Real Estate Math

The percentage 125% can also be expressed in what ways?

1.25, 10/8, 20/16

What investment is necessary for a yield of $1,000 per month at 8% interest?

$1,000 x 12 months = $12,000 yield per year divided by .08 interest = $150,000.

The owner's total mortgage payment is $1,202.34 and this includes principal, interest, taxes, and insurance. The interest rate is 7.25%, the annual taxes are $1,809, insurance is $325 per year. If the principal portion of the payment is $203.00, what is the loan balance?

$1,809 divided by 12 months = $150.75 per month for taxes. $325 divided by 12 months = $27.03 per month for insurance. So $1,202.34 - $150.75 - $27.03 - $203.00 = $821.56 interest x 12 months = $9,858.72 divided by .0725 = $135,982.34.

A list price was decided based on leaving the owner with $104,000 after a 6% commission was deducted from the sales price. what was the list price?

$104,000 is left after a 6% commission so $104,000 is 94% of the list price. $104,000 divided by .94 = $110,638.29.

A broker pays his sales agent 60% of the commission for listing and selling a property. The commission is 7%. A sales agent received $3,600 on a property which she both listed and sold. What was the selling price?

$3,600 divided by .60 = $6,000 divided by .07 = $85,714.28.

An investor made 9% when he purchased a property for $100,000. The economy has changed and the next buyer wants to realize a 12% return but the rents and expenses have not changed. What would the second investor need to purchase the property for in order to get 12%?

$400,000 x .09 = $36,000 divided by .12 = $300,000.

A listing price was going to leave the owner with $90,000 after a 6% commission was deducted from the price. What was the list price?

$90,000 is what is left after 6% commission so $90,000 divided by .94 = $95,744.68.

A fully rented 10-unit apartment building rents for $500 per unit per month. Expenses run $1,200 per month. What is the annual gross income?

10 units x $500 = $5,000 x 12 months = $60,000 annual gross income. Expenses are not subtracted to calculate gross income.

A house measures 40 feet across and 30 feet from front of the house to back. It has a basement plus the main floor and an upper floor, all of which have the same measurements. What is the total square footage of this home?

40 x 30 = 1,200 x 3 levels = 3600 total square feet

A rectangular property on Main Street is 1/2 of an acre and the property measures 97 feet deep. What percentage of a mile is the frontage of this property on the road?

43,560 sq ft divided by 1/2 = 21,780 divided by 97 feet = 224.54 feet divided by 5,280 feet in a mile = .0425 or 4.25%.

How many questions requiring math should a licensee candidate anticipate on the general portion of the licensing exam?

8 out of 80

An acre has how many square yards in it?

An acre has 43,560 square feet. In order to calculate square yards, you must divide by 9, so 43,560 divided by 9 = 4,840 square yards.

What did the owners originally pay for their home if they sold it for $98,672, which gave them a 12% profit over their original cost?

If $98,672 is 1.12 times the amount of the original cost, then $98,672 divided by 1.12 = $88,100.

A family will have a new home constructed on a lot that is 70 feet across the front x 120 feet deep. The city requires the front and back setbacks of a minimum of 20 feet and side setbacks of 8 feet. What is the largest single level house this family can build on this site?

The 70 feet of frontage means the house could be 54 feet wide, since you'd have to deduct 8 feet for each setback, so 70-8-8=54 feet. The depth of the house could be 80 feet because the 120 foot depth - 20-20 for front and back setback requirements = 80. So 54 x 80 = 4,320 square feet.

An insurance company has been asked to insure a property with a total value of $340,000. The lot the home sits on is worth $75,000. What is the dollar amount of the coverage this policy provides assuming there is a charge of $3.40 per $1,000 value and the yearly insurance fee is $901?

The total value of $340,000 - $75,000 lot = $265,000. Or $901 annual fee divided by $3.40 = 265 x 1,000 = $265,000.

The commission on a sale was $14,100, which was 6% of the sales price. What was the sales price?

$14,100 divided by .06 = $235,000.

A $140,000 mortgage with 8% interest has monthly payments of $1,140. After the second monthly payment, what is the principal balance due on the mortgage?

$140,000 x .08 = $11,200 annual interest divided by 12 months = $933.33 for the first month. $1,140 - $933.33 = $206.66 applied to principal. $140,000 - $206.66 = $139,793.34 x .08 = $11,183.47 annual interest divided by 12 months = $931.96 so $1,140 - $931.96 = $208.04 applied to the principal. So $139,793.34 - $208.04 = $139,585.30 principal at the end of the 2nd month.

A sales agent sells a property for $158,500. The contract he has with his employing broker gives him 40% of the total commission earned. The commission due to the broker from the seller is 6%. What is the sales agent's commission check amount?

$158,500 x .06 = $9,510 x .40 = $3,804.00.

What could a buyer reasonably be expected to pay for a building that was producing $16,280 annual net income and other buildings in the area have cap rates at 9%?

$16,280 divided by .09 = $180,888.

A loan-to-value ratio for a $120,000 property where the buyer made a down payment of $18,000 is:

$18,000 divided by $120,000 = a down payment of 15% so the loan-to-value is 100% - 15% = 85%.

An office manager who also holds her real estate license was paid $1,000 per month plus 1/4 of 1% of all office sales. For November, she received $2,780. The amount was based on monthly sales in November of how much?

$2,780 - $1,000 = $1,780 attributable to sales. $1,780 divided by .0025 = $712,000.

Trent purchased 4 lots for $20,000 each and divided them into 6 lots that were sold for $15,000 each. What was the percentage of profit Trent realized in this set of transactions?

$20,000 x 4 lots = $80,000 cost. $15,000 x 6 lots = $90,000 selling price. $90,000 selling price - $80,000 cost = $10,000 profit divided by original cost $80,000 = .125 or 12.5%.

The annual rate of interest on a mortgage loan is 8.5 %. The monthly interest payment is $201.46. What is the principal amount of the loan?

$201.46 x 12 months = $2,417.52 annual interest divided by .085 = $28,441.41.

If a lender loans you 90% on your purchase of a house priced at $210,000 and you gave your agent a $2,100 earnest money then how much money must you bring to the settlement assuming your closing costs will total 5% of the sales price?

$210,000 x .10 (100%-90%) = $21,000 - $2,100 = $18,900 plus $10,500 (5% of $210,000) = $29,400.

The buyers and sellers have negotiated a transaction in which the buyers will actually move into the property four months before they can close, since they are waiting for the proceeds from another transaction to have sufficient funds for their down payment. The seller has agreed to have the buyers pay the interest portion of their underlying existing mortgage as rent. The original mortgage taken out was for $250,000 but the sellers have paid the balance down to $212,500. Their rate is 8%. What was likely negotiated as the monthly rental amount?

$212,500 x .08 interest rate = $17,000 divided by 12 months = $1,416.67.

A real estate agent will earn 55% share of any commission they generate. If the total selling price of the house is $250,000 and the broker receives the total commission of 3%, then what is the agent's share of the commissioner?

$250,000 x .03 = $7,500 x .55 = $4,125.

The broker and agent's IC agreement has a commission schedule that calls for the agent to be paid 50% of the first $250,000 and 75% of any amount over that. If the total commission was 5% of the sales price and the commission received by the agent was $10,000, what was the sales price?

$250,000 x .05 = $12,500 and the agent would have received 50% of that = $6,250 but the agent received $10,000 - $6,250 = $3,750 more than the $6,250 and that portion was cut at 75% so $3,750 divided by .75 = $5,000, then $5,000 divided by .05 (5% commission) = $100,000 + $250,000 = $350,000.

The buyer is purchasing a $300,000 home and will make a 10% down payment. If she's going to pay 2.5% for her loan discount points and 1% origination fee. She will also have 2% of the total price in other loan and settlement costs. She already paid the broker a $5,000 earnest money. What amount will she need to bring to the settlement to close this transaction?

$300,000 x .90 (100% loan - 10% down payment) = $270,000 loan. The loan discount points and origination fee are calculated on this amount so $270,000 x .025 = $6,750 for discount points and $270,000 x .01 = $2,700 for the origination fee. Her other closing costs are based on the sales price of $300,000 x .02 = $6,000 so she is purchasing a property for $300,000 and will receive a credit for her earnest money of $5,000 and her loan amount of $270,000 but will have expenses of $6,750, $2,700, and $6,000. $300,000 - $270,000 - $5,000 = $25,000 + $6,750 + $2,700 + $6,000 = $40,450.

How much interest will the seller owe the buyer for a closing date of January 10 if the loan balance is $310,000 and the interest rate is 4.5% on an assumable loan and the last payment was made on January 1? Pro-rations are to be calculated through the date of closing and using a statutory year.

$310,000 x .045 interest rate = $13,950 divided by 360 days = $38.75 x 10 days into January = $387.50.

A property was purchased for $230,000 and is worth $345,000 ten years later. How much average appreciation per year has this property experienced?

$345,000 - the original purchase price $230,000 = $115,000 income or increase in value. Knowing that I=RxV, $115,000 divided by $230,000 = 50% appreciation over a 10 year period so divided by 10 = .05 or 5% appreciation per year on average.

Two brokers participated in a sale of a home for $350,000 with a commission of 6% and agreed to split the commission equally. The listing broker's agreement with their sales person was to give the agent 60% of the commission. The selling broker's agreement with their sales person was to give them 70% of the commission. How much more did the selling sales person earn?

$350,000 x .06 = $21,000 divided by 2 = $10,500 x .60 = $6,300 for listing. $10,500 x .70 = $7,350 for selling. $7,350-$6,300 = $1,050 more.

An investor purchased a property for $450,000 which sits on a lot worth $100,000. If the investor is going to use a 27.5 year straight line depreciation, how much will he be able to deduct on his taxes each year that he owns this property?

$450,000 - $100,000 land that cannot be depreciated = $350,000 divided by 27.5 years = $12,727.27.

An owner agrees to list his cabin on the condition he will receive at least $47,300 after paying a 5% commission and paying $1,380 in other closing costs. At what price must it sell?

$47,300 divided by .95 (100%-5%) = $49,789.47 + $1,380 in other closing costs = $51,169.47.

You attempt to determine the value of a 20-unit apartment house employing the income approach. You discover each unit rents for $475 per month, an amount that seems consistent with like rental units in the area. For the past 7 years, the annual expenses of operation have averaged $62,440 per year. This complex has maintained a consistent vacancy rate of just 3%. A potential investor is interested in a return of 8%. What value would you arrive at using these facts?

$475 x 20 units = $9,500 per month x 12 months = $114,000 gross scheduled income minus a 3% vacancy rate of $3,420 ($114,000 x .03) and also minus annual expenses of $62,440 = $48,140 divided by .08 (8% return) = $601,750.

After deducting $5,850 in closing costs and a 5% broker's commission, the sellers received their original cost of $175,000 plus a profit of $4,400. What was the sales price of the property?

$5,850 plus $4,400 = $10,250 plus the seller's original cost of $175,000 = $185,250 which is 95% of the selling price if the broker was paid a 5% commission, so $185,250 divided by .95 = $195,000.

What investment is necessary for a yield of $500 per month at 6% interest?

$500 per month x 12 months = $6,000 annual income divided by .06 = $100,000.

A duplex is being sold for $145,000. The rents are $520 per unit. The security deposits were $300 per unit. The closing will occur on December 15. The title company will prorate based on the calendar month. What amount will the seller credit to the buyer as the new landlord on the settlement statement?

$520 x 2 = $1,040 divided by 31 days = $33.55 rental income per day x 16 days = $536.77 plus the security deposits for each unit so $536.77 + $300 + $300 = $1,136.77. This is the amount the buyer should be credited at their closing on December 15. When these tenants move out in the future, the new owner will have the deposits to return to them.

An agent sold a $520,000 home for which the seller willed the agent's broker a 6% commission. The agent will earn 65% of the commission on the first $250,000 and 90% of the commission above that. What will the broker's commission amount be?

$520,000 x .06 = $31,200. $250,000 x .06 = $15,000. $520,000 - $250,000 = $270,000 x .06 = $16,200. So the agent should received $15,000 x .65 = $9,750 and $16,200 x .90 = $14,580 = $24,330 will go to the agent. Taking the original $31,200 for the total commission and subtracting the portion the agent will receive ($31,200 - $24,330) leaves the broker receiving $6,870.

The fraction 2/5 can also be expressed in what ways?

.40, 40%

There is a tract of land that is 1.50 acres. The lot is 150' deep. If the lot will sell for $175 per front foot, what will the sales price be?

1.50 acres x 43,560 square feet per acre = 65,340 divided by 150 feet deep = 435.60 front footage x $175 per front foot = $76,230.

A broker has 1.87 acres of land listed for sale at 55.5 cents per square foot. What is the total asking price?

1.87 acres x 43,560 sq ft = 81,457.20 x .555 cents per acre = $45,208.75.

A fully rented 20-unit apartment complex rents their one bedroom units for $700 per month and their two bedroom units for $850 per month. They have an equal number of each type of unit. Their expenses are $1,150 per month. They have a 5% vacancy rate. What is the net operating income per year?

10 units x $700 per month = $7,000 x 12 months = $84,000 and 10 units x $850 per month = $8,500 x 12 months = $102,000, so $102,000 + $84000 = $186,000 x .95 (100%-5% vacancy) = $176,700 - expenses of $1,150 per month x 12 months so $13,800 = $162,900, the net operating income of this rental complex.

A house sold for $145,650 giving the owner of the property a profit of 10% over its original cost. What was the original cost of the property rounded to the nearest dollar?

10% profit + 100% original cost = 110% = 1.10 so $145,650 divided by 1.10 = $132,409.

A home purchased four years ago for $50,000 has increased in value by 10% over each preceding year since it was purchased. The home is now worth how much?

100% value + 10% increase = 1.10 for the 1st year so $50,000 x 1.10 = $55,000 at end of 1st year x 1.10 = $60,500 at end of 2nd year x 1.10 = $66,550 at end of 3rd year x 1.10 = $73,205 at end of 4th year.

What is the total cost of driveway that is 15 feet wide by 50 feet long and 6 inches thick if concrete costs $75.00 per cubic yard and the labor costs $1.50 per square foot?

15 feet x 50 feet = 750 square feet of surface area x .5 (6 inches) = 375 cubic feet of concrete for this driveway. There are 27 cubic feet in a cubic yard, so 375 divided by 27 = 13.88 cubic yards of concrete needed x $75 = $1,041 plus the cost of the labor. At $1.50 per square foot x 750 square feet = $1,125 for the labor cost; + $1,041 for materials = $2,166 total cost.

An agent lists a home of split-entry styling. The garage is off to the side of the home; the main floor and the basement of the home each measure 40 feet wide by 20'6" deep. What is the square footage of this home?

20 feet 6 inches = 20.5 feet x 40 feet = 820 x 2 (main floor & basement) = 1,640 square feet.

A seller paid $132,000 for a residence. The seller wants to list it and make a 20% profit after paying a broker a 6% commission. What should the new listing price be?

20% profit + 100% original cost = 120% or 1.20 so $132,000 x 1.20 = $158,400. Since we need to find out what the new 100% price will be after paying a 6% commission, we need to subtract 1.00 - .06 = .94 so $158,400 divided by .94 = $168,510.64 is what the seller needs to list the property for in order to net a 20% profit after paying a 6% commission on the new price.

A 30-acre rectangular parcel is 660 feet wide. What is the depth of the parcel?

30 acres x 43,560 feet = 1,306,800 total square feet divided by 660 feet wide = 1,980 feet deep.

A 30-acre rectangular parcel has 660 feet on the street side. What is the depth of the parcel in feet?

30 acres x 43,560 square feet in an acre = 1,306,000 square feet divided by the known dimension of 660 feet = 1,980 feet of depth.

Max buys 348,480 square feet of land at $1.25 per square foot. He divides the land into 1/3 acre lots. If Max keeps 3 lots for himself and sells the others for $25,000 each, what percent of profit will he realize?

348,480 x 1.25 = $435,600 original purchase price. 348,480 divided by 43,560 square feet in an acre = 8 acres. Dividing the property into third acre lots, there will be 8 x 3 = 24 lots. If Max keeps 3 of those lots for himself and sells the other 21 lots at $25,000 each, that's 21 x $25,000 = $525,000. $525,000-$435,600 = $89,400 so the percentage of profit realized is .205 or 20.5%.

The S 1/2 of the N 1/2 of the SW 1/4 of the NE 1/4 of the SE 1/4 is going to have a huge deck installed over it. The deck materials will cost $2.36 per square foot. What will the total cost of the decking be?

A section contains 640 acres. Working backwards, 640 acres in a section divided by 4 = 160 divided by 4 = 40 divided by 4 = 10 divided by 2 = 5 divided by 2 = 2.5. So there will be 2.5 acres of decking and since an acre is 43,560 square feet x 2.5 acres = 108,900 square feet of decking required x $2.36 per square foot = $257,004.

Amanda is going to have a driveway installed that is 24'4" wide x 35.5 feet long. The concrete will be 4 inches thick. J&J Concrete has given her a bid of $11 per square foot for the job, including materials and labor. Bob's Paving, Inc. has given her a bid of $30 for the materials per cubic foot and $20 per square yard for the labor cost. Both bids will round to the nearest dollar. How much lower or higher is one bid over the other?

Bob's Paving, Inc. is $968 higher than J&J Concrete. 24'4" is 24.33 feet x 35.5 feet = 863.72 square feet x $11 per square foot = $9,501 = J&J Concrete bid. To calculate the cubit feet, you need to multiply the 863.72 above x .33 (4 inches is .33 of a foot) = 285 cubic feet x 30 = $8,550. Then the square yardage can be calculated by dividing that same 863.72 square feet by 9 feet in a square yard = 96 x $20 = $1,919 + $8.550 = $10,469. Bob's $10,469 - J&J $9,501 = $968 higher.

An apartment complex has a gross income of $87,500. For taxes, the owner depreciates $8,500 and has expenses, including principal reduction of $7,200, management fees of $26,800, property taxes of $5,100 and other operating costs of $14,100. What is the annual cash flow?

Depreciation is not deductible for calculation of cash flow, so the rest of the expenses totaled are $7,200 + $26,800 + $5,100 + $14,100 = $53,200; then $87,500 - $53,200 = -$34,300.

The primary source of tax shelter in real estate investments comes from which accounting concept?

Depreciation, or cost recovery, allows an investor to recover the cost of an income-producing asset through tax deductions over the asset's useful life.

Find the number of square feet in a lot with a frontage of 75'6" and a depth of 140'9".

First, convert the feet and inch measurements to feet only so 6/12 = 5/10, so 75'6" = 75.5 feet and 9/12=.75, then 140'9"=140.75 feet; so 75.5 feet x 140.75 feet = 10,626.63 total square feet

A backyard is drawn on the plan 6.5 in x 3 in. If the scale is .5 in = 5 feet and sod costs $15 per square yard, how much would it cost to sod this yard?

If there are 5 feet to every half inch, then there are 10 feet to one inch. 6.5 in x 10 feet = 65 feet and 3 in x 10 feet = 30 feet, but the sod costs are given in yards, so we can divide these numbers by 3 feet in a yard so this backyard is 21.66 yds x 10 yds = 216.6 square yds, so 216.6 x $15 per square yard = $3,249. (Round up)

The sale of a four-plex is scheduled to close on December 28. The rent per unit is $450. What amount will be prorated to the buyer at closing for the rent if the title company uses a calendar year?

If there are four units x $450 = $1,800 for the month of December divided by 31 days = $58.06 per day x the 3 days for which the buyer will own the property = $174.19.

In order to determine the square footage of a rectangular home, what would you do?

Multiply the width in feet x the depth in feet.

An owner's tax bill is $980.60. The tax rate or mill rate is 42 per $1,000. The property is assessed at 58.25 percent of its value. What is the total tax value of the property?

Tax rate/42 mills = 42/1,000 or .042; $980.60 divided by .042 = $23,347.62; $23,347.62 divided by .5825 = $40,081.75.

A couple has just purchased a home that needs some work. One of the last things they will do after painting, replacing light fixtures, and redoing the kitchen is to re-carpet the home. The house is 40 feet wide and 30 feet deep and they will carpet the entire home. The carpet they've selected costs $28 per yard. What will the expense be for carpeting?

The house is 40 x 30 = 1,200 square feet but the carpet is charged per square yard, so 1,200 divided by 9 square feet in a square yard = 133.33 x $28 per square yard = $3,733.33.

A homeowner wishes to refinance his loan to lower his monthly mortgage payment. Assuming his loan balance is $98,000 and his current payments are $1,056.36, including an escrow for taxes and insurance are $264.28 per month and principal reduction of $158 per month, what is the highest interest rate he could accept and still lower his payments?

The payment of $1,056.36 - escrow of $264.28 - principal reduction of $158.00 = $634.08 x 12 months = $7,609 annual interest divided by $98,000 = current interest of .0776 or 7.76%.

What is the capital gain on a rental property that was purchased for $230,000 and sold for $340,000, assuming the sellers have made improvements of $6,000, have taken $20,000 depreciation over the years, will have closing costs of $2,340, and will pay a commission of 8% of the sales price?

The selling price is $340,000. The seller is going to pay an 8% commission so $340,000 x .08 = $27,200. The seller will also pay $2,340 in closing costs so $340,000 - $27,000 - $2,340 = $310,460. But you still have to deduct the adjusted basis, the basis is $230,000 + the capital improvements of $6,000 = $236,000 - the depreciation that has been taken of $20,000 so $216,000. If you take $310,460 - the adjusted basis of $216,000 = $94,460 capital gain.

A property with an annual income of $20,000 was purchased. The only expense is 11% interest payment on a $100,000 straight mortgage loan. Assuming a down payment of $10,000 was made, what is the owner's percentage of return on their initial down payment?

$100,000 x .11 interest = $11,000 annual interest; $20,000 income - $11,000 annual interest expense = $9,000 net income; $9,000 divided by $10,000 initial down payment = 90% return.

The Sweet Shop pays rent of $1,000 per month plus 3% of the gross annual sales in excess of $60,000. What was the average monthly rent paid last year if the gross annual sales were $122,000.

$122,000 - $60,000 = $62,000 x .03 = $1,860 divided by 12 = $155 + $1,000 = $1,155 rent per month average.

The monthly interest payment due on a loan balance of $480,000 is $2,400. What is the interest rate on this loan?

$2,400 x 12 months = $28,800 yearly interest divided by loan balance of $480,000 = .06 or 6%.

The tax assessment is calculated at a mill rate of 65 mills. So what is the value of the property whose yearly property taxes are $2,416?

$2,416 divided by .065 = $37,169.23.

An investor purchased a property for $400,000. It's rental income was $4,000 per month and the expenses of operation were $500 per month. What annual return will this investor realize on his purchase?

$4,000 - $500 = $3,500 divided by $400,000 = .875 x 12 = .105 or 10.5%.

If Don borrows $4,400 agreeing to pay back principal and interest in 32 months, what annual interest rate is Don paying if the total payback is $5,394.84?

$5,394.84 - $4,400 = $994.84 divided by 32 months = $31.09 per month x 12 months = $373.08 yearly interest divided by $4,400 original loan amount = .085 or 8.5% interest.

If Tom borrows $4,400 agreeing to pay it back with interest in 18 months, what annual interest rate is Tom paying if the total payback is $5,588?

$5,588 - $4,400 = $1,188 in total interest divided by 1.5 years = $792 annual interest divided by the original $4,400 = 18%.

If taxes on a property are $5,800 based on an assessed value of $145,000, what is the mill rate?

$5,800 divided by $145,000 = .040 x 1,000 to convert it to mills = 40 mills.

An agent sold two building lots for a seller. The seller agreed to pay a 7% commission on each of them. The total commission charge was $9,100. Assuming one lot was twice the price of the other, what was the smaller lot priced at?

$9,100 divided by .07 = $130,000 total sales price. But the small lot was worth a price (X) and the other lot was worth twice that price (2X) so the total of X + 2X = 3X which is = to $130,000. So $130,000 divided by 3 = $43,333 = the smaller lot x 2 = $86,666, which equals $130,000.

What percentage of profit is made on a sale if the selling price is $90,000 and the purchase price is $75,000?

$90,000 - $75,000 = $15,000 profit. $15,000 = ? rate x $75,000 so $15,000 divided by $75,000 = 1.20 = 120% rate of return. $15,000 divided by $75,000 =.20 or 20% profit.

Kim is selling an investment property for $145,000 she originally purchased for $90,000. She will pay an 8% commission and will have $1,200 in other closing costs. Three years ago, she made $15,000 worth of capital improvements to the property. Depreciation is $30,509. What is Kim's adjusted basis in this property?

$90,000 original cost + $15,000 = $105,000 - $30,509 depreciation = $74,491. The other expenses listed are not deducted to calculate adjusted basis.

What is the interest on $954.00 for 8 months, 15 days, at 7.5% per annum?

$954 x .075 = $71.55 per year divided by 12 months = $5.96/month interest x 8.5 months = $50.65.

If the monthly payment is $957.52 and we know the rate is 12%, then what is the loan amount?

$957.52 x 12 months = $11,490.24 annual interest divided by .12 = $95,752 principal balance.

A tract of land containing 2,613,600 square feet sold for $375 per 1/2 acre. What was the total sales price?

2,613,600 divided by 43,560 sq ft in an acre = 60 acres; $375 per 1/2 acre x 2 = $750 per acre x 60 acres = $45,000.

The value of a frame house at the end of 6 years is $135,000. What was the original cost of the home if the yearly rate of depreciation is 2.5%?

2.5% = .025 x 6 years = 15% total depreciation. 100% - 15% = 85% so $135,000 divided by .85 = $158,823.53.

What is the rate of return on a property purchased for $75,000 and sold for $90,000?

20%.

A builder is subdividing a 4.5 acre tract into 50' x 100' lots. After allowing 71,020 square feet for the necessary streets, how many lots can be divided into the tract?

4.5 acres x 43,560 feet = 196,020 total square feet - 71,020 for the streets = 125,000 remaining square feet; 50' x 100' lots = 5,000 square feet for each lot. 125,000 divided by 5,000 = 25 lots.

How many acres are in the N 1/4 of the S 1/2 of the NE 1/4 of the S 1/2 of a section?

640 acres in a section, so starting backwards; 640 divided by 2 = 320 divided by 4 = 80 divided by 2 = 40 divided by 4 = 10.

There is a large piece of land containing three equal size building lots situated side by side. Two of these lots are owned by Owner A but the other lot is owned by Owner B. What percentage of the entire piece of land is owned by Owner A?

67% or two-thirds.

A lot is 70' x 120'. What fraction of an acre is this?

70 x 120 = 8,400 square feet divided by 43,560 square feet in an acre = .1928 or approximately 1/5 of an acre.

How many feet are there along the eastern side of the N 1/2 of the northernmost 1/4 of the S 1/3 of a section in a township?

A township is 6 miles squared and there are 36 sections within that township so there is 1 mile along each side of a section. 1 mile is 5,280 feet. Taking 5,280 feet and working backwards, 5,280 divided by 3 = 1,760 divided by 4 = 440 divided by 2 = 220.

An insurance company is valuing a single-family home in a residential area for purposes of insuring it. Which appraisal approach would they most likely be interested in?

Cost replacement approach. An insurance company will be most interested in what it will cost to rebuild the property if it were destroyed.

The settlement statement shows a sale price of $485,000. Annual taxes of $8,120 should be paid before November 30 but the transaction is closing on September 18. How will this be reflected on the settlement statement?

Credit to the buyer of $5,818 and a debit to the seller of $5,818. September 18 means the seller will have lived in the home for 8 months 18 days = 8 months x 30 days in a month = 240 + 18 days = 258 days. The buyer will be responsible for the remainder so $8,120 divided by 360 days in a year = $22.55 per day x 258 days = $5,818, which is the seller's portion. The buyer will pay the entire tax bill when it is due in November.

The formula for calculating rate of return, net income and/or value is:

Income = Rate x Value

The formula for determining percentage of profit is:

Profit amount divided by the original cost.

A property was valued at $250,000 using a 7% cap rate. If an investor wishes to use a cap rate of 9% then how much should he pay for the property?

Rate x Value so $250,000 x .07 = $17,500 must be the income. $17,500 divided by the new cap rate of .09 = $194,444.

To determine an interest rate, you should:

Take the interest earned divided by the principal. For example, if there was $6,000 earned from a $100,000 investment, the formula would be $6,000 divided by $100,000 = .06 or 6%.

How many acres are 348,480 square yards?

There are 9 sq ft in 1 sq yd. 348,480 x 9 = 3,136,320 total square feet divided by 43,560 square feet in one acre = 72 acres.

A rectangular piece of property has 50 feet of highway frontage. If it is a 4.25 acre parcel, how far back does the lot go?

An acre is 43,560 feet x 4.25 = 185,130 divided by 50 feet of frontage = 3,702.60 depth.

A buyer and seller close a transaction where the buyer was credited on their settlement statement for seller's portion of the anticipated yearly taxes of $4,212. The transaction closed on August 15. When the buyer received their tax bill with the new assessment for that year, the bill is for $8,100. How much more was this amount than the anticipated yearly tax amount the credit was originally determined from?

August 15 means the seller should have credited the buyer for 7 months x 30 days = 210 days + 15 days = 225 days. If the credit was for $4,212 for 225 days = $18.72 per day x 360 days = $6,739.20 for the entire year. So $8,100 - $6,739.20 = $1,360.80 more.

Assume that 3 rental buildings had sales prices and rents as follows: $107,250 and $16,500, $105,625 and $16,250, $112,125 and $17,250. What value would most likely be indicated on a similar building if rents were $16,750?

Based on the three properties, the gross rent multiplier is 6.5; in other words, the sales prices were 6.5 times the annual rents; therefore $16,750 x 6.5 = $108,875.