Finance Unit 5 Math
A property was worth $ 500,000. It was assessed at 25% of its value. The tax rate is 2% of the assessed value. Taxes would be:
$ 2,500.00 $500,000. X .25 = $125,000. x .02 = $2,500
An apartment building is valued at $1,200,000, using a cap rate of 11%. If the cap rate had been 9%, what would be the value?
$1,466,666.66 I/R = V, I/V = R, R x V = I First determine the NOI. .11 x $1,200,000 = $132,000 (NOI) $132,000 / .09 = $1,466,666.66
The buyer agreed to pay 55% of the closing costs, and the seller agreed to pay the other 45%. Closing costs were $500 for title insurance and $366 for other costs. How much more in dollars did the buyer pay than the seller. Round to nearest dollar.
$87
Sandy bought a note for $6,750 that was discounted by 25%. What was the original balance on the note?
$9,000.00 You are looking for the original balance that was discounted. This would mean you need to divide the current amount paid by the part. 6750/.75 (100 - 25 = 75)
Your client has just sold her apartment building for $1,250,000. She is happy with the 35% profit over her initial purchase price. Rounded to the nearest dollar, what did she pay for the property initially?
$925,926 On these the profit needs to be added to the total sale price in order to determine the initial price. 1 + .35 = 1.35 (with 1 representing the original price), 1250000 / 1.35 = 925,925.926
John and Joann own a lot that is 75 feet wide and 150 feet deep. The front setback is 25 feet, the rear setback is 20 feet and the side setbacks are 15 feet. What is the largest possible home that can be built on the lot?
4,725 square feet 150 - 25 - 20 = 105 feet deep; 75-15-15 = 45 feet wide; 105 * 45 = 4,725
A property valued at $250,000 earns $950 per month. What is the annual percentage return?
4.6%
The average of 73.25%+23.95% +62.34%+ 17.89% +65.45% is:
48.576%
Your listing is at $125,000, with a 6% commission. The offer of $115,000 is acceptable to your client if you pay the current owners' association fees of $250. What is the percentage commission you have accepted rounded to the nearest 1/10 of a percent?
5.8%
A next monthly interest payment on a loan with a principal balance of $19,531 is $109.86. What is the interest rate on the loan?
6.75% 19531 x ? = 1318.32 (109.86 x12) $1,318.32 / $19,531 = .0675
A property owner needs to replace his driveway. If the driveway is 25 feet long, 19 feet wide, and 6 inches thick, how many cubic yards of concrete will be needed. (You cannot order a partial cubic yard.)
9 25 * 19 * .5 [6" = 1/2'] = 237.5 cu ft; there are 27 cu ft in 1 cu yd so 237.5 / 27 = 8.8 rounded up to 9 cu yds
A 40 x 45 ft. house is on a 1/2-acre of land. What approximate percentage is NOT taken up by the house?
92% Study Hint: 1/2 acre = 21,780 sq. ft.: 40 ft. * 45 ft. = 1,800 sq. ft.: 1,800 / 21,780 = .083 = 8% house: Therefore, 92% is remaining land
Ad valorem taxes
Are taxes levied on real estate that are based on value. Ad valorem taxes are taxes levied on real estate that are based on value.
A room in a home measures 13' x 34'. If it cost $30 a square yard to carpet the room, what would be the total cost?
$1,473.33 (Total square feet / 9) * Cost per square yard = (442 / 9 ) * 30 = $1,473.33
You have just purchased an apartment complex that generates rent payments of $25,675/month. Annual expenses are $25,750 for taxes, $52,500 for utilities, $16,000 for maintenance, and $30,000 for management. Using a capitalization rate of 11.5 percent, what is the value of the building to the nearest dollar?
$1,598,696.00 NOI = $ 25,675 x 12 = $308,100 (annual rent) - 25,750, 52,500, 16,000, 30,000 = 183,850/ .115 =$ 1,598,696
As a manager you leased a store to a client for 3 years. First year's rent is $1,100 per month. The rent increases 11% each year. Your commission is 6% the first year, 5% the second year and 2% the last year. What is your total commission?
$1,849.87 What is your total commission? YR 1. 1100 x 12 = 13200 annual rent x .06 = $792 YR 2. 13200 x .11 = 1452 + 13200 = 14652 annual rent x.05 = $732.6 YR 3. 14652 x .11 = 1611.72 + 14652 = 16263.72 annual rent x .02 = 325.27 1849.87 total
$2,500.00 was earned in 3 months on an investment yielding 10%. The principal was?
$100,000 ? x .10 = $10,000
Of the following transactions, the highest net proceeds to the seller will be a sales price of:
$110,000, 7% commission & $1,280 closing costs
John needs to receive $122,200 from the sale of his home after paying a 6% commission in order to payoff his loan. What must the minimum list price be?
$130,000
John needs to receive $122,200 from the sale of his home after paying a 6% commission in order to payoff his loan. What must the minimum list price be?
$130,000 $122,200 / .94 = $130,000
Your client purchases 45 acres and divides the tract into 7.5-acre lots. Each lot sells for $37,500. Your commission is 7.5%. If you both list and sell all lots, what is your total commission?
$16,875 45 acres / 7.5 acres = 6 lots, 6 x 37,500 = 225,000 x .075 = $16, 876
Monthly rent for a storage warehouse is $1.15 per cubic yard. The warehouse is 24 feet by 150 feet, and is 10 feet high. What is the annual rent?
$18,399.96 24 x 150 x 10 = 36,000 cubic feet. 36,000 divided by 27 (a cubic yard has 27 cubic feet) = 1333.33 cubic yards. 1333.33 cubic yards x $1.15 = $1,533.33/month. $1,533.33 x 12 months = $18,399.96
Monthly rent for a storage warehouse is $1.15 per cubic yard. The warehouse is 24 feet by 150 feet, and is 10 feet high. What is the annual rent?
$18,399.96 Cubic Yards are 3x3x3 feet, 24 feet by 150 feet x 10 feet high = 36,000 cubic feet 36,000 is divided by 27 because a cubic yard has 27 cubic feet (3x3x3) = 1333.33 cubic yards 1333.33 x $1.15 per yard = $1,533.33 per month in rent $1,533.33 x 12 months = $18,399.96 in annual rent.
You have just inherited a building that is leased at $4,750/month. Annual expenses are $5,600 for taxes, $12,500 for utilities, $6,000 for maintenance, and $3,300 for management. Using a capitalization rate of 9.5 percent, what is the value of the building to the nearest dollar?
$180,000 1500 x 12 / .1 = $180,000
The loan is 80% of the property's value. The interest rate is 8.5%, and the total interest earned during the first year of the loan was $13,260. With this information, what is the property's value?
$195,000 ? x .085 = 13,260 = $156,000 / .8 = $195,000
Your client has agreed to purchase a ranch for $350,000, with $50,000 down and interest only payments at 11% per year, with the balance due in 6 years. How much interest will your client have paid at the end of this agreement?
$198,000 300000 x .11 = 33000 x 6 = $198,000
The lot is 90 feet by 110 feet. The fence is to be 6 feet tall. Cost for the fence is $3.00 per linear foot, plus $.40 per square foot for labor. What is the total cost of the fence?
$2,160 90 + 90 + 110 + 110 = 400 linear feet. 400 linear feet x $3 = $1200. 6 feet x 400 feet = 2400. 2400 x .4 (sq feet for labor) = $960. 1200 + 960 = 2160
On a $350,000 30-year mortgage at 8 percent, the monthly PI payment is $2,568.18. On the first payment, how much is applied to reduce the principal?
$234.85 $350,000 x .08/ 12 = monthly interest payment $2333.33 $2568.18 - $2333.33 = $234.85
The property returns net cash flow to your client of $2,500 per month. The local market is requiring at least a 12.5% return on this type of investment. To meet this requirement, at what price will you list the property?
$240,000 ? x .125 = $30,000 (2500 x 12) = $240,000
A broker lists a 2,000 square foot living area home. The owner insists that the list price reflect $95.00 per square foot of living area, plus $54,000.00 for the site, and include a 5% sales commission. The broker should list the property for:
$256,842.00 $2000 x 95 = 190,000 + 54,000 = 244,000/ .95 = $256,842 Commission as a Ratio: T-Bar Method List price = 100% minus 5% Commission = 95% net to seller. Remember the value of the home and land is 95% of the amount it must sell for to yield a 5% commission. The commission is NOT based on the $244,000.
Janet purchased a property several years ago for $250,000 and has decided to sell it. The sales commission and other closing costs will be 10% of the sales price. How much must the home have appreciated in value for Janet to break even?
$27,778 $250,000 / 90% = $27,778
There are 5 units in the complex, and expenses are shared in proportion to the original purchase price. The units sold at $107,500, $175,000, $195,000, $158,500 and 165,500. If the common area annual costs come to $26,900, what is the share for the least expensive unit, rounded to the nearest dollar?
$3,607
Your client has agreed to purchase a ranch for $500,000, with $150,000 down and interest only payments at 9.5% per year, with the balance due in 10 years. How much interest will your client have paid at the end of this agreement?
$332,500 $350,000 x .095 x 10 = $332,500
Your client has found a new office building. The listing broker tells him it has an annual gross income of $125,000. The net income is 35% of gross. You client wants a 12% return on the purchase price. Rounded up to the nearest 100 dollars, the maximum price your client would be willing to pay is:
$364,600 125,000 x .35 = 43,750 43750/.12 = $364,583.33
The lot is 150 feet by 90 feet. The fence is to be 8 feet tall. cost for the fence is $4.50 per linear foot, plus $.75 per square foot for labor. What is the total cost of the fence?
$5,040 90 + 90 + 150 + 150 = 480 linear feet 480 x $4.50 = $2,160 8 feet x 480 feet = 3,840 square feet. 3,840 square feet x $.75 = $2,880 $2,160 + $2,880= $5,040
If John receives $1,000 per quarter from an investment that earns 8 percent interest, how much is John's investment?
$50,000 ? x .08 = $4000
If the interest on a loan at 11 percent per annum for 7 months was $3,500, what was the amount of the loan?
$54,545.45 7/12 * Total Interest = 3,500: Loan Amount = [(3500 * 12)/ 7] / 11%: 3,500 * 12 = 42,000: 42,000 / 7 = 6,000: 6,000 / .11= 54,545.45
Dennis purchased 4.5 acres of land for $78,400. Jim, the neighbor , wants to purchase part of Dennis's land measuring 150 feet by 100 feet. What should this strip cost the adjoining owner if Dennis sells it for the same price per square foot he originally paid for it?
$6,000 43,560 (feet in an acre) x 4.5 = 196,020 square feet. $78,400 / 196,020 = .4 per foot (price Dennis paid per foot). 100 x 150 = 15,000 square feet (part of the land that Jim wants to buy) $.40 x 15,000 square feet = $6,000
A 40-acre commercial building site sold for $3,500 per acre. The lot is 900 feet deep. What is the price per front foot?
$72.31 The site sold for 40 * $3,500 = $140,000; The dimensions are 900 x 1,936 (43,560 x 40 = 1,742,400 sq ft. / 900 = 1,936); $140,000 / 1,936 = $72.31 per front foot
A broker gets 6 percent of the first $150,000 and 2 percent of any amount over $150,000. What would be the loss to the broker if a house listed for $190,000 has to be reduced by 20 percent?
$760
In 2004 the rent at a 10-unit apartment building was $650 a month per unit. The management company was paid a fee of 10% of gross rent collected plus a bonus of one- half of one month's rent each time a new tenant signed a one-year lease. One apartment remained vacant for three months and four new leases were signed. How much did the property management company earn last year?
$8,905 9 * $650 * 12 + $650 * 9 = 76,050: 76,050 * .10 (10%) = $7,605: 4 * $325 = $1,300 bonus: $7,605 + $1,300 = $8,905
A one-acre parcel was listed for sale based on a price of $1.95 per square foot. What was the asking price of the parcel?
$84,942 43,560 x 1.95 = $84,942
A rectangular parcel contains 9 acres. The side on the main highway is 250 feet wide. To the nearest foot, how deep is the parcel?
1,568 feet
A rectangular parcel of land is 50 acres. One side is 1,000 feet and faces County Line Road. How deep is the parcel?
1. 2,178 feet 50 * 43,560 = 2,178,000; 2,178,000 / 1000 = 2,178
A property valued at $250,000 earns $950 per month. What is the annual percentage return?
1. 4.6% 950 * 12 = 11,400: 11,400 / 250,000 = .0456
How much concrete will be needed for a parking area that is 25 feet wide, 40 feet long, and 3 ½ inches high?
10.80 cubic yards First convert 3 ½ inches to feet. 3.5 / 12 = .291667 Then 25 * 40 * .291667 = 291.67 cubic feet or 291.67 / 27 =10.80 cubic yards.
The driveway for your client's home must be repaired before you list the house. It is 45 feet long, 20 feet wide, and the concrete will be poured to a depth of 4 inches. To the nearest yard (be sure to round up whenever estimating concrete), how many cubic yards of concrete are needed?
12 cubic yards 45 x 20 x .333 / 27 = 11.1 Round up.
What percentage profit is made on a sale, if the selling price is $225,000 and the purchase price is $190,000?
18% $225,000 - $190,000 = $35,000 profit: $35,000 / $190,000 = .18 or 18% profit
A triangular lot has 750 feet on one side of a 90-degree angle and 500 feet on the other side of the angle. How large is the property?
187,500 square feet A right triangle is ½ of a rectangle. 750' x 500' = 375,000 sq. ft. divided by 2 = 187,500 sq. ft.
Marc bought 9 adjacent unimproved lots for $8,500 each and plans to divide them into 14 lots and sell them for $7,000 each. He paid $5,200 to install water and sewer lines and miscellaneous improvements. What will Marc's profit be?
20% Marc spent: $8500 x 9 = 76,500 + $5,200 = $81700 He plans to profit: 14 x $7000 = $98,000 - $81700 = $16300 16300/ 81700 = .20
A house appreciates each year by 5 percent. This is equivalent to what percent for five years?
28% P (1.05) x (1.05) x (1.05) x (1.05) x (1.05) = P(1.276) = 28%
A salesperson received $3,000 for selling a house. This was 40 percent of the total commission on the sale of a $200,000 house. What was the commission rate on the sale?
3.75% $200,000 x ? = $7500
A house sold for $295,000 and the rate of commission was 5.6 percent. If the salesperson got $4,956, what percentage of the commission did the salesperson get?
30%
The site your client has selected to build her new warehouse is 2.59 acres. Local codes restrict the footprint of the building to 30% of the site. How large can the main floor of the building be?
33,846 square feet 2.59 x 43560 = 112820.4 x .3 = 33.846 square feet
Marc bought 9 adjacent unimproved lots for $8,500 each and plans to divide them into 14 lots and sell them for $7,000 each. He paid $5,200 to install water and sewer lines and miscellaneous improvements. What will Marc's profit be?
4. 20% $8,500 * 9 = 76,500; 76,500 + $5,200 = $81,700; 14 * $7,000 = $98,000; $98,000 - $81,700 = $16,300; $16,300 / $81,700 = .1995 or 20%
Next month's interest payment on a loan balance of $108,900 is $750.75. What is the interest rate on this loan?
8.3% 108900 x ? = 9009
If you plan to live in a home for three years and then sell, which of the following $100,000 loans would be to your best interest?
9% adjustable rate mortgage with a 1% yearly cap and no discount points. (1st year monthly payments of $804, 2nd year of $876 and 3rd year of $950.) Compare total cash outlay by multiplying payment amount (x) number of payments and add amount of discount points paid if applicable. • 9% fixed rate, amortized loan with a cost of 3 1/2 discount points (monthly PI payments of $804). $804 x 3 years + $3500 = $5912 • 9% adjustable rate mortgage with a 1% yearly cap and no discount points. (1st year monthly payments of $804, 2nd year of $876 and 3rd year of $950.) 804 + 876 + 950 = $2630 • 8% fixed rate, amortized loan with a cost of 6 discount points (monthly PI payments of $733) $733 x 3 years + 6000 = $8199
You want to build a barn with feed storage on the second floor. The dimensions are 45 feet wide, 60 feet deep and 30 feet high, with a flat roof. Builder A offers to build it for $7.50 per square foot. Builder B offers to build at $.475 per cubic foot. Which bid is lower, and by what amount?
A's bid by $18,225 Builder A is offering to work per square foot - so that math is; 60x45 = 2700 sq ft x $7.50 per sq ft = $20,250 Builder B is offering to work per cubic foot - so that math is; 60x45x30 = 81,000 cb ft x $.475 per cb ft = $38,475 Builder A's bid is lower by $18,225. When using square footage we only measure the length by the width. Cubic feet requires to measure the length by the width by the height.
You want to build a storage warehouse 30 feet wide, 160 feet deep and 24 feet high, with a flat roof. Builder A offers to build it for $8.50 per square foot. Builder B offers to build at $.375 per cubic foot. Which bid is lower, and by what amount?
A's bid by $2,400 The formula for Square feet is:length × width The formula for Cubic feet is:length × width × height Builder A = 160 x 30 x 8.5 =40800 Builder B = 160 x 30 x 24 x .375= 43200
A real estate closing is to take place June 15 and property taxes in the amount of $1300 are to be prorated based on a 360-day year with the seller owing up to and including the day of closing.
Debit the seller $595.83 and credit the buyer $595.83. 1300 / 360 = 3.6111111111 * 165 = 595.83
A property has a market value of $100,000. The assessed valuation is 26% of the market value. The mill rate for your property is 75. Your property taxes for the year would be
Involves taxation based on value Property taxes for the year involves taxation based on value.
Joe Green purchased a lot for $15,000 and listed it a year later for 30% more than he paid. There was little interest at that price so he reduced the price 20%. He soon found a buyer at the reduced price and paid a sales commission of 6%. What was Joe's profit or loss?
Loss of $336 15000 x .3 = 195,000, 195000 - .2 = 15600 15600 - .06 = 936 15600 - 936 = 14664 15000 - 14664 = $336 loss
The most frequently used system for legal descriptions in urban areas within the United States is the:
Lot and block system The most frequently used system for legal descriptions in urban areas within the United States is the Lot and Block system.
Your client purchased an extra lot in the subdivision, adjacent to his house, at $25,000. He wants to sell it for 50% more than he paid. You list it at that amount, but no one will buy. You reduce the price by 25%. The lot sells, and total commission and selling costs are 8% of the price. What was the profit or loss to your client?
Profit of $875 25,000 / .50=12,500 25,000 +12,500 =37,500 37,500 x .25 = 9,375 37,500 - 9,375=28,125 28125 x .08 = 2250 28125 (Sold price) - 25000 (original price) - 2250 (commission) = 875 (profit)
Assessed value
Relates to ad valorem taxes. Assessed value relates to ad valorem taxes.
Which of the following will result in the greatest net for the seller?
Sale price of $125,000, with commission of 7%, and closing costs of $2,508.
The previous year's taxes are $1320. The property was sold and closing took place on August 18, 2005. The seller was responsible for the day of closing. How would the taxes be prorated based on a 360 day year?
Seller owes $836, purchaser receives $836. 1320 / 360 = $3.66 daily rate x 228
Taxes are paid on a calendar year. Taxes of $2,987.50 were paid by the seller for the year. Closing was February 23, with the seller paying for the date of closing. Which of the following is correct?
seller credit of $2,545.78 Seller is responsible for 31 days in January and 23 days in February, or a total of 54 days. $2,987.50 divided by 365 = $8.18 per day. 53 x $8.18 = $441.72. Seller has paid $2,987.50 and used $441.72, so is entitled to a credit of $2,545.78
