042.29 In the first month, Juan pays $1,044.79 in interest ([$295,000 x .0425] ÷ 12). His monthly payment (stated in the question) is $1,750, so that means he paid the principal down $705.21 ($1,750 - $1,044.79). His new principal balance is $294,294.79 ($295,000 - $705.21). We use the new principal balance amount to calculate interest for the next month. Juan pays $1,042.29 in interest ([$294,294.79 x .0425] ÷ 12).
A buyer with a 20-year, $419,000 loan at a 4.25% interest rate has a monthly principal and interest payment totaling $2,594.59. If $1,483.95 is interest, how much is applied toward principal for that payment?
$1,110.64
A buyer has a 15-year, $250,000 loan with a 5.5% interest rate. How much of the first monthly payment is interest?
$1,145.83 ($250,000 x 0.055) ÷ 12 = $1,145.83
How much is the annual interest on a $155,000 loan with an interest rate of 7.5%?
$11,625
A buyer with a 15-year, $250,000 loan at a 5.5% interest rate has a monthly principal and interest payment totaling $2,042.71. What is the total amount of interest the borrower will pay over the course of the loan?
$117,687.80
If her commission rate is 7%, what would her commission be on a $375,000 home, the average price for the new neighborhood they are interested in exploring? Assume she splits the commission 50/50 with the listing agent, and earns 100% of the remainder.
$13,125
Ruth sold her property for $180,000 and made $36,000, which was a 25% profit. What was her original purchase price for the home?
$144,000 180,000 / (100% + 25%) = 180,000 / 1.25 = 144,000
Calculate six months' interest on a $4,000 loan at 7.5%. Round to the nearest dollar.
$150
What type of measurement is used with three-dimensional shapes?
Volume
A basic calculator is useful for....
most common math tasks (e.g., addition, subtraction, multiplication, division, square root, percentage). It also usually has some memory functions.
A(n) ______ fraction is where the numerator is less than the denominator.
proper
The secret to using formulas correctly is to ....
put the information you've got into the right spot(s) in the formula.
To find the original price when a profit was made use this formula:
take the amount the seller sold the property for and divide it by 100% plus the profit rate.
A borrower has a 30-year, $500,000 loan with an interest rate of 6.25%. His monthly principal and interest payment is $3,078.59. What's the total amount he'll pay over the life of the loan?
$1,108,292.40 To find the total amount paid back, multiply the monthly payment by the total number of payments: $3,078.59 x 360 = $1,108,292.40
A homeowner sold her property for $125,000, which gave her a 12% profit over the original cost. What was the original cost?
$125,000 / 112% (1.12) (calculated by 100% profit + 12%) = $111,607
The current value of a property is $105,000. What was the original cost of the property if there has been a 30% loss in value?
$150,000 Take the current value of the property divided by the total depreciation: 100% ‒ 30% = 70%, then $105,000 ÷ 0.70.
A buyer has a 30-year, $400,000 loan with a 7% interest rate. How much of the first month's mortgage payment is interest?
$2,333.33
The Smiths sold their property for $225,000, which gave them 10% profit over their original cost. What was their original cost?
$204,545 $225,000 / 0.110 = $204,545
Let's say you're working with your clients to determine the value of their property. You measured the front feet and found the total to be 150 feet, and you know that the value per front foot in the neighborhood is $1,400. Calculate the front foot value.
$210,000
A property sold for $250,000 (part), five years after it sold for 270,000 (total). What w as the loss (rate%)?
$250,000 / $270,000 = 0.93% or 93% 7% loss
Charlie and Wendy bought a $350,000 house by taking out a 30-year $335,000 loan at an interest rate of 5%. Their monthly principal and interest payment is $1,798.35. What is the total amount the couple will have paid toward interest at the end of 30 years?
$312,406 $1,798.53 x 360 = $647,406 - $335,000= $312,406
Calculate nine months' interest on a $6,500 loan at 6.5%. Round to the nearest dollar.
$317
A buyer with a 15-year, $250,000 loan at a 5.5% interest rate has a monthly principal and interest payment totaling $2,042.71. What's the total amount the borrower will pay back over the life of the loan?
$367,687.80 To find the total amount paid back, multiply the monthly payment ($2,042.71) by the total number of payments (180 = 12 payments/year x 15 years). The total paid back is $367,687.80.
A property is sold for 15% (rate) above the original price. The amount of the profit the seller realized was $37,500 (part). What was the sales price (total) for the home?
$37,000 / 0.15 = $250,000
Grant and Adela arrange a $150,000 loan at 4.5% annual interest with their lender. What's their monthly interest amount?
$562.50
Calculate the front foot price of a lot that has 500 front feet if the value per front foot is $1,200.
$600,000
Brian took out a 30-year $500,000 loan with an interest rate of 6.25%. His monthly principal and interest payment is $3,078.59. How much will he have paid in total interest at the end of the loan term?
$608,292.40 360 (total payments), $3,078.59 (monthly payment), and $500,000 $3,078.59 x 360 = $1,108,292.40 ‒ $500,000 = $608,292.40.
Your clients get a loan from Cityville Bank to help pay for their home purchase. Find the interest on the loan if they borrowed $10,000 at 6.5% for one year.
$650 $10,000 x .065
A lot with dimensions measuring 400 feet by 500 feet sold for $275,000. What was the cost per front foot?
$687.50 per front foot 275,000/400 (since the first # is always the front footage) = $687.50 per front. foot
A buyer with a 30-year, $750,000 loan at a 5.75% interest rate has a monthly principal and interest payment totaling $4,376.80. If $3,593.75 is interest, how much is applied to principal?
$783.05
You're working with buyers who are pre-approved for a loan of as much as $200,000. Assuming they lock in a 5.25% interest rate at closing, how much of their first payment will go toward interest?
$875 The formula is loan balance x interest rate divided by months per year. Loan balance is: $200,000 x .0525 = $10,500 ÷ 12 = $875.
Your clients are buying a home and borrow $10,000 from the bank at a 9% rate. Find the interest they'll pay on this loan in the first year.
$900 $10,000 x .9
To find the rate of profit or loss, use the following formula:
(price sold ‒ purchase price) / (purchase price)
How the T-bar works
-Shows the relationship between the part, total and rate -If the bar is horizontal (top of the T) then you divide -If the bar is vertical (base of the T) then you multiply
You have your eye on a property that's been on the market at a price of $250,000. You meet with your real estate professional, and learn that the seller has just lowered the price by 12%. What's the new sale price?
1. Sales price = 100% - 12% = 88%, so the list price is 88% of the original list price. 2. Change the percent to a decimal. 88% becomes 0.88 (We get this by dividing 88 by 100 or simply moving the decimal two places to the left). 88/100=0.88 3. Multiple the original sales price by 0.88 ($250,000 x 0.88). 4. The answer is $220,000. 5. Ask yourself: Is $220,000 less than the original sales price and within the realm of possibility of being 12% less? If it is, then you have correctly solved this word problem. (The formula is sale price = original price - discount price.)
If your client purchased land for $10,000 and sold it for $11,800, what is the profit margin?
18%
A buyer with a 15-year, $250,000 loan at a 5.5% interest rate has a monthly principal and interest payment totaling $2,042.71. How many payments will the borrower make over the course of the loan?
180
What percentage of loss would Gene, a homeowner, take if he paid $123,500 for a home and then sold it for $100,000?
19% loss of profit $123,500 - $100,000= $23,500 / $123,500= 0.19 = 19%
What is 1/2 x 2/3?
2/6 = .333= 1/3
Find the area of a square flower bed where each side measures 4.5 m.
20.25 meters squared
A lot has an area of 30,000 square feet. How many acres is that?
30,000/43,560 sq. ft = 0.69 acres
Convert the following decimal to a percent: 0.35.
35%
Circular measures
360 degrees = circle 180 degrees = semi circle 1 degree = 60 minutes 1 minute = 60 seconds
Your buyer client wants to replace the crown molding in the living room of the house he's planning to buy, so he wants to find out how many linear feet the room has so he can determine the cost of new molding. The room is a 9-foot by 10-foot rectangle. What's the total linear feet?
38 linear feet 9+10+9+10
Multiplying Percentages Solve the following problem: 400 x 40%
400 x .40%= 160
Dividing Percentages Solve the following problem: 400 ÷ 40%
400 ÷ .40= 1,000
What's the interest rate on a $14,000 loan that requires a semi-annual interest payment of $550? Round to the nearest percent.
8%
You're working with buyers who are pre-approved for a loan of as much as $200,000. Assuming they lock in a 5.25% interest rate at closing, how much of their first payment will go toward interest?
875 The formula is loan balance × interest rate ÷ months per year. Loan balance is: $200,000 × .0525 = $10,500; $10,500 ÷ 12 = $875
Real Estate calculator
A real estate calculator has functions to calculate payment amount, loan amount, term, interest, interest-only, future values, amortization, and remaining balances.
Amortization Chart
A schedule of monthly payments that varies according to interest rates and number of monthly payments
Acreage and Hectares
Acreage= property size (sq. ft.) / 43,560 sq. ft. Hectares= property size (acres) / 2.47 acres
Ensuring you've answered the word problem correctly is which of the following steps?
Checking
Which step involves selecting the correct formula?
Choosing
Mortgage payments consist of:
Mortgage payments consist of principal, interest, taxes, and insurance—or PITI.
Converting Percentages to Decimals
Moving 2 places to the left For example: 5 = 5.00 5% = 0.05 0.25 ---> percent 25%
Profit calculation
Purchase price = sales price ÷ (100% + percent profit) Purchase price = $50,000 ÷ (100% + 25%) (remember that 125% = 1.25) Purchase price = $50,000 ÷ 1.25 Purchase price = $40,000
Calculating loss
Purchase price = sales price ÷ (100% - percent of profit)
Which of the following is the proper order for the recommended steps to solving a word problem?
Read the problem, identify the information, choose the formula, solve
Your clients ask you how much money they will save in interest over 20 years if they start making one extra payment each year. What type of calculator should you use?
Real estate calculator
Example of Multiplying Percentages
To multiply 75% by 25%, we must: 1. Convert any percentages to decimals (or a fraction). We start with 75% and 25%. a. 75/100 = 0.75 b. 25/100 = 0.25 2. Perform the operation specified. (In this case, we're multiplying the two numbers.) a. 0.75 x 0.25 = 0.1875 3. Convert the result back to a percentage. We do this by multiplying the resulting number by 100 and adding the percent sign.a. 0.1875 x 100 = 18.75%
Total interest paid over life of the loan
Total interest paid over the life of a loan may be calculated by multiplying the number of payments over the loan term (e.g., a 30-year loan will have 360 payments) by the monthly payment amount, then subtracting the original loan amount.
Calculating Volume
Volume can be defined as the space taken up by an object in three dimensions. The most commonly used units of area are mm3, cm3, and m3. Rectangular prism= Volume = length x width x height Ex. If the garage is 40 feet wide and 60 feet long with a ceiling height of 9 feet, you would have a volume of 21,600 ft3 (V = lwh). Cube= Calculated by multiplying one side by another side by another side or side 3 (V = s3). Take a can with a radius of 3 inches and a height of 5 inches. To find the volume of a cylinder (a can), start by finding the area of the base (2) multiplied by the height (V = hr2). Cone= A cone's volume is found by taking the area of the base (2) times the height times one-third. (V =(h/3)2).
Front foot price
When calculating the front foot price, make sure you multiply the front footage by the value per front foot.
Hectares
When discussing even larger parcels of land, it will be helpful to know about hectares. A hectare is 10,000 square meters, or approximately 2.47 acres in U.S. measurements. So, if you wanted to find out how many hectares were in a 45-acre tract of land, you would divide the total acres by 2.47. So, 45/2.47 = 18.21 hectares.
Example of Dividing Percentages
When we divide 25% by 50%, we must follow the same steps outlined above. 1. Convert any percentages to decimals (or a fraction). We're starting with 25% and 50%. a. 25/100 = 0.25 b. 50/100 = 0.502. Perform the operation specified. (In this case, divide the first number by the second.) a. 0.25 ÷ 0.50 = .503. Convert the result back to a percentage by multiplying the resulting number by 100 and adding the percent sign. a. 0.50 x 100 = 50%
Acres
You may hear the word "acre" used when talking about lot size. An acre is land that contains 43,560 square feet. So, if you need to find out what percentage of an acre a parcel is that has 28,675 square feet, just divide the number of square feet in the property (28,675) by the number of square feet in an acre (43,560) to get .66, or 2/3 of an acre.
Profit is made when
a property is sold for more than the purchase price. If sold for less then its a loss.
Identify the keys you would use to solve the following problem: Find the monthly payment on a 30-year loan of $120,000 at 7.5% annual interest rate.
-Loan Amt -Pmt -Term -Int
Identify the keys you would use to solve the following problem: How long does it take to pay off a loan of $275,000 at 6.5% interest if you make payments of $1,700 each month?
-Loan Amt -Pmt -Term -Int
Jack and Jill originally purchased their home for $150,000. They received an offer that is 11% less than their purchase price. What can you multiply the original home purchase price by to determine the current offer?
.89
Convert 65% to a decimal.
0.65
Multiplying Fractions
1. Always multiply the numerator (top number) by the numerator (top number). 2. Always multiply the denominator (bottom number) by the denominator (bottom number). For example, you want to figure out what 1/2 x 2/5 equals. Step 1: Multiply the top numbers of each fraction together: 1 x 2 = 2 Step 2: Multiply the bottom numbers of each fraction together: 2 x 5 = 10 Step 3: Put it together: 1/2 x 2/5 = 2/10 Step 4: Simplify, if possible: 2/10 can be simplified to 1/5
Find Area of Irregular shapes
1. Divide the shapes into squares, rectangles and triangles 2. Find the area of each separate shape 3. Add the area of the separate shapes together
Dividing Fractions
1. Flip the second fraction in the problem. 2. Multiply the fractions. For example, you want to figure out what 2/3 ÷ 1/3 equals: Step 1: Flip the second fraction, so that 1/3 becomes 3/1, but keep the first fraction the same: 2/3. Step 2: Multiply the top numbers: 2 x 3 = 6 Step 3: Multiply the bottom numbers: 1 x 3 = 3 Step 4: Put it together: 2/3 x 3/1 = 6/3. Step 5: Simplify, if possible. For instance, 6/3 can be simplified to 2.
Solving word problems
1. Read the whole problem. Don't start solving the problem before you've finished reading it, because you'll add new numbers to the problem that may confuse matters. 2. Determine what information you have, and what information is missing. 3. Draw and label pictures if that's helpful to you. 4. Look for key words and phrases that may indicate mathematical operations, such as, "less," "more," "total," "per," "out of," "gave away," and "difference between." 5. Decide which formula you need (what the word is problem asking you to solve), and put the known numbers into the formula. 6. Solve the formula. 7. Check your answer to see if it makes logical sense (would you really end up with more cookies if your friend ate half of them?)
What's 3/4 multiplied by 2/3?
1/2
A lot has an area of 10 acres. How hectares is that?
10/2.47 acres= 4.05 hectares
Calculate the volume (in cubic centimeters) of a rectangular prism that's 5 cm long, 4 cm wide, and 5 cm high.
100 centimeters cubed 5 cm long x 4 cm wide x 5 cm high
A property has a rectangular patio that is 10 feet by 15 feet. What's the area of this patio?
150 square feet
The current value of a property is $105,000. What was the original cost of the property if there has been a 30% loss in value?
150,000 Take the current value of the property divided by the total depreciation: 100% ‒ 30% = 70%, then $105,000 ÷ 0.70.
The rain barrel on the property for sale is a large, above-ground rectangular prism that measures 84 inches by 84 inches by 84 inches. What volume of water can this barrel hold? Hint: You'll need to convert your answer to gallons, and there are .004329 gallons per cubic inch.
2,566 gallons 84x84x84 = 592,704 x .004329 = 2,566 gallons
A vacant lot that was purchased for $18,000 three years ago has appreciated 15%. What would its value be today?
20,700 Take the sale price of the property multiplied by the total profit (100% + 15% = 115%) and calculate $18,000 × 1.15.
What percentage of profit would the seller make if he paid $18,000 for a vacant lot, built a home on the lot that cost $145,000, and then sold the property for $200,599? Round your answer to the nearest percent.
23% Add the costs of the lot and the house together to get the total cost ($163,000). Next, subtract the sales price from the total cost to get the amount of profit ($37,599). Finally, divide the total cost by the profit amount ($37,599 ÷ $163,000).
The Wright's receive an offer for their home for $225,000. How much of a loss is this for them if they originally purchased the home four years ago for $349,000?
36% To find the percent of change, divide the offer by the original price: $225,000 ÷ $349,000 = .6446. Then: 100 - 64 %=36%.
Betty Lou is interested in a house that has an area footprint of 1,600 square feet on a property that's 3,400 square feet. What percentage of the property is taken up by the home?
47.05% To find the ratio as a decimal, divide the area of the house by the area of the property: 1,600 ÷ 3,400 = .4705 To convert the decimal to a percent, move the decimal to the right two places = 47.05%. The house uses 47.05% of the total property.
You're working with buyers who are pre-approved for a loan up to $150,000. If they estimate paying $625 per month toward interest, what interest rate are they assuming?
5% So, $7,500 (which we get by taking $625 per month times 12 months per year) is divided by $150,000.
What percentage of loss would the seller have if he paid $18,000 for a vacant lot, built a home on the lot that cost $145,000, and then sold the property for $153,000? Round your answer to the nearest percent.
6% Add the cost of the lot and the cost of the house together to get the total cost ($163,000). Next, subtract the sales price from the total cost to get the amount of loss ($10,000) he took. Finally, divide the total cost by the loss amount ($10,000 ÷ $163,000).
The Gatlins' lender tells them they can afford a monthly payment of $1,830 on their new home loan. What interest rate are the Gatlins getting if this is an interest-only loan with a principal balance of $349,000?
6.29%
The Gatlins' lender tells them they can afford a monthly payment of $1,830 on their new home loan. What interest rate are the Gatlins getting if this is an interest-only loan with a principal balance of $349,000?
6.29% Annual payment ÷ loan balance = interest rate. $1,830 x 12 to get the annual payment of $21,960. Then divide the annual payment by the loan amount: $21, 960 ÷ $349,000 = .0629, or 6.29%.
The property you're going to list has an addition that was built a few years ago. The addition is a master bedroom measuring 20 feet by 30 feet and a master bath that measures 10 feet by 10 feet. What's the total square footage of the entire addition?
700 square feet
Shane is the agent for Barney, who purchased a home recently for $167,000. Shane shares a 50% commission split with his brokerage. His portion of the commission was $6,680.00. What is the total commission rate percentage?
8%
What is 2/3 ÷ 1/4?
8/3
Which step involves determining what's being asked in the word problem?
Analyzing
Calculating the Interest Rate
Annual interest amount ÷ loan balance = interest rate Example If you have sellers who paid $7,000 in interest and have a balance of $140,000 ($7,000 ÷ $140,000), they're paying an interest rate of .05, or 5%.
Area
Area is the surface size of a two-dimensional object. Real estate professionals work with area calculations frequently when determining the square footage of living space in a home. The other most commonly used units of area are mm2, cm2 and m2.
Carol needs to compute her real estate commission. What type of calculator should she use?
Basic calculator
Amort
Displays the range of payments, total interest, total principal, total payments, and remaining balance for an entered number of years or per
Loan Amt
Enters or solves for the initial loan amount or present value
Term
Enters or solves for the number of years
Pmt
Enters or solves for the periodic principal and interest (P&I) payment
Int
Enters or solves the annual interest rate
If a property sold for $100,000 and this was $15,000 more than the original cost, the seller has made a 35% profit. (T/F)
False The original price of the house is $100,000 - $15,000 = $85,000. To find the percent of profit, divide the amount of profit by the original price: $15,000 / $85,000 = .1765 and move the decimal to the right two places to convert it to a percentage: 17.65 %. Then we can see this statement is false because the profit is not 35%, it is 17.65%.
Jon, a mortgage broker, needs to compute how payments on a loan will be affected, depending on different repayment terms. What type of calculator should he choose?
Financial or real estate calculator
Principal and Interest
If the buyer and the property both qualify, the lender will provide the funds to purchase the home. In return, the buyer will make payments back to the lender. These payments will consist of principal, or the loan balance, and interest, which is essentially the fee the lender is assessing for letting others borrow their money. (Taxes and insurance will also likely be part of the payment, but we'll leave that off for now.)
The Beedalls are looking for a property with a patio that's at least 225 square feet. Which of the following dimensions would match their needs?
Length of 15 feet and width of 20 feet
Linear measurements
Linear measurement is a dimension of length.
Calculating Interest Amount
Loan balance x interest rate = annual interest amount Monthly interest amount = ( loan balance x interest rate) ÷ number of payments annually Example A $70,000 loan has an interest rate of 6.5%. Remember, 6.5% is the same as .065. Multiply these numbers together ($70,000 and .065) and you get an annual interest amount of $4,550. To see what that would be on a monthly basis, just divide the annual amount by 12 and that will give you the monthly interest amount: $4,550 ÷ 12 = $379.17.
Scientific calculator
Scientific calculators will seldom be used in real estate, but are often used to perform calculations in science, engineering, and mathematics. Remember slide rules?These are their updated cousins.
Specialized calculator
Specialized calculators exist for real estate and other financial functions. Printing financial calculators allow you to compute and print out the results of complex business, financial, and statistical functions.
Find Perimeter
Square= 4 x length Rectangle= (2 x length) + (2 x width) Any other shapes= add lengths of each side
Find Area
Square= side x side Rectangle= length x width Triangle= (0.5 x base) x height
Rectangles, Triangles, and Squares
Take a rectangular building, for example. Length times width gives you the area. So, if that building were 40 feet by 20 feet, the area would be 800 square feet. A square's area is calculated by multiplying one side times another side. A triangle's area is found by taking half the length of the triangle's base and multiplying by its height.
The cone's radius is 4 feet and the height is 12 feet. What is the volume? Problem: Your client has a piece of property that has a storage facility on it, but no one can remember how much it can hold. The facility is a rectangular prism that measures 5 meters long, 4 meters wide and 2.5 meters high. Find its volume. Start by reading the problem twice and underlining the key terms (rectangular prism and volume)
The formula is: Volume = length x width x height. V= 5m x 4m x 2.5m V = 50m3
If the last agent that sold the Beedalls a house earned a commission of $7,800 with a rate of 8%, the selling price of the home was $97,500. (T/F)
True $97,500 x 0.08 = $7,800
Front Foot
The front foot of a property (often referred to as frontage) is simply the linear portion that abuts a waterway, highway, or street. To determine the front-foot measurement, you simply measure the length or width of the property that abuts this area. So, if you had a 200 x 50-foot property, but it was the 50-foot portion of the property that abutted the road, you would have 50 front feet, or a 50-foot frontage. Keep in mind that, when given two dimensions for a piece of land, such as 400 feet by 500 feet, the first number is the frontage or width of the property.
What's the definition of area?
The size of a two-dimensional shape
Allegra has found a few properties in the area with a total of 150 front feet. If the value per front foot in this particular neighborhood is $1,600, which of the following statements is the most accurate regarding the front foot value?
The total front foot value would be $240,000.
Price Per Square Foot
This is found by taking the home's sale price and dividing it by the area. So, if we have our 800-square-foot rectangular building, and it sells for $75,000, that equates to $93.75 per square foot ($75,000/800 = $93.75).
Converting Fractions to Decimals
To convert a fraction to a decimal, divide the numerator (top number) by the denominator (bottom number).
Calculating linear footage
To determine the linear footage, add the lengths of the four sides together.
Cost per front foot
To figure the cost per front foot, take the price the property sold for and divide it by the frontage measurement.
What percentage of profit would the homeowner make? The homeowner paid $123,500 for the home, and then sold it for $150,000.
To find the rate of profit, take the profit amount (the sales price minus the original cost of the home) and divide it by the original cost of the home. 21% rate of profit $150,000 - $123,500= $26,500/$123,500= 0.214 = 21%
Commission Calculation
Total commission = Sales price x Commission rate 1. Since you've just sold the house, you know exactly what the sales price is. 2. And of course your commission rate is stated in your contract.
Which of the following statements is true regarding calculations with fractions?
When multiplying fractions, always multiply the numerator (top number) by the numerator (top number). Then multiply the denominator (bottom number) by the denominator (bottom number).