Texas Real Estate Math Questions

An owner of a home listed it at a price which would leave him $16,800 after the broker received a 6% commission. If the broker sold the property at the listed price, how much commission would he receive?

$1,072. $16,800 divided by 94% = $17,872 - $16,800 = $1,072 commission.

A buyer is obtaining a conventional loan that requires 29/33 ratios. He earns $75,000 a year, and has a $450 car payment. What is his maximum PITI payment?

$1,612.50 $75,000 + 12 = $6,250 monthly income. $6,250 x .29 = $1812.50 front end qualifier. $6,250 x .33 = 2062.50— $450 debt = $1612.50 back end qualifier. The maximum PITI (Principal, Interest, Taxes, and Insurance) is the lower of these two qualifiers.

Ken purchased a property for $16,380. If he wants to sell it without a loss for a price which would include a 9% commission, the value of the property would have to appreciate:

$1,620. $16,380 divided by .91 = $18,000. $18,000 - $16,380 = $1,620.

Sue sold her property for $27,500 and realized a 7% profit over what she paid for it. Her profit was:

$1,800. The selling price of $27,500 = cost + 7% or 107% of selling price. $27,500 divided by 107% = $25,700 purchase price. $27,500 - $25,700 = $1,800 profit.

A loan was made for $14,000 at an interest rate of 6% per year for a 20-year period. The total interest that would be paid over the entire loan period if the monthly payment for this fully amortized loan is $7.17 per $1,000, would be approximately:

$10,000. $7.17 per $1,000 x 14 thousands = $100.38 monthly payment;|20 years x 12 months = 240 monthly payments;|$100.38 x 240 = $24,091.20;|$24,091.20 - $14,000 (money borrowed) = $10,091.20 total interest paid.

If a lender agrees to make a loan based on an 80% LTV, what is the amount of a loan for a property appraised for $135,000 and a sale price of $137,800?

$108,000 80% LTV is based on the lesser of the appraised value or the sale price; $135,000 x .80 = $108,000.

There was fire insurance on a building valued at $12,000. The cost of the policy was $166.40 for a three-year period. The policy became effective on March 1, 1992. On November 16, 1992, the owner sold the building and canceled the policy. What was the value of the unused portion of the policy?

$127.13 $166.40 divided by 36 = $4.62 x 8.5 = $39.27. $166.40 - $39.27 = $127.13.

Frank just sold his house for 6% more than he paid for it. The selling price was $140,450. What was the original purchase price?

$132,500 $140,450 divided by 106% = $132,500.

A deposit receipt states, "Buyer to assume existing first trust deed of $9,600 at 5-1/2% paid per quarter." If Mr. Taylor took possession February 15th and the first interest payment was due on March 15th, how much would Mr. Taylor pay on the next interest date?

$132.00 $9,600 x 5-1/2% = $528.00 interest per year. $528 divided by 12 (months) = $44 interest per month. $44 x 3 (1/4 of a year) = $132.00 per quarter.

A property is sold for $75,600 in cash. If transfer taxes are $.55 per $300 of value, how much transfer tax is due?

$138.60 $75,600 ~ $300 = $252; $252 x $.55=$138.60.

A homeowner paid 4 points for a bank loan. The bank sold the loan to an insurance company at 5-1/2 point discount and received a check for $15,000. The original amount of the loan was:

$15,873.02. 100% - 5.5% = 94.5%. $15,000 divided by 94.5% = $15,873.02.

A property is valued at $200,000 using a capitalization rate of 8%. What would the value of the same property be using a capitalization rate of 10%?

$160,000 $200,000 x .08 = $16,000 divided by .10 = $160,000.

Bill paid $240,000 for some income units. The land was valued at $16,500, and improvements at $35,640. Using the previous figures for depreciation for income tax purposes, which of the following most nearly reflects the depreciable amount?

$164,160 $16,500 (land) + $35,640 (improvements) = $52,140. $35,640 divided by $52,140 = .684 (68.4%). $240,000 (total cost) x .684 = $164,160 improvements. Land is not depreciable for tax purposes.

Ms. Williams purchased a house in a run-down condition and spent an amount equal to 10% of the purchase to fix it up and bring it to its present value. The house in now worth $18,700. The cost of the house is equal to the existing loan of the property. The amount of the loan is:

$17,000. $18,700 = 100% purchase price + 10% fix-up money. $18,700 divided by 110% = $17,000.

A lot sold for $18,950. This included a profit of 7%. The original cost of the home was approximately?

$17,700 $18,950 divided by 1.07 = $17,710.28. Closest answer is $17,700.

In order to be able to earn $90.00 per month from an investment that yields a 6% return, you must invest?

$18,000 $90.00 per month x 12 = $1,080 per year. $1,080 divided by .06 = $18,000. Remember to work the problem using the annual income and the annual interest rate.

What is 75% of $250,000?

$187,500 Convert 75% to a decimal and multiply; $250,000 x.75 = $187,500.

Broker John and Broker Jay agreed to divide a 4 1/2% commission equally on the sale of a home, which sold for $180,000. Sue, the listing salesperson, works for Broker John on a 50-50 commission split. Sue would receive approximately how much commission as a result of the sale?

$2,025 $180,000 x 4 1/2% = $8,100 total commission. $8,100 divided by 2 = $4,050 commission to Broker John's office. $4,050 divided by 2 = $2,025 commission to Sue.

Mr. Jones, an owner of a packaging firm, purchased a new machine in 1991 and paid $5,500. It was estimated at the time of the purchase to have a total economic life of 10 years and a salvage value of $550. Using the straight line method of depreciation, the book value at the end of 7 years would be:

$2,035. Salvage value must be deducted before computing depreciation. $5,500 - $550 = $4,950 divided by 10 = $495 per year x 7 years = $3,465. $5,500 - $3,465 = $2,035 (book value).

Jerry spends 25% of her gross monthly income on her apartment rent of $600. What is her gross monthly income?

$2,400 $600 divided by 25% = $2,400.

The lender's underwriting criteria would accept a housing expense to income ratio of 33% and a ratio of total debt service of up to a maximum of 38% of monthly gross income. The applicant has an outstanding college loan payable at the rate of $150.00 per month and a car payment of $450.00 monthly. Gross annual income is established at $100,000 per annum. What is the maximum PITI the lender will approve?

$2,566.67 ($100,000/12) x 0.38 is $3,166.67 - ($150 + $450) = $2,566.67

Brad bought a parcel of land in 1989 and subdivided it into four separate lots. Five years later, he sold each lot for $75,000. The adjusted basis for each lot was $25,000. Brad's capital gain on these transactions is:

$200,000. $25,000 x 4 lots = $100,000 adjusted basis. $75,000 x 4 lots = $300,000 total selling price. $300,000 - $100,000 = $200,000 capital gain.

Sam paid $310,000 for an income property. His tax bill showed the assessments to be as follows: Land $20,120, improvements $37,200. In arriving at a figure to be used for depreciation for income tax purposes, he used his assessment figures as a basis. Which of the following most nearly reflects the depreciable amount:

$201,500. $20,120 (land) + $37,200 (improvement) = $57,320. $37,200 divided by $57,320 = 65% improvement. $310,000 x 65% = $201,500. Land is not depreciable for tax purposes.

Mr. Stewart has an investment in a 20-unit apartment building which is adjacent to a freeway. Because of its proximity to the freeway, the owner lost $150 per month rent. If the capitalization rate were set at 8%, the loss in value to the property was:

$22,500. 12 x $150 = $1,800 divided by 8% = $22,500.

A property sold for $110,000. Buyer Tom financed 90%. Approximately how much will the monthly PMI increase his payment if the renewal rate is .30%?

$24.75 $110,000 x 90% = $99,000 (amount of loan) x .30% = $297 yearly renewal rate. 297 divided by 12 = 24.75 monthly increase.

When there is an existing assessment lien against a property and the buyer assumes that lien, the cost basis of the property is then the original cost, plus the amount of the lien. If Juan and Rosa bought a home for $240,000, and assumed an existing assessment lien in the amount of $2,000, what is their cost basis?

$242,000 The cost basis of a property is the purchase price plus any liens and capital improvements.

How much money must be loaned to receive $15,000 if the money is loaned for five years at 12% interest?

$25,000 $15,000 (total interest) divided by 5 = $3,000 (interest per year). $3,000 divided by 12% = 25,000 loan amount.

A property is valued at $35,000 and is insured for $30,000 at a rate of 15 cents per $100. The premium for a 3-year policy is 2-1/2 times the premium for 1 year. For a 3-year policy, the monthly cost will be:

$3.13. $30,000 divided by 100 = 300 x .15 = $45.00 (per year) x 2.5 = $112.50 (3 years). $112.50 divided by 36 = $3.13 per month.

An income property has a net income of $40,000. How much value would be lost if the current capitalization rate in the area changed from 5% to 8%?

$300,000 Divide the net income of $40,000 by 5%. It will give you a value of $800,000. You divide the same net income of $40,000 by 8%. It gives you a value of $500,000. The net difference is a $300,000 decrease in value.

An income property has a value of $400,000 and returns a net of 8% to its owner. What would the value of this property be to a new purchaser who wished to receive an 10% return on his money?

$320,000 The trick is getting the NET INCOME. The net income is determined by recognizing that the property nets its present owner 8% of $400,000 which is $32,000 (400,000 x 8% = $32,000). Now knowing the net income is $32,000 and the investor wants and 10% return on a property with a $32,000 net, you divide the $32,000 (net income) by 10% (the cap rate) to get $320,000 (the appraised value).

FHA mortgage insurance premium is calculated at a rate of 0.5% annually. How much is the premium for the month in which the remaining principal owed is $92,347?

$38.48 The annual premium on $92,347 would be $461.74 ($92,347 x 0.005). One month's premium is $38.48 ($461.74/12).

Mr. Stevens received a straight loan on which he paid only the interest at 6%, all due and payable in one year. His monthly interest payment was $23.00. What was the amount of the loan?

$4,600 $23.00 x 12 = $276 divided by .06 = $4,600.

A real estate investor purchased a property for $15,000. He paid $5,000 down and executed a non-interest bearing note for $10,000 in favor of the seller. Before the end of the first year and before he had made any principal payments, he sold the property for double what he paid for it. Each $1.00 of his investment is now worth?

$4.00 The owner's equity is based upon the difference in value and loan amount. $30,000 - $10,000 = $20,000. $20,000 / $5,000 = $4. His $5,000 investment is now worth $20,000 or $4 for each $1 invested.

Property "A" has a monthly gross income of $500. Property "B" has a monthly gross income of $900. Using a monthly gross multiplier of 120 and calculating the difference in value between the two properties, the result would be:

$48,000. $500 x 120 = $60,000. $900 x 120 = $108,000. $108,000 - $60,000 = $48,000.

What will the amount of taxes payable be if the property's assessed value is $85,000 and the tax rate is 50 mils in a community where the equalization factor is 120%?

$5,100 Calculate the tax by multiplying the assessed value times the equalization factor divided by 1,000 multiplied by the mill rate; $85,000 x 1.20 = $102,000 / 1,000 = 102 x 50 = $5,100.

Mr. Johnson bought a house for $64,500. He later sold the house and broke even, after paying 8% of the selling price in commission, and escrow fees. How much had the lot increased in value

$5,609 $64,500 divided by 92% = $70,109 selling price. $70,109 - $64,500 = $5,609 increase in value in order to break even.

Ted purchased a building for $250,000. The terms of purchase were $175,000 cash, and a purchase money deed of trust for the balance. If the land is valued at $50,000 what is the adjusted cost basis of the property after it is fully depreciated?

$50,000, the value of the land.

The Hatchers have a gross income of $60,000. The lender wants them to spend no more than 28% of their income on their housing expenses. A house they can buy for $240,000 has $2,400 in annual property taxes. Homeowners insurance would cost about $400 a year. At today's interest rates, monthly payments would be $6.65 per $1,000 borrowed on a 30-year mortgage. What is the smallest amount they can expect to spend for a cash down payment?

$64,510 The Hatchers' monthly gross income is $5,000 ($60,000 ~ 12). The lender allows them a monthly mortgage payment no higher than 28% of $5,000 = $1,400. From that $1,400, a month's property taxes must be subtracted ($2,400 ~ 12 = $200.00) and a month's homeowner insurance premium ($400 ~ 12 = $33.33). That leaves $1,167 to pay for the mortgage itself, principal, and interest. At $6.65 per thousand dollars, $1,167 will pay for $175.49, or $175,490 borrowed on a mortgage ($1,167 ~ $6.65= $175.49). If they buy for $240,000 and borrow $175,490, the Hatchers will need $64,510 as a cash down payment ($240,000 - $175,490).

Mr. Johnson listed his home with Broker Smith for $165,000 with a commission rate of 6%. Broker Smith brought an offer at 10% less than the listed price. Mr. Johnson said he would accept the offer if the broker reduced his commission by 16-2/3%. If they all agreed to these terms, what amount of commission would Broker Smith receive?

$7,425 16-2/3% is 1/6. 1/6 of 6% is 1% (so total commission is 5%). $165,000 x 90% (100% - 10%) = $148,500 selling price. $148,500 x 5% = $7,425.

A lender is providing 90% of the financing for a new house. If the house appraises for $75,000, what is the buyer's down payment?

$7,500 The down payment is the difference between the sales price and the loan amount. 100% - 90% = 10% down payment. Convert 10% to a decimal and multiply. $75,000 x .10 = $7,500

Several years ago, Mr. Matthews bought property for $12,000, paying $2,000 in cash with the seller taking back a trust deed for the balance of the purchase price. Before any payments had been made on the trust deed note, he sold the property several months later for $24,000. His invested dollar in these circumstances is worth:

$7.00. $12,000 (purchase price) - $2,000 (cash paid) = $10,000 (trust deed). $24,000 (sales price) - $10,000 (trust deed) = $14,000 (cash from sale). $14,000 divided by $2,000 = $7.00.

What is the salesman's 40% of a 6% commission on a $32,000 sale?

$768 $32,000 x .06 = $1,920 x .40 = $768

Broker Bob listed a home for sale for $200,000. He presented the seller with an offer which was 15% less than the listed price. The seller said he would accept the offer if the Broker Bob agreed to reduce her 6% commission by 16-2/3%. If Broker Bob agreed, how much commission would he receive?

$8,500 $200,000 x 15% = $30,000. $200,000 - $30,000 = $170,000 (amount of the offer). 16-2/3% = 1/6 (memorize this). 6% reduced by 1/6 = 5% commission. $170,000 x 5% = $8,500 commission to Broker Bob.

To receive a 12% return on an investment of $750,000, what would be the required net operating income?

$90,00 Net income = purchase price x capitalization rate. $750,000 x 12% = $90,000.

What would the transfer tax be on the sale of a lot that sold for $10,500 with a loan assumed at $10,400?

0 Transfer tax is paid on the difference between the selling price and any existing trust deeds that are assumed by the buyer in excess of $100. The first $100 is exempt.

Ken purchased a property for $16,380. If he wants to sell it without a loss for a price which would include a 9% commission, the value of the property would have to appreciate:

1,620 $16,380 divided by .91 = $18,000. $18,000 - $16,380 = $1,620.

A property sold for $19,000 with a first trust deed assumed at $15,500. Deducting commission of 8% and costs at $260, how much would the seller receive from escrow?

1,720 $19,000 - $15,500 = $3,500 - $260 = $3,240. $19,000 x .08 = $1,520. $3,240 - $1,520 = $1,720.

John buys a piece of property as an investment for $15,000. John's capital investment is $5,000. He pays 5% interest on a loan of $10,000, and the property appreciates 8%. After one year the property is sold. What percent of profit did he realize on his initial invested capital?

14% $16,380 divided by .91 = $18,000. $18,000 - $16,380 = $1,620.

Steve purchased a note worth $6,000 for $5,500. Interest rate on the note is 5%. What was his percentage of profit made on his investment if the note is paid off in one year?

14.5% $6,000 x .05 = $300. $6,000 - $5,500 = $500. $300 + $500 = $800 divided by $5,500 = .145 (14.5%).

If a person borrowed $10,000 on a straight note and paid $50 interest every 90 days, what would be the interest rate?

2% $50 x 4 = $200 interest per year divided by $10,000 = 2%.

Rita Morgan has $86,576 left on her 8.5% mortgage. Her monthly payment is set at $852.56 for principal and interest (she pays her own taxes and insurance). How much of her next payment will go to reduce the principal?

239.31 A year's interest on the present debt would be $7,358.96 ($86,576 x 0.085). A month's interest is $613.25 ($7,358.96 ~ 12). The principal portion of her payment is $239.31 ($852.56 —$613.25).

The S 1/2 of the SE 1/4 of Section 4, the N 1/2 of the NW 1/4 of Section 8, and the N 1/2 of the NE 1/4 of Section 15 contain how many acres?

240 The S 1/2 (640 acres to a section divided by 2 = 320) of the SE 1/4 (320 divided by 4 = 80) contains 80 acres. The N 1/2 of the NW 1/4 and the N 1/2 of the NE 1/4 both contain 80 acres. 80 x 3 = 240 acres.

Bert purchased a property for 20% less than the listed price and later, he sold the property for the original listed price. What percentage profit did he make?

25 If a property were listed at $100,000 and it was purchased at 20% discount (purchased for $80,000) and then sold for the list price ($100,000), this would be a profit of $20,000. Based on an investment of $80,000, there would be a profit of 25%.

A lender loans borrower Smith a sum of $1,800 and takes back a note and deed of trust. The note was set up to be fully amortized over a 1-year period, interest at 8% per year, payable at $162 per month. When the note was drawn, it was immediately sold to an investor for a 15% discount. If the loan were fully paid off at the end of the year, what percent return would the investor make on this investment?

27% 12 monthly payments x $162 per month (includes principal and interest) = $1,944 total amount received. $1,800 x 15% (discount) = $270. $1,800 - $270 = $1,530 (cost to investor). $1,944 (amount received) - $1,530 (cost to investor) = $414 profit made. $414 divided by $1,530 x 100 = 27% return.

How many acres are in the S 1/4 of the SE 1/4 of Section 10 and the N 1/2 of the NW 1/2 of Section 3 and the N 1/2 of the NE 1/4 of Section 16?

280 40 + 160 + 80 = 280 acres.

What percentage profit would an investor make if he purchased two lots for $16,000 each and then divided into three lots and sold them for $14,000 each?

31% $16,000 x 2 = $32,000 cost of lots. $14,000 x 3 = $42,000 selling price. $42,000 - $32,000 = $10,000 profit. $10,000 divided by $32,000 = 31.25% profit

Steve bought a piece of property for 25% less than the listed price. He later sold it for the listed price. His gain was:

33%. If the listing price is $100,000, 25% less would be $75,000. Later selling at $100,000 would be a gain of $25,000 divided by $75,000 = .33 (33%).

A person sold his home and took back a second trust deed for $3,740. He immediately sold it for $2,431. What was the rate of discount?

35% $3,740 - $2,431 = $1,309 (amount discounted) divided by $3,740 = .35 (35%).

Jill sold a house and carried back a promissory note for $13,340, secured by a 2nd trust deed. She then sold the note at close of escrow to an investor for $6,670. What was the amount of the discount?

50% $13,340 - $6,670 = $6,670 discount. $6,670 divided by $13,340 = 50% discount.

The entire stock of a retail store was sold for $9,400 to Bill Smith. Mr. Smith then sold the stock for 20% more than he paid for it, but due to some debts he lost 10% of the selling price. The net profit on Mr. Smith's' investment was:

752 $9,400 x 20% = $1,880 (profit). $9,400 + $1,880 = $11,280 x 10% (loss) = $1,128 loss. $11,280 - $1,128 = $10,152 (sales price less 10% loss). $10,152 - $9,400 (purchase price) = $752 (net profit).

John bought a house four years ago for $80,000. He just sold it for $86,900. What was the percent of profit?

8.6% $86,900 - $80,000 = $6,900 (profit) divided by $80,000 = .086 (8.6%).

Jim bought a second trust deed and note that had a face amount of $1,800 on which he was allowed a 20% discount. If he received payments of $120 per month, including 8% interest, for 1 year, what was his percentage of return on his investment?

No return was received on the investment $1,800 x 20% = $360. $1,800 - $360 = $1,440. $120 x 12 = $1,440 - $1,440 = 0. No return on this investment.

The Smiths offer to buy the Brown's house for $125,000, with the closing scheduled for June 15. The Browns sign a written acceptance, with the provision that the closing is to be on June 16. At this point, which of the following can occur?

The Smiths can back out of buying the house with no penalty.

Two appraisers, one using a capitalization rate of 10% and the other one 8%, both agree that the net income of a building was $11,200. The higher capitalization rate made the price of the building:

lower by 20%. $11,200 divided by 10% = $112,000. $11,200 divided by 8% = $140,000. $140,000 - $112,000 = $28,000 or 20% lower.

Jessie Petersen makes a written offer to buy Sam Lewis's house for $120,000. She confides in Sam's agent, George Smith, that if necessary she'd pay $10,000 more, but she doesn't want Sam to know that. George should:

warn Jessie that he must pass on to Sam anything useful he knows.