Unit 1: Real Estate Math

What is the total cost of a driveway that is 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 volume = length × width × height. 4 in ÷ 12 in = 0.333 ft. L × W × H: 15 ft × 40 ft × 0.333 ft = 199.8 cu. ft. ÷ 27 cu. ft. in a cubic yard = 7.4 cu. yd 7.4 cu. yd. × $60/cu. yd. = $444 concrete cost. length × width = area; 15 ft × 40 ft = 600 sq. ft. × $1.25/sq. ft. = $750 labor cost. The total cost of the driveway is the concrete cost plus the labor cost: $444 + 750 = $1,194.00 total cost.

What was the price per front foot for a 100-foot-by-125-foot lot that sold for $125,000?

$1,250. If two dimensions are given for a tract of land, *the first dimension is the frontage* if they are not labeled. The *second dimension is the measurement for the depth* of the lot. To find the sales price per front foot, divide the sales price by the front footage: $125,000 ÷ 100' = $1,250.

The broker receives $10,500 on a house that sold for $175,000. The rate of commission is

$10,500 ÷ $175,000 = 0.06 (6%)

With an outstanding loan balance of $12,000 at an interest rate of 9% and a *monthly* payment of $100, the amount of the second payment that goes toward the principal is

$12,000 × 0.09 = $1,080. $1,080 ÷ 12 (months) = $90. From the $100 payment, $90 goes toward interest and $10 goes toward the principal. $12,000 - $10 × 0.09 = $1,079.10. $1,079.10 ÷ 12 = $89.93 89.93 goes toward interest and $10.07 goes toward the principal.

A home is listed at $525,000 but is only appraised at $490,000. How much are annual property taxes, based on $3.00 per $100 valuation?

$14,700 (based on the appraised value of the property)

The seller owes $2,400 in taxes for the current year. With a May 28 closing date and using a calendar year, the seller will be debited how much? (Assume it is NOT a leap year.)

$2,400 ÷ 365 = $6.575 tax owed Then calculate the time to be debited from the seller Jan. = 31 + Feb. = 28 + Mar. = 31 + Apr. = 30 + May = 28. Total = 148 days $6.575 × 148 = $973.10. The seller will be debited (charged) $973.10 buyer will be credited $973.10 at closing

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 10.5% , and the last payment was paid on August 1. Prorations are to be done through the day of closing, using a statutory year.

$43,580 (total) × 10.5% (rate) × 1/12 (time) = $381.325 month's interest $381.325 ÷ 30 days in a statutory month = $12.711 day's interest August 1 through August 10 equals 10 days. $12.711 daily interest × 10 days = $127.11 interest proration

Eight years ago the homeowner purchased the property for $500,000. The market in that price range has basically been stagnant since then, and the owner now tells his sales agent (working on a 5.5% commission) he wants to sell the property and at least break even. How much should he list it for?

$527,500, the original cost plus commission

area of a triangle

(base × height) ÷ 2

profit

100% + % profit = % sales price sales price ÷ % sales price = original cost (total)

How many square feet are in a right triangle property that is 600 feet at the base and 400 feet on the right side?

120,000 square feet

The seller offers to take back a second mortgage of $25,000 at a simple interest rate of 4.5%. The loan is amortized over 10 years. How much is the buyer paying on the second?

25,000 ÷ 120 (12months x 10 years) =$208.33 per month 208.33 x 4.5% (added to each payment) = $9.37 208.55 + 9.37 = *$217.70*

If a lender agrees to an $80,000 loan at 9% for 15 years with 2 loan discount points, what amount will be charged at closing for the points?

80,000 × 0.02 (2 points equal 2%) = *$1,600 loan discount point* An $80,000 loan amount - $1,600 loan discount points = a $78,400 net loan.

Property owners on one street have petitioned the city to install paved alleys behind their homes. If Marcus has a rectangular lot that measures 90 feet by 140 feet, on what amount would he pay the special assessment?

90 feet; If two dimensions are given for a tract of land, the first dimension is the frontage if they are not labeled. The second dimension is the measurement for the depth of the lot: 140 feet. The special assessment would be based on the alley width, which would be the same as the street frontage since the lot is rectangular in shape.

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?

950

Discount Points

A fee charged by the lender at settlement that results in increasing the lender's effective yield on the money borrowed. One discount point equals one percent of the loan amount.

statutory year

A year composed of 12 months, each with 30 days, for a total of 360 days in a statutory year. Also known as a banker's year; contrast with a calendar year, which has 365 days, or 366 in a leap year.

To find the area, which of the following would you divide into identifiable parts, calculate the areas of those parts, and add them?

Irregular figure

accrued items.

Items for which the buyer is credited at the time of closing

prepaid items

On a closing statement, items that have been paid in advance by the seller, such as fuel costs and some real estate taxes, for which the seller must be reimbursed by the buyer.

Intrest

On loans for less than one full year, a monthly interest amount must be determined, then multiplied by the number of months: ($) x (%) x (x/12) = interest per x months $12,000 × 0.08 × 4/12 = $320.

Loan Discount

Prepaid interest; increasing the lender's yield on a loan without increasing the interest rate

percentage formula

T (value of the property or *total*) × % (*percent* or rate) = Pt (income to the broker or *part*). T × % = Pt.

A room measures 12 feet by 17 feet. At a cost of $55 per square yard, how much would it cost to install wall-to-wall carpeting?

The area of the room (12 feet × 17 feet) is 204 square feet which is divided by 9 (the number of square feet in a yard)totaling 22.66 square yards. 22.66 square yards times $55 per square yard is $1,246.

Current ad valorem property taxes owed by the seller that have NOT yet been billed at the time of closing are an example of

accrued items.

Prorated Taxes

annual taxes ÷ 12 months = taxes per month monthly taxes ÷ days = taxes per day taxes per month × x months = $ taxes per day × x days = $ (taxes per month × x months) + (taxes per day × x days) = Answer

cubic feet in a cubic yard

divide 27

feet to square yards

divide the area value by 9

linear measurement

measurement made on a line. The linear measure of a 4-foot square is 16 feet

Amortization

paying off a loan in equal installments; loan where the principal as well as the interest is payable in monthly or other periodic installments over the term of the loan.

In 2016, taxes on Don Mark's home were paid in full and amounted to $1,468. He sold the home to Chuck Harris and closed the sale on August 29, 2017. What was the prorated tax amount, using a statutory year and prorating through the day of closing?

per day: $1,468 taxes/year ÷ 360 days = $4.077 taxes/day. Calculate the period: January + February + March + April + May + June + July = 7 months × 30 days in a statutory month = 210 days + 29 days in August = 239 days in the *proration period*. Multiply the charge per day by the time period: $4.077/day × 239 days = $974.40 *tax proration*.

Volume

size in cubic units (cubic inches, etc.) of a three-dimensional figure such as a cube. volume = length × width × height

When computing prorations, Texas-promulgated sales contracts provide that

the seller owns the property on the day of the closing.

Interest on a mortgage

total monthly payment × %rate × 1/12 = interest for the month of closing interest for the month of closing ÷ 30 days = daily charge daily charge × days in month/year = $ prorated interest

A warehouse is 80 feet wide and 120 feet long with ceilings 14 feet high. If 1,200 square feet of floor surface has been partitioned off, floor to ceiling, for an office, how many cubic feet of space will be left in the warehouse?

volume: length × width × height. 80' × 120' = 9,600 sq. ft. 9,600 sq. ft. - 1,200 sq. ft. = 8,400 sq. ft. 8,400 sq. ft. × 14 ft = 117,600 cu. ft. left in the warehouse.

Prorations

Expenses, either prepaid or paid in arrears, that are divided or distributed between buyer and seller at the closing.

Price per front foot is

To find the sales price per front foot; divide the sales price by the front footage if they are not labeled *first dimension is the frontage second dimension is depth*

Under Texas law, who owns the property on the day of closing, and therefore is responsible for any expenses up to that day (or is owed any rents on a rental property up to that day)?

Under Texas law, the seller owns the property on the day of closing and is responsible for expenses and/or may collect rents.