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WorksheetsRE Math Part 1
Total questions: 71
Worksheet time: 18hrs 15mins
Percent problems contain what three elements?
Percentage, Total, Part
Percentage, Whole, Base
Percentage, Part, Rate
Percentage, Base, Total
Which of the following three are normally expressed as rates?
Mortgage Transfers, Capitalization, Down Payment
Rental Payments, Insurance Deductions, Transfer Premiums
Property taxes, Insurance Premiums, Transfer taxes
If PART is unknown (a)
If PART is known (a)
When you divide, always enter the (a) into the calculator first.
0.10 means:
1%
10%
1/10
1/100
0.01 means:
1%
10%
1/10
1/100
.001 means
1%
.01%
.1%
1/10,000
1/1000
.0001 means:
1%
.01%
.1%
1/10,000
1/1000
How do you convert a fraction to a decimal fraction?
By dividing the numerator by the denominator.
By dividing the denominator by the numerator.
By multiplying the numerator by the denominator.
By multiplying the denominator by the numerator.
Convert ¾ to the equivalent decimal fraction: (a)
Convert ¼ to the equivalent decimal fraction: (a)
Another way to solve real estate percentage problems is to visualize a 'T', The 'T' will represent the relationship between PART, TOTAL, and RATE. This method is known as the T-Bar Method.
Using the T-Bar method, insert the known figures in the correct places inside the circle. Multiply if the line between the figures is vertical to get the unknown, and divide if the line between the figures is horizontal to get the unknown. If dividing, always input PART first into the calculator.
a
b
c
d
Another way to solve real estate percentage problems is to visualize a 'T', The 'T' will represent the relationship between PART, TOTAL, and RATE. This method is known as the T-Bar Method.
Using the T-Bar method, insert the known figures in the correct places inside the circle. Multiply if the line between the figures is vertical to get the unknown, and divide if the line between the figures is horizontal to get the unknown. If dividing, always input PART first into the calculator.
Do you understand?
To convert a percentage to a decimal, move the decimal two places
to the left and drop the percent sign. For example, convert the following into its decimal equivalent: 60%
(a)
To convert a percentage to a decimal, move the decimal two places
to the left and drop the percent sign. For example, convert the following into its decimal equivalent: 175%
(a)
To change a percentage to a fraction, place the percentage over 100. For example, 50% = 50/100. The fractions may then be reduced to make it easier to work the problem.
To reduce a fraction, determine the LARGEST number by which BOTH the numerator and the denominator can be EVENLY divided. For example, 50/100 ÷ 50 = 1/2 (the numerator & denominator by 50, the largest number they BOTH can be divided by)
Do you understand?
Percent x Whole = (a)
Percentage problems contain three elements: percentage, total, and part. To determine a specific percentage of a whole, multiply the percentage by the whole: percent × whole = part (Example: 5% × 200 = 10). Remember, to convert a percentage to a decimal, divide by 100. So 25% is 25/100, or 0.25.
For example, a broker is to receive a 7% commission on the sale of a $100,000 house. What is the broker’s commission?
(a)
This formula is used in calculating mortgage loan interests, broker’s commissions, loan origination fees, discount points, amount of earnest money deposits, and income on capital investments.
A variation of the percentage formula is used to find the total amount when the part and percentage are known: total = part ÷ percent. Remember, to convert a percentage to a decimal, divide by 100. So 25% is 25/100, or 0.25.
A realty company received a $4,500 commission (part) for the sale of a house. The broker’s commission was 6% (percent) of the total sales price. What was the TOTAL sales price of this house?
(a)
This formula is used in computing the total mortgage loan principal still due if the monthly payment and interest rate are known. It is also used to calculate the total sales price when the amount and percentage of the commission are known, and the market value of the property if the assessed value and the ratio (percentage) of assessed value to market value are known.
For example, a seller clears $160,200 from the sale of her property after paying a 10% commission.
How much did the property sell for?
Note: Taking 10% (the commission) of $160,200 is an incorrect approach to this type of problem because the commission was based not on the seller’s net but on the FULL price,
which would be the TOTAL (an unknown sales figure); $160,200 represents 90% of the sales price.
(a)
Property taxes, transfer taxes, and insurance premiums are usually expressed as rates. A rate is
the cost expressed as the amount of cost per unit. For example, tax might be computed at the
rate of $5 per $100 assessed value. This formula may be used to find the tax rate when taxes and assessed value are known or the commission rate if sales price and commission amount are known. The formula for computing rates is: value ÷ unit × rate per unit = total
For example, a house has been assessed at $90,000 and is taxed at an annual rate of $2.50 per $100 assessed valuation. What is the yearly tax?
Helpful Hint: Any problem that has either a rate or a percentage as one of its elements can be solved using the following formula: part = rate × base
(a)
To solve for an unknown element in the circle, multiply sideways for the top number; divide the top number by one of the bottom ones for the other bottom number. When figuring out what to put where in the circle, it is always easiest to first identify R, which is always a percentage or identified by the word rate. Once this is done, decide whether the missing number is going to be the larger or smaller of the two remaining sums: in most cases, if it is bigger, it is the base and goes on the bottom; if it is smaller, it is part and goes on top.
An exception to this rule is in the calculation of depreciation; in that case, remember that the base is the starting value, and that amount is higher than the depreciated final dollar amount. A second exception to this rule is in the calculation of profit; in that case, remember that the base is the original amount invested, and that amount is lower than the final part.
A home was purchased a year ago for $172,300. Property in the neighborhood is said to
be increasing in value at a rate of 3% annually. What is the current market value of the
real estate?
(a)
A home was purchased a year ago for $98,500. Property in the neighborhood is said to be decreasing in value at a rate of 5% annually. What is the current market value of the real estate?
(a)
A home was purchased a year ago for $98,500. Property in the neighborhood is said to be INCREASING in value at a rate of 5% annually. What is the current market value of the real estate?
(a)
The IRV formula, presented in Unit 16, is basic to investment problems. It is really the same as the PRB formula: income = rate × value
An investor wants to make an offer on an apartment building whose annual income is
$225,000 after deducting for expenses. To go through with the purchase, the investor
insists on a 10% capitalization rate. What is the most she would pay for the property?
(a)
Important Point: In any IRV or PRB problem, the rate (interest, appreciation, etc.) is usually an annual rate, and income is annual income. If monthly income is given, multiply it by 12 before using it in the circle.
A woman owns a four-family home. Rents are $525, $575, $600, and $650 a month.
Her operating expenses average $375 a month. If investors expect a cap rate of 11%,
what should she expect to receive for the property.
Remember: Income = Rate × Value
(a)
To compute the area of a square or rectangular parcel, use the formula: width × length = area. For example, the area of a rectangular lot that measures 100 ft wide by 200 ft deep is: 100' × 200' = 20,000 sq ft.
The first figure given always represents front feet; a lot described as “80' × 150'” is 80 ft across and 150 ft deep. Area is always expressed in square units. To compute the amount of surface in a triangular-shaped area, use the formula: area = base × height ÷ 2.
The base of a triangle is the bottom, on which the triangle rests. The height is an imaginary straight line extending from the point of the uppermost angle straight down to the base (see image).
Question: A triangle’s base is 50 ft, and its height is 30 ft. What is its area?
(a)
To compute the area of an irregular room or parcel of land, divide the shape into regular rectangles, squares, or triangles. Next, compute the area of each regular figure and add the areas together to obtain the total area.
(a)
The cubic capacity of an enclosed space is expressed as volume, which is used to describe the amount of space in any three-dimensional area, for example, an ice cube, or in measuring the interior airspace of a room to determine what capacity heating unit is required. The formula for computing cubic or rectangular volume is: volume = length × width × height. Volume is always expressed in cubic units.
Question: The bedroom of a house is 12 feet long, 8 feet wide, and has a ceiling height of 8 feet. How many cubic feet does the room enclose?
(a)
A rod is ___________
16½ feet
17½ feet
15½ feet
16 feet
15 feet
A chain is ________
66 ft
100 links
120 links
60 ft
How many feet are in a mile?
10,000
5,280
1,000
5,000
How many square feet are in an acre?
34,650
43,750
45,056
43,560
A section of land (in the government survey method) is one square mile and contains _________ acres
640
650
660
670
a quarter section contains _________ acres
140
150
160
170
180
A quarter of a quarter section contains ______ acres
30
40
50
60
70
A salesperson works on a 50/50 commission split with her broker. If she lists a house at $146,000 for 6% commission and sells it for $144,000, how much does the salesperson receive?
$8,760
4,380
$8,340
$4,320
The broker’s commission on a sale was $14,100, which was 6% of the sales price. What was the sales price?
$235,000.00
$154,255.31
$846,000.00
$234,500.00
Happy Valley Realty recently sold a home for $79,500. The broker charged the sellers a 6½% commission and paid 30% of that amount to the listing salesperson and 25% to the selling salesperson. What amount of commission did the listing salesperson receive from the sale of this home?
$5,167.50
$1,550.25
$3,617.25
$1,291.87
A salesperson receives a monthly salary of $500 plus 3% commission on all of his listings that sell and 2.5% on all his sales. None of the listings that the salesperson took sold last month, but he received $3,675 in salary and commission. What was the value of the property sold by this salesperson?
$147,000
$127,000
$122,500
$105,833
The home on Grove Street is valued at $95,000. Property in the area is assessed at 60% of its value and the local tax rate is $2.85 per hundred. What is the amount of the monthly taxes for this home?
$1,111.50
$926.30
$111.15
$135.38
A house is valued at $98,000. It is to be insured for 80% of its cost. Insurance costs $0.60 per $100. What is the annual insurance premium?
$470.40
$47.04
$588.00
$58.80
Four investors pooled their savings and purchased a vacation home for $125,000. If one person invested $30,000 and two others each contributed $35,000, what percentage of ownership was left for the fourth investor?
20%
24%
28%
30%
An investor bought a building lot for $45,000 and sold it two years later for a 15% profit. How much did it sell for?
$51,750
$52,941
$54,450
$58,500
A house was listed for $249,999. The buyers offered $225,000, the sellers countered with $235,000, which the buyers accepted. The buyers are making a down payment of 20% and financing the est at 5.25% for 30 years. How
much will their monthly principal and interest payment be?
$1,039.64
$1,106.99
$1,244.50
$1,299.50
The landlord leases the 13 apartments in the Overton Arms for a total monthly rental of $4,500. If this figure represents an 8% annual return on the landlord’s investment, what was the original cost of the property?
$675,000
$450,000
$54,000
$56,250
The seller received a net amount of $168,000 from the sale of his house after paying $1,200 in legal and other fees and 6% sales commission. What was the selling price of the house?
$180,000
$178,080
$179,200
$179,280
The sellers receive two offers for their property at the same time. The first buyers offer $95,000 all cash. The second buyers offer $100,000 subject to obtaining a conventional mortgage loan with 20% down payment and ask the sellers to pay three points to their lending institution. The sellers decide to accept the all-cash offer. If they had accepted the second buyers’ offer instead, the would have received
$2,600 more at closing.
$2,000 more at closing.
$2,400 less at closing.
$3,000 less at closing.
An FHA loan on a house priced between $50,000 and $100,000 requires a loan-to-value ratio of no more than 97.76%. If the buyer is financing the purchase of a $95,000 house with an FHA loan, how much cash must she have for a down payment?
$976.60
$2,128
$2,240
$9,766
A lending institution allows its borrowers to spend 25% of their income for housing expenses. What is the maximum monthly payment allowed for a
family with an annual income of $37,000 and no
other debts?
$9,250
$770.83
$925
None of the above
A man’s monthly mortgage payment for principal and interest is $628.12. His property taxes are $1,800 a year, and his annual insurance premium is $365. What is his total monthly payment of PITI (principal, interest, taxes, and insurance)?
$808.54
$1,921.24
$778.12
None of the above
A first-time buyer is purchasing a home for $129,500. His lender requires a 20% down payment and 2 points at closing. In addition, the buyer has $750 in closing costs. What is the total amount he needs to close?
$25,900
$28,490
$28,722
$29,240
The buyers offer to buy a house for $120,000 and seek a fixed-rate loan of $90,000 for 25 years. One lender offers them a 10% loan with no points and monthly payments of $817.85. A second lender requires two points for a 9.5% loan, with monthly payments of $786.35. If the buyers decide to pay the points and take the lower-interest loan, how long will it take before the savings on their lower payments have made up for that extra cost at
closing?
Two years, eight months
Three years, two months
Four years, nine months
Seven years, four months
A father is curious to know how much money his son and daughter-in-law still owe on their mortgage loan. He knows that the interest portion of their last monthly payment was $391.42. If the owners are paying interest at the rate of 7%, what was the outstanding balance of their loan before that last payment was made?
$46,970.50
$67,100.57
$135,640.02
$273,994.00
A 30-year fixed-rate amortized mortgage for $100,000 at 7% interest requires monthly payments of $665.30. What is the total amount of interest paid on this loan during the life of the mortgage?
$139,508
$239,508
$258,106
$665,300
In a sale of residential property, real estate taxes for the current year amounted to $975 and have already been paid by the seller. The sale is to be closed on October 27. What is the amount of real estate proration to be credited to the seller?
$173.33
$162.50
$798.96
$83.96
The buyer is assuming the seller’s mortgage with an interest rate of 5%. The unpaid balance after the most recent payment was $161,550. The seller made the payment due on September 1, and the sale is to be closed on September 23. What is the amount of mortgage interest proration to be credited to the
buyer at the closing?
$113.08
$493.64
$807.75
None, the buyer owes the seller.
If the frontage of a half-acre lot is 75 feet, how deep is it?
189 feet
272 feet
290 feet
346 feet
A rectangular lot measures 60 feet wide and has an area of 1,200 square yards. What is the length of the lot?
20 feet
180 feet
20 yards
90 yards
A five-acre lot has front footage of 300 feet. How long is it?
145.2 feet
726 feet
88 feet
160 feet
A buyer signed an agreement to purchase a condominium apartment. The contract stipulates that the sellers replace the damaged bedroom carpet. The carpet the buyer has chosen costs $16.95 per square yard, plus $2.50 per square yard for installation. If the bedroom dimensions are as illustrated, how much will the sellers have to pay for the job?
$271.74
$189.20
$277.16
$2,774.46
A lot measuring 120' × 200' is selling for $300 a front foot. What is its price?
$720,000
$60,000
$36,000
$800,000
A 100-acre farm is divided into house lots. The streets require one-eighth of the whole farm, and there are 140 lots. How many square feet are there in each lot?
35,004
31,114
27,225
43,560
If building requirements call for a 25' setback for a building, 10' on each side, and 15' from the rear property line, what is the buildable area in square feet for a lot that is 150' × 200'?
3,000
18,000
20,800
30,000
The property owner intends to put up a fence between his lot and his neighbor’s. The fencing comes in six-foot sections. For a fence that is 120 feet long, how many fence posts are required?
19
20
21
22
23
When a residence has proved difficult to sell, the salesperson suggests it might sell faster if they enclose a portion of the backyard with a privacy fence. If the area to be enclosed is as illustrated, how much would the fence cost, at $6.95 per linear foot?
$1,911.25
$1,654.10
$1,615.88
$955.63
The buyers agree to a purchase price of $200,000 and make a 5% earnest money deposit. Ten days later, the buyers give an additional $20,000 toward the purchase price. What is their balance due in cash at closing if they are securing an 80% loan-to-value mortgage?
$5,000
$10,000
$20,000
$25,000
A property closes on June 7. The annual taxes of $775 and a special assessment of $86 for the current calendar year were paid in full on January 1. If these payments are prorated, what amount is returned to the seller?
373
416
488
508
A percentage lease calls for $460 a month rent, plus 4.5% of the annual gross over $100,000. If the business paid $7,780 last year, what was the gross income of the business?
$110,170
$150,222
$262,207
$272,889
An investor buys a small rental property on January 1 for $300,000, with the land accounting for 20% of its value. The IRS allows him to depreciate the building over a period of 27½ years. How much can the investor charge on his tax return as an expense?
$6,000
$8,727.27
$10,909.09
$24,000
