Chapter 18: Real Estate Arithmetic

If the interest rate is 12% per year simple interest and the monthly interest payment is $115, what is the amount of the loan?

$11,500 $115 × 12 months = $1,380 ÷ .12 = $11,500

If a house sold for $290,000, which was 19% more than it originally cost, what was the original cost? (in whole dollars)

$243,697 If the house sold for 19% more than the original cost, it sold for the full amount of the original cost plus 19% of that price. Expressed as a percentage this would be 119% of the original price. Convert the percentage to a decimal by moving the decimal two places to the left. Then divide the converted percentage into the sale price of the property. ($290,000 / 1.19 = $243,697.47).

A house sold for $314,500. After closing costs of $1,400 and a broker's commission of 6%, the owner earned a profit of 9%. What was the original cost of the house? (Round your answer to the nearest whole dollar)

$269,936 The first step is to solve the unknown dollar amount of the commission. To do this, multiply the commission rate times the sale price of the property. ($314,500 x .06 = $18,870). Next, the total costs of sale must be calculated. Therefore, add the commission and closing cost figures together. ($18,870 + $1,400 = $20,270). The total costs of sale must next be subtracted from the gross sales price of the property. The result will be how much the homeowner actually realized on the sale. ($314,500 - $20,270 = $294,230). Once the amount of net sale proceeds is determined, then the final calculation to determine the original purchase price of the property can be made. This calculation is made by dividing the net sale proceeds by the profit percentage earned. First the 9% profit percentage must be converted to a decimal. A 9% profit means that the property sold for the full amount paid for the property plus 9% of that price. In other words, it sold for 109% of its original purchase price. As a decimal 109% is expressed as 1.09. The final calculation would then be $294,230 / 1.09 = $269,935.77. Therefore, the house originally cost $269,936.

A seller wants to sell her existing house and owes $290,000 on mortgage. At closing of the sale she will pay $1,400 in closing costs, plus a 6% brokerage fee. She wants to realize at least $55,000 for a down payment for the purchase price of a new house. What is the minimum amount she must sell her house for to net $55,000?

$368,510 To solve this problem, first determine the total amount which must be paid at closing. These items include the existing mortgage of $290,000, closing costs of $1,400, plus the amount of $55,000 that the seller wants to net on the sale. ($290,000 + $1,400 + $55,000 = $346,400). This is the total of the known items which must be realized or paid at closing. Once this number is known, the house will have to sell for a price which includes a 6% brokerage fee. This means that the $346,400 must equal 94% of the sale price of the property. The other 6% of the sale price is represented by the brokerage fee. Therefore, convert 94% to a decimal (.94) and divide into the $346,400. ($346,400 / .94 = $368,510.64). The house would have to sell for $368,510 in order for the owner to realize her objectives.

6 1/4 % expressed as a decimal rounded to four decimal places is:

0.0625 First express 1/4 as a decimal. 1/4 expressed as a decimal is .25. Next, attach the whole number, 6, to .25. The result is 6.25%. To express 6.25% as a decimal, the decimal point must be moved 2 places to the left, which becomes .0625.

A house 32 feet wide by 63 feet long has walls 9 inches thick. What is the square footage of the floor area inside the house? (round to the nearest whole number)

1,876 sq. ft. First calculate the amount of square footage of the walls. Since each side of the structure has a 9" wall, the total amount of wall must be subtracted from the perimeter of the structure. Therefore, the 9" wall must be doubled for each side and must be converted to feet. ( 9" + 9" = 18" or 1.5 feet) For the perimeter dimension of 32 feet, 1.5 feet will be subtracted ( 32' - 1.5' = 30.5 feet). For the perimeter dimension of 63 feet, 1.5 will be subtracted. (63' - 1.5' = 61.5 feet) This will give the net perimeter dimensions. The net perimeter dimensions will then be multiplied to calculate the interior square footage. (30.5' x 61.5' = 1,875.75 sq. ft., or 1,876 rounded up)

A city lot measures 100 feet x 250 feet. The city zoning ordinance specifies that maximum lot coverage is 40% of the lot. What is the maximum size for a building on this lot?

10,000 square feet 100' x 250' = 25,000 sq. ft. 40% of 25,000 sq. ft. is 10,000 sq. ft. (25,000 sq. ft x .40 = 10,000 sq. ft.)

.02 as a percent would be:

2% To convert to a percent, move the decimal point 2 places to the right, which turns .02 into 2%.

3/10 as a percent would be:

30% Divide 3 by 10. The result of dividing 3 by 10 is .30, and to convert to a percent move the decimal point 2 places to the right or 30%

How many acres are there in a triangular parcel of land that measures one mile wide by one and a half miles deep?

480 acres. An acre is a measurement of area, and a mile is a measurement of distance. We need to determine the area by calculating the two distance points. 1 mile = 5,280 feet1.5 miles = 7,920 feet The area of a triangle can be found by multiplying the base times the height and then divide by 2. 5,280 ft × 7,920 ft = 41,817,600 sq. ft ÷ 2 = 20,908,800 sq. ft. To determine the amount of acres, divide the total square feet by the amount of square feet in an acre, which is 43,560 square feet. 20,908,800 sq. ft ÷ 43,560 sq. ft. = 480 acres

Nate borrowed $62,000 at 9.4% interest per year. If he owed a total of $910.90 interest when he repaid the loan, how many days did he keep the money for? (use a 365 day calendar year to calculate)

57 days. Calculate the annual interest by multiplying the amount of the loan by the annual interest. ($62,000 x .094 = $5,828). Next, divide the total annual interest by the number of days in a year to determine the daily dollar interest charge. ($5,828 / 365 = 15.967%) Then determine the number of days he paid interest by dividing the actual amount of interest paid by the daily interest figure. ($910.90 / 15.967% = 57 days)

The owner of a duplex has a scheduled gross income of $3,000 per month. The vacancy rate is 5% and expenses average $19,300 per year. If a buyer purchases the property for $241,500, and the income and expenses stay the same, what will the buyer's rate of return be?

6% First determine the net income of the duplex on an annual basis. To do this first calculate the amount of the gross annual rents. ($3,000 x 12 = $36,000) Since the vacancy rate is 5%, subtract 5% vacancy from the gross rents. This can be accomplished in one of two ways. First method: Multiply the gross rents times the vacancy rate and subtract this number from the annual gross rents to arrive at the gross rents less vacancy number. ( $36,000 x .05 = $1,800) ( $36,000 - $1,800 = $34,200) Second method: The remaining balance of gross rents after subtracting the vacancy rate would be 95% of gross rents. Therefore multiply the gross rent figure times 95% to arrive at the gross rents less vacancy rate figure. ( $36,000 x .95 = $34,200) Next determine the net operating income. To do this take the gross rent figure less the vacancy factor and subtract from this number the annual expenses of $19,300. ($34,200 - $19,300 = $14,900) Divide the net income by the purchase price of the duplex to determine the rate of return. ($14,900 / $241,500 = .06) Then convert the decimal to a percentage by moving the decimal two places to the right. (6.0%)

A developer is selling lots measuring 55' x 125'. Each lot contains how many square feet?

6,875 sq. ft Multiply the length times the width. The product of this equation is the total area expressed in square feet. (55' x 125' = 6,875 sq. ft.)

What is the number of cubic feet in a brick wall that measures 2 feet deep, 6 feet high, and 55 feet long?

660 cu. ft. The formula to find an area of a cube is multiply the length times the width times the depth. (2' x 6' x 55' = 660 cubic feet)

Jeff buys a house on a rectangular lot that measures 150 feet along the street. The lot has a total of 12,000 square feet. How deep is the lot?

80 ft. Divide the known side of the rectangle (150 feet) into the total areas of the rectangle (12,000' / 150' = 80')