Ch 17

sales price $950,000 Commission rate 7% Ralph's share 60% Ralph's commission?

$39,900

On occasion you will be asked to distinguish between area and volume. Area refers to surface area.For example, if you want to re-tile a 450 square-foot room in your house, and the tiles you will be using have flat dimensions of 1 foot by 1 foot, you will need 450 tiles to cover the surface area of the floor.

15 x 30 = 450 sq. ft

On the other hand, volume is three-dimensional. It has width, length, and height. Suppose you're using a storage unit that's 15 feet wide, 30 feet deep, and 8 feet high.Your unit is 450 square feet in area and 3,600 cubic feet in volume.It can hold 3,600 cube-shaped boxes with dimensions of 1 foot by 1 foot by 1 foot, if they are stacked to the ceiling.

15 x 30 x 8 = 3,600

Another alternative for determining the area of a triangle is to multiply the base times half the height. 1/2 x 75' = 37.5'

37.5' x 50' = 1,875

A broker arranged a 25-year lease on a commercial property for a rent of $60,000 per year. His commission was to be paid as follows: 7% of the rent for the first year, 5% of the rent for the next four years, 3% of the rent for the fifteen years following that, and 1% of the rent for each of the remaining years of the lease. How much total commission will the broker have received by the end of the 19th year of the lease? Select your answer below: A.$41,400 B.$42,000 C.$43,200 D.$43,800

A.$41,400 The amount of commission at each rate will need to be calculated separately. The first year's commission will be $4,200 ($60,000 × .07 = $4,200). The total for the following four years will be $12,000 ($60,000 × .05 × 4 = $12,000). Fourteen more years take the broker up to the end of the 19th year, for an additional $25,200 ($60,000 × .03 × 14 = $25,200). Add the amounts earned at the three different rates to calculate the total commission ($4,200 + $12,000 + $25,200 = $41,400)

Bill says to Amy, who just got her real estate salesperson's license, "Sell my property for $256,000 and I'll keep $240,000." Amy responds, "I'll sell your property for $256,000 and you'll keep $232,000." What percentage commission is the principal offering to pay? Select your answer below: A.6.25% B.7% C.8% D.9.375%

A.6.25% Bill is the principal in this transaction; to calculate the commission amount, subtract the seller's net from the sales price ($256,000 - $240,000 = $16,000). Then calculate the commission rate; you know the part and the whole, so use the formula P ÷ W = % ($16,000 ÷ $256,000 = .0625).

You can figure the problem out three different ways

A=1/2 BxH A = B x 1/2H A=(BxH) / 2

Now let's see what happens when you approach the same problem with different pieces of the puzzle. Maybe you know that the room contains 300 square feet and that it's 15 feet wide, but you need to find out how long it is. Once again, we'll look at the four steps in the next four frames.

Again, you'll use the formula for the area of a rectangle: A = W x L. This time L is unknown. Put the numbers from the problem into the formula.300 sq. ft. = 15' x L To calculate the answer, first rearrange the elements in the formula so that the unknown, L, appears by itself on one side of the equals sign. A ÷ W = L 300 sq. ft. ÷ 15' = L L = 20 feet

A tract of rural land is 395,340 square feet. The county owns a small corner of the land, measuring 30 feet by 110 feet. The private portion of the land sold for $10,500 per acre. What was the amount realized from the sale? Select your answer below: A.$10,500 B.$94,500 C.$96,090 D.$95,295

B.$94,500 First, determine the area of the county-owned portion of the land (30' × 110' = 3,300 square feet). Subtract that portion from the total area of the land (395,340 - 3,300 = 392,040 square feet). Convert that area into acres (392,040 square feet ÷ 43,560 square feet per acre = 9 acres). Finally, multiply the number of acres by $10,500 (9 acres × $10,500 = $94,500).

Now let's try an investment problem.Jackie invested some of her savings in a limited partnership and her earnings after one year totaled $2,875. That was a 6¼% return on her money. What was the amount of her investment? Try to solve the problem, and then advance to the next frame for the answer and explanation.

Big Number Percentage Small Number ? x 6 1/4 = $2,875 2 x 3 = 6

Although 2 times 3 equals 6 doesn't involve a percentage, you can use it as a model when solving the majority of percentage problems. As you can see, if the unknown component in the equation is the equivalent of 6, it's a multiplication problem. When the number in the middle (in the 3 position) is the unknown component, it's once again a division problem. If the unknown component in the equation is on the left (in the 2 position), it becomes a division problem. 6 divided by 3 equals 2.

Big Number Percentage or Rate Small Number $100,000 10% $10,000

Before moving on, we'll look at a couple more commission problems. Try this:Broker Smith earned a $12,950 commission on a sale of $185,000. What rate of commission did he charge?When you're done with your calculation, advance to the next frame for the answer and explanation.

Big Number percentage or Rate Small number 185,000 X ? = $12,950 2 x 3 = 6 12,950 divide by 185,000 = 7 %

A buyer purchased a rectangular lot, zoned for commercial use, for $387,200, at $8.80 per square foot. The property is 200 feet deep. What is the property's price per front foot? Select your answer below: A.$220 B.$880 C.$1,760 D.$1,936

C.$1,760 First, determine the square footage of the lot ($387,200 ÷ $8.80 per square foot = 44,000 square feet). Then divide the square footage by the depth to calculate the frontage (44,000 square feet ÷ 200 feet = 220 feet). Finally, divide the purchase price by the frontage to determine the price per front foot ($387,200 ÷ 220 feet = $1,760 per front foot).

A house sold for $575,000 and the listing broker received a 6% commission. The listing broker and selling broker agreed to split the commission 50/50. The selling salesperson received 70% of the selling office's commission. What amount did the selling salesperson receive? Select your answer below: A.$5,175 B.$8,625 C.$12,075 D.$16,905

C.$12,075 First, determine the amount of the commission ($575,000 × .06 = $34,500). Next, determine how much of the commission the selling broker receives ($34,500 × .5 = $17,250). Finally, determine how much of the commission the selling salesperson receives ($17,250 × .7 = $12,075).

A borrower took out a straight loan of $265,000 for 10 years at a 15% per annum interest rate. How much interest would he pay over the course of the loan? Select your answer below: A.$167,500 B.$176,666 C.$397,500 D.$795,000

C.$397,500 A straight note is one where the entire principal amount will be paid as a balloon payment at the end. Therefore, the interest is calculated on the entire principal amount each year. First, calculate each year's interest payment; you know the whole and the percentage, so use the formula W × % = P ($265,000 × .15 = $39,750). Multiply that figure by 10 years to calculate the total amount of interest ($39,750 × 10 = $397,500).

A buyer obtained a loan for 80% of the value of his property. The loan had a 9% interest rate, and the amount of interest paid in the first year totaled $40,500. What is the value of the property? Select your answer below: A.$450,000 B.$525,000 C.$562,500 D.$579,500

C.$562,500 First, calculate the loan amount; we know the part and the percentage, so we would use the formula P ÷ % = W ($40,500 ÷ .09 = $450,000). Next, calculate the actual value of the property; again, we know the part and the percentage, so use the formula P ÷ % = W ($450,000 ÷ .8 = $562,500).

The way to convert a fraction into a decimal is to divide the top number of the fraction (the numerator) by the bottom number of the fraction (the denominator).

Here's an example. The fraction one-fourth can be changed to a decimal number by dividing the numerator, which is 1, by the denominator, 4.

A farm's southern boundary runs for 7,920 feet along an east-west road. Its western boundary extends northward for 7,920 feet from the road. Its eastern boundary extends northward for 3,960 feet from the road. The northern boundary is an irrigation canal that connects the open sides. How many acres is this farm? Select your answer below: A.270 acres B.540 acres C.1,080 acres D.1,440 acres

C.1,080 acres Because one of the edges of the farm is a diagonal line, we'll need to break the farm down into component shapes to solve this problem. There should be a triangle that is 3,960 feet high and 7,920 feet wide, and below that should be a rectangle that is 3,960 feet high and 7,920 feet wide. First, calculate the area of the triangle (1/2 × 3,960 feet × 7,920 feet = 15,681,600 square feet). Next, calculate the area of the rectangle (3,960 feet × 7,920 feet = 31,363,200 square feet). Add the two areas together (15,681,600 square feet + 31,363,200 square feet = 47,044,800 square feet) and divide into acres (47,044,800 square feet ÷ 43,560 square feet per acre = 1,080 acres).

A two-story commercial building is 50 feet wide and 80 feet long. The first story is 16 feet high; the second story is 14 feet high. The replacement cost for the first story is $2.50 per cubic foot; the replacement cost for the second story is $2 per cubic foot. What would be the replacement cost for the entire building? Select your answer below: A.$18,000 B.$268,000 C.$270,000 D.$272,000

D.$272,000 Multiply the width by the length of the building to calculate each floor's square footage (80 feet × 50 feet = 4,000 square feet). For the first story, calculate the cubic footage (4,000 square feet × 16 feet = 64,000 cubic feet) and multiply that by $2.50 to calculate the first story's replacement cost (64,000 × $2.50 = $160,000). For the second story, calculate the cubic footage (4,000 square feet × 14 feet = 56,000 cubic feet) and multiply that by $2 to calculate the second story's replacement cost (56,000 × $2 = $112,000). Add the two replacement costs to calculate the total cost ($160,000 + $112,000 = $272,000).

A broker received a 6% commission on a sale of a property. The salesperson employed by the broker received 40% of the broker's share. The salesperson received $9,300. What was the selling price of the property? Select your answer below: A.$23,250 B.$62,000 C.$258,333 D.$387,500

D.$387,500 First, calculate the total amount of the broker's commission; you know the part and the percentage, so use the formula P ÷ % = W ($9,300 ÷ .4 = $23,250). Then calculate the purchase price; once again you know the part and the percentage, so use the formula P ÷ % = W ($23,250 ÷ .06 = $387,500).

Instead of calling for semiannual payments, a question might give you interest payments every 90 days.Those are quarterly payments in a banker's year. (For the sake of simplicity, a banker's year is 360 days, and every month has 30 days, including February.)The 90-day interest payment will be made four times annually.

For example, Sharon's mortgage loan agreement calls for interest payments in the amount of $3,162.50 every 90 days.If her loan balance is $230,000, what is the loan's interest rate?Advance to the next frame for the answer and explanation.

Gordon obtains a real estate loan that calls for semiannual interest-only payments in the amount of $16,250. If his interest rate is 6%, what is the amount of the loan? Advance to the next frame for the answer and explanation.

Step 1 take $16,250 x 2 = $32,500 annual interest. Step 2 take the interest of $32,500 divide that by the interest rate of 6% to get the loan amount of $541,667

What if your trying to find out commission on a 110 x 80 sq.foot of parcel of land that sells for $11 per sq. ft.

Step 1. take 110 x 80 to get the sq ft of area: 8,800 Step 2 take 8,800 sf. feet x $11 per sq. ft. the price would then be $96,800. Step 3 take sales price $96,800 x commission rate of 0.06 (6%) and you get $5,800 for your commission.

An acre is divided into four rectangular lots of equal size. Each lot is parallel to each other and 240 feet in depth. How wide is each lot? Select your answer below: A.45.375 feet B.87.8 feet C.181.5 feet D.726 feet

The correct answer is A One acre is equal to 43,560 square feet. If each of the four lots is of an equal size, you can divide 43,560 by 4 to find that each lot is 10,890 square feet. Since you know that each lot is 240 feet deep, divide 10,890 by 240 to find the width (10,890 ÷ 240 = 45.375).

Formula to determine the area

The formula for finding the area of a rectangle is: Area = Width x Length. So you would write: A=W x L Substitute the numbers from the problem (15 feet and 20 feet) into the formula. One dimension of the room is the width of the rectangle; the other is the length. ? = 15' x 20' Multiply W times L to find your answer. A equals 300, which means that the area of the room is 300 square feet. 15' x 20' = 300 square feet

Here's an example. International Bank made an interest-only real estate loan in the amount of $250,000 to Hyun. Hyun was required to make annual payments of $12,500 for five years, at which time the entire principal amount would be due and payable. What was Hyun's interest rate? Solve the problem if you can, and then advance to the next frame for the answer and explanation

The known components are the loan amount and the interest paid. 2 x 3 = 6 250,000 x 5% = 12,5000

Similarly, the percentage formula W × % = P can also be stated as P ÷ W = %, or P ÷ % = W.

The part divided by the whole equals the percentage. The part divided by the percentage equals the whole. Which version of the formula you use depends on which component is the unknown.

Let's consider another problem that calls for this formula. A landlord is charging a monthly rent of $20 per square foot for office space in this building.One of the offices measures 40 feet by 27 feet. How much is the total monthly rent for that office?

To calculate the area of an office to determine the cost per sq. ft the formula would be 27 x 40 = 1,080 - rent would be $21,600 pr month

Now let's learn how to find the area of a triangle. The formula is: Area = ½ Base × Height.

To see how the triangle formula works, take a rectangle and find the area (Area = Base × Height).Then imagine the rectangle cut in half diagonally, as shown to the left.You now have a triangle, and its area is half the area of the rectangle you started with.So the formula for the area of a triangle is ½ Base × Height.

area problems concern the measurement of a surface or space

area of a vacant lot or a room Area = width x length