Real Estata Math

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IntroductIonThis appendix will explain the basic mathematical procedures you will need to be successful in your new real estate career. Many people are intimidated by the word math, but in this case the concepts presented for your understanding are mainly a review of information you already possess—and probably use in your daily life. An understanding of the principles and formulas explained in this appendix will help you as a licensee in solving math problems you will meet everyday.

California Real Estate Principles, 14th Edition

566 California Real Estate Principles M

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Learning objectivesAfter reading this appendix, you should be able to:

• calculatethesellingpriceofaproperty.

• calculatethebroker(anysalesassociate)splitofacommission.

• calculatetheoriginalamountofanote.

• calculatetheyieldonadiscountedtrustdeedpurchase.

• prorateinsuranceinescrow.

• calculatedocumentarytax.

• calculatenetoperatingincomeandpropertyvalue.

• calculateapercentageofprofit.

• calculateacreageinmultipleparcels.

BAsIc MAtH PrIncIPLesIt is important to review math basics including terminology, decimals, percentages, measurements, conversions, and formulas before starting our study of how to solve various real estate problems.

terminologyDecimal point The period that sets apart a whole number from a

fractional part of that number.

Divisor A number by which another number is divided.

Dividend A number to be divided by another number.

Interest The charge for the use of money.

Principal The amount of money borrowed.

Proration Theprocessofmakingafairdistributionofexpenses, through escrow, at the close of the sale.

Rate The percentage of interest charged on the principal.

Time The duration of a loan.

Annual Once per year

Semiannual Twice per year at 6-month intervals

Biannual Twice per year

Monthly Every month

Bimonthly Every 2 months

Semimonthly Twice a month

1 year For escrow and proration purposes, 360 days, 12 months,52weeks

1 month For escrow purposes, 30 days

Appendix A Real Estate Math 567

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decimals and PercentagesIt will be beneficial to review the concept of decimals here before starting our study of how to solve various real estate problems. The period that sets apart a whole number from a fractional part of that number is called a decimal point. The value of the number is determined by the position of the decimal point.

Any numerals to the right of the decimal point are less than one. The 10th position is the first position to the right of the decimal point, the 100th posi-tion is the second to the right of the decimal point, the 1,000th position is the third to the right of the decimal point, and so forth.

The whole numerals are to the left of the decimal point. The units are in the first position to the left of the decimal point, the 10s in the second position to the left of the decimal point, the 100s in the third position to the left of the decimal point, the 1,000s in the fourth position to the left of the decimal point, and so forth.

equivalent AmountsPercentage Decimal Fraction

4 1/2% 0.045 45/1000

6 2/3% 0.0667 1/15

10% 0.10 1/10

12 1/2% 0.125 1/8 16 2/3% 0.1667 1/6 25% 0.25 1/4 33 1/3% 0.33 1/3 50% 0.50 1/2 66 2/3% 0.667 2/3 75% 0.75 3/4

100% 1.00 1/1

converting Percentages to decimalsLookingatanumberexpressedasapercentage,suchas10%or20%,thedecimal point is assumed to be on the right side of the number. Move the decimal point two places to the left to remove the percentage sign and add a zero if necessary.

Example: 6.0% becomes 0.06 30.0% becomes 0.30 2.3% becomes 0.023 210.0% becomes 2.10


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converting decimals to PercentagesReverse the above process to convert a number expressed as a decimal to a per-centage; in other words, move the decimal point two places to the right.

Example: 0.02 becomes 2.0% 0.57 becomes 57.0% 0.058 becomes 5.8% 9.02 becomes 902.0%

Addition of decimal numbersAll numbers must be in a vertical column when adding numbers with deci-mals. Always be sure to line up the decimals vertically.

Example: 902.360 2.053 Add 387.100 1,291.513

subtraction of decimal numbersInsubtractingnumberswithdecimals,thesameprocessisused,makingsureto line up the decimals vertically.

Example: 43,267.23 Subtract 235.10 43,032.13

Multiplication of decimal numbersAfter multiplying the numbers just as you would in a non-decimal problem, count the total number of decimal places in the numbers being multiplied and place the decimal point in the answer that many places from the right.

Example: 4.3270 Multiply 82.2000 355.6794

division of decimal numbersThe decimal point must be removed before solving the problem when there is a decimal in the divisor. Move the decimal point in the divisor to the right, then move the decimal point in the dividend the same number of places to the right. Add zeros to the dividend if it has fewer numerals than are needed to carry out this procedure. Put the decimal point in the answer directly above the new decimal point in the dividend.


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Example: 840 ÷ .021 = 40,000

840,000 ÷ 21 = 40,000

Quotient

40,000

21 840,000

Dividend

Measurements

1 foot 12 inches

1 square foot A unit of area equal to 1 foot by 1 foot square (144squareinches)

1boardfoot 144cubicinches(1footx1footx1inch =144cu.inches)

Square footage The number of square feet of livable space in a home

Perimeter The distance measured around the outside of a geometric shape

1 yard 36 inches or 3 feet

1 square yard 9 square feet

1 mile 5,280 feet or 320 rods

1 rod 16 ½ feet

1 acre 43,560 square feet

conversions

Convert feet to inches: multiply the number of feet by 12

Convert inches to feet: divide the number of inches by 12

Convert yards to feet: multiply the number of yards by 3

Convert feet to yards: divide the number of feet by 3

Convert sq. feet to sq. inches: multiple the number of sq. feet by 144

Convert sq. inches to sq. feet: divide the number of square inches by 144

Convert sq. yards to sq. feet: multiply the number of sq. yards by 9

Convert sq. feet to sq. yards: divide the number of sq. feet by 9


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Basic real estate FormulasThere are usually only three variables in any real estate problem—two things thatareknownandonethat isunknown. Onewaytosolvethesetypesof problems is to imagine a circle divided into three sections. One third is labeled Made, one third is labeled Paid, and the last third is labeled Rate or Percentage.

Here are the 3 variations of the Made-Paid formula. Made equals Paid times Rate Paid equals Made divided by Rate Rate equals Made divided by Paid

Usethissimplewaytosolvemostrealestatemathproblemsandlookcarefully at the circle until you grasp this easy concept.

Whenever you have a math problem, one of these formulas probably can be used.Youwillalwaysknowtwoofthequantitiesandwillbeaskedtofindthethird. From the information given in the problem, you must decide whether tomultiplyordividethetwonumbersthatyouknowinordertofindtheunknownthirdnumber.

Whenyouareaskedtofindanamountresultingfromaninterestrate, itusuallywillbeanannualnumber.Makesureyouannualize,orconvertanymonthly figures to annual figures by multiplying the monthly figures by 12.

Some math problems will have a two-step solution. In other words, some process(add,subtract,multiply)willhavetobeperformedeitherbeforeorafter the above formula can be applied. Use the circle concept as an easy waytosolvethemathproblemsincludedhere.Onceyouknowintowhichsection of the circle your information fits, simply perform the math function indicated.

The circle concept for basic real estate formulas.

• Made = Paid x Rate• Paid = Made ÷ Rate• Rate = Made ÷ Paid


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soLvIng reAL estAte ProBLeMsThe following problem-solving techniques are explained for the beginning math student or someone who has not used math techniques for quite some time and just needs a little practice to become proficient.

There are several ways any of the following examples may be solved, and we have attempted to be consistent in our explanations for the beginner. Some students will recognize the algebraic solutions presented, and will use their own techniques for solving the problems.

The math problems presented are similar to those you will experience in real life. Learn to recognize the type of problem, and the math solution it requires, and you will be proficient in your real estate career.

Here are several guidelines for you to follow to answer some of the most basic math questions you will need to solve.

The amount MADE, or earned income, is shown as “I” in the formulas. It stands for different types of income. For example: commission Income earned by a real estate agent, interest Income earned by the lender or investor and paid by the borrower, net operating Income from an income property, and earned Income from an investment. There are two dollar amounts in a problem: a small amount and a large amount. The amount MADE is the smallerof the twoamounts. Forexample, thebroker’s commissiononaproperty that sold for $200,000 is never going to be $300,000—that is larger than the sales price! On the following chart, the small “$” sign represents the smaller amount of money.

The amount PAID is also shown as “P” in the formulas. It stands for differ-ent types of amounts paid. For example, sales Price for a property, Principal amount of a loan, the Property value, or the amount Paid for an investment. The amount PAID is the larger of the two amounts because it represents the large amount that is paid or invested. On the following chart, the large “$” sign represents the larger amount of money.

The RATE is also shown as “R” in the formulas. The “R” stands for differ-ent percentage rates. Whenever you see a “%”, it is referring to a rate. For example, commission Rate, interest Rate, capitalization Rate, and Rate of return.


AtH Review – Solving Real Estate Problems

$ $ % MADE PAID RATE I P RCommissions Commission Income Sales Price Commission RateLoans Interest Principal Interest RateAppraisal Net operating Income Property value Cap RateInvestment Earned Income Amount Paid Rate of ReturnSelling Price Increase Purchase Price Rate of ProfitSeller’sNet Net Income Sales Price Commission Rate

commission Problems

Commission problems involve these three variables:

Made = I = $ = Amount of commission IncomePaid = P = $ = Selling Price of the property

Rate = R = % = Commission Rate

Formulas:1.Whentheamountofsellingpriceandthecommissionrate(%)aregivenandyouaresolvingforthecommissionpaid(smaller$),use:

I=PxR (CommissionIncome = Sales Price x % Rate)

2. When the commission income and commission rate are given and you aresolvingforsalesprice(larger$),use:

P=I÷R(SalesPrice = Commission Income ÷ % Rate)

3. When the commission income and the sales price are given and you are solving for %(commissionrate)use:

R=I÷P(%Rate = Commission Income ÷ Sales Price)

The circle concept for commission problems.

• Paid = Selling Price of Property• Made = Amount of Commission• Rate = Commission Rate


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Practice Problem #1

Effie, a real estate salesperson, found a buyer for a $600,000 house. The selleragreedtopaya6%commissiononthesaletoEffie’sbroker.Effieisona50-50splitwithherbroker.What is the amount of her commission?

Known: P (Sales Price, $) and R (Commission Rate %)

P = $600,000

R = 6% or 0.06

Unknown: I (Commission Income, $)Whatwedonotknowisthedol-lar amount of the commission paid to the salesperson Effie. First, the total commissionpaidtothebrokermustbecalculated,thencalculatetheamountdue Effie.

Formula: I = P x R, or Commission Income = Sales Price x Rate

I = P x R

I = $600,000 x 0.06

I= $36,000(Totalcommissionincomeearnedbythebroker.)

Effie’scommission=½ofthetotalcommissionearnedEffie’scommission=$36,000÷2Effie’scommission=$18,000

The circle concept for Practice Problem #1.


AtH Practice Problem #2

Paul,arealestatebroker,listedaparceloflandfor$500,000,withacommis-sion of 10%. A few days later he presented an offer which was 5% less than thelistedprice.Theselleragreedtoacceptthepriceifthebrokerwouldreducehiscommissionby15%.IfPaulagreestotheseller’sproposal,how much will his commission be?

Known: P (Sales Price, larger $) and R (Commission Rate, %)

P= $500,000less5%($25,000)=$475,000

R = 10% less 15%

[Firstcalculate15%of10%(0.15x0.10=.0150),thensubtractitfrom10%(.10-0.015=0.085,or8.5%]

Unknown: I (Commission Income, smaller $)

Whatwedonotknowistheamountofthecommissionincome.

Formula: I = P x R, or Commission Income = Sales Price x Rate

I = P x R

I = $475,000 x 0.085

I = $40,375



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Interest and Loan ProblemsThe charge for the use of money is called interest. The rate of interest that is charged will determine the total dollar amount of the payments. When money is borrowed, both the principal and interest must be repaid according to the agreement between the borrower and lender.

Review – Interest Terms(P)Principal: dollaramountofmoneyborrowed,loanamount(I)Interest: chargefortheuseofmoney(R)Rate: percentageofinterestcharged(T)Time: durationofloan

When using the Circle Formula to solve interest and loan problems, MADE is the dollar amount of interest, PAID is the principal amount of the loan, and RATE refers to the annual interest rate of the loan.

Interest and loan problems involve these three variables:

Paid = P = $ = Principal

Made = I = $ = Interest

Rate = R = % = Interest Rate

Formulas:

1.Whentheamountofprincipalandinterestrate(%)aregivenandyouaresolvingforamountofinterestearned(smaller$),use:

I = P x R x T (Interest= Principal x Rate x Time)

The circle concept for solving interest and loan problems.


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2. When the interest income and interest rate are given and you are solvingfortheprincipal(larger$),use:

P = I ÷ (R x T) [Principal = Interest÷(%Rate x Time)]

3. When the interest income and the principal are given and you are solvingfor%(interestrate),use:

R = I ÷ (P x T) [Rate = Interest÷(Principal x Time)]

Practice Problem #3

Andrea borrowed $6,000 for one year and paid $520 interest.

What was the interest rate she paid?

Known: I (Interest Income), P (Principal), and T (Time)

P=$6,000(Principalamountofloan)

I=$520(Interestincomebankmadeontheloan)

T = 1 year

Unknown: R (Interest Rate)

WhatwedonotknowistheinterestrateAndreapaid.

Formula: R = I ÷ (P x T), or Rate = Income ÷ (Principal x Time)

R= I÷(PxT)

R=$520÷($6,000x1)

R = $520 ÷ $6,000

R = 0.0867 or 8.67%



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Practice Problem #4

Ifonemonth’sinterestis$50onafive-year,straightinterest-onlynote,andtheinterest rate on the note is 10% per year, what is the amount of the loan?

Known: I (Interest Income), R (Rate), and T (Time)

I=$600(Interestincomebankmadeontheloan) ($50permonthx12months=$600)

R = 10% or 0.10

T = 1 year

Unknown: P (Principal)Whatwedonotknowisthelarger$amountoftheloan.

Formula: P = I ÷ (R x T), or Principal = Interest ÷ (Rate x Time)

P= I÷(RxT)

P= $600÷(0.10x1)

P = $600 ÷ 0.10

P = $6,000

The majority of real estate loans are fully amortized, fixed rate loans. By using a calculator or mortgage tables, you can calculate the monthly pay-ment of principal (P) and interest (I). If a lender has requested an impound account to collect taxes and insurance,theborrowerwillmakemonthlypaymentsofprincipal(P),interest(I),propertytaxes(T),andhazardinsurance(I).


Review - Monthly Loan PaymentMnemonic = PITI Principal Interest Taxes Insurance


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Discounting NotesAs you recall, when someone buys a note at a discount, it means the buyer pays less than the dollar amount shown on the note, and the profit is the difference between what the buyer paid and the amount paid when the note is due. In other words, a certain amount is paid for the note, but a greater amount is received when the note is paid off.

Whenusing theMade/Paid formula fordiscountingnotes remember: (1)Madeisthetotalinterestpaymentplusthediscountamount,(2)Paidistheoriginalnoteamountlessthediscountamount,and(3)Rateistherateofreturn on the investment. Before the rate of return can be determined, the dollaramountofprofitmadebytheinvestormustbeknown.

Formulas:

1. When the amount of money paid and the rate of return are given and you are solving for income or profit, use:

I=PxR(Income = Amount Paid x Rate)

2. When the income and rate of return are given and you are solving for the amount paid, use:

P=I÷R (AmountPaid = Income ÷ Rate)

3. When the income and the dollar amount invested are given and you are solving for %, use:

R=I÷P (Rate = Income ÷ Amount Paid)

The circle formula for discounting notes.

•Made= I = $ = Income(Interest+discount)

•Paid =P = $ = Amount Paid(Noteamountlessdiscount)

•Rate =R = % = Rate of return on investment

Discounting note problems involve these three variables:


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Practice Problem #5

Texsignedanotefor$3,000,infavorof(orowedto)aprivatelender,whichis to be paid off in 12 months. He owes the $3,000 plus 9% interest when the note is due. An investor buys the note at a 20% discount. What is the rate of return on the amount invested by the investor?

Known: I (Income) and P (Amount Paid)

I=Income(Calculatetheinterestandthediscount) Interest=$3,000x0.09=$270(interestowedondue date).

Discount=$3,000x0.20=$600(20%discountallowed investor)

I=$870($270+$600)

P=AmountPaid(Calculatethediscountandsubtractfromthe amountofthenote.) Discount = $3,000 x 0.20 = $600

P= $2,400($3,000-$600)

Unknown: Rate (Rate of Return on amount invested) Whatwedonotknowistherate(%).

Formula: R = I ÷ P or Rate = profit) ÷ Paid (invested):

Rate = Profit ÷ Amount Invested

Rate = $870 ÷ $2,400

Rate = 36.25%

The circle formula for Practice Problem #5.

Discounting note problems involve these three variables:


AtH Capitalization Problems

Capitalization problems involve these three variables:

Made = I = $ = Net Operating Income(NOI)

Paid = P = $ = Value of Property

Rate = R = % = Capitalization Rate(CapRate)

Formulas:

1.Whentheamountofvalueofthepropertyandthecaprate(%)aregivenandyouaresolvingfortheNOI(smaller$),use:

I= PxR(NOI = Property Value x Cap Rate)

2. When the NOI and capitalization rate are given and you are solving forthevalueoftheproperty(larger$),use:

P =I÷R(Property Value = NOI ÷ Cap Rate)

3. When the NOI and the property value are given and you are solving for%(capitalizationrate),use:

R= I÷P(CapRate = NOI ÷ PropertyValue)

The circle concept for capitalization problems.

• Paid = Value of Property• Made = Annual Net Income or Loss• Rate = Capitalization Rate


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Practice Problem #6

A duplex brings in $600 per month per unit. Gail and Kevin are interested inbuyingthepropertyasaninvestment,andneedaninvestmentrate(capi-talizationrate,orcaprate)ofa10%return.What should Gail and Kevin pay for the duplex?

Known: I (NOI) and Rate (Cap Rate)

I = $600 per unit x 2 units = $1,200 net income per month $1,200 x 12 months = $14,400 annual net income

R = 10% or 0.10

Unknown: P (Value of the Property)

Whatwedonotknowiswhattheyshouldpayfortheduplex.

Formula: P = I ÷ R, or Property value = NOI ÷ Cap Rate

P = I ÷ R

P = $14,400 ÷ 0.10

P = $144,000


• Paid = Value of Property• Made = Annual Net Income or Loss• Rate = Capitalization Rate



Shirley paid $900,000 for an eight-unit apartment building. The gross income is $800 per month per unit, with expenses of $4,000 annually. What capitalization rate (%) will Shirley make on her investment?

As you recall, net operating income, rather than gross income is used to calculate a capitalization rate. Therefore, the first step is to calculate the gross income and then subtract the annual expenses to arrive at the net operating income.

Gross Income = $800 per month x 8 units = $6,400 per /month x 12 months = $76,800 annual gross income.

Annual Expenses = $4,000

Net Operating Income = $76,800 - $4,000 = $72,800

Known: I (NOI) and P (Property value)

I = $ 72,800

P = $ 900,000

Unknown: R (Cap Rate)

Whatwedonotknowisthecapitalizationrate.

Formula: R = I ÷ P, or Cap Rate = NOI ÷ Property value

R = I ÷ P

R = $72,800 ÷ $900,000

R = .081 or 8.1%

• Paid = Amount Invested or Investment• Made = Income or Profit Earned• Rate = Rate of Return or Profit



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Investments

Investment problems involve these three variables:

Made = I = $ = Income or profit earned

Paid = P = $ = Amount Paid or invested in the Property

Rate = R = % = Rate of Return or Profit

Formulas:

1.Whentheamountofmoneyinvestedandtherate(%)aregivenandyouaresolvingfor$(smallerdollaramount)use:

I=PxR(Income=AmountPaidxRateofReturn)

2. When the income and rate of return are given and you are solving for $(largerdollaramount)use:

P=I÷R(AmountPaid=Income÷RateofReturn)

3. When the income and the dollar amount invested are given and you aresolvingfor%(percentageofrateofprofit)use:

R=I÷P(RateofReturn=Income÷AmountPaid)

The circle concept for investments.

• Paid = Amount Invested or Investment• Made = Income or Profit Earned• Rate = Rate of Return or Profit



Steve has a savings account and wants to earn $100 per month in interest. If the account pays 4% interest, how much should Steve keep in the account?

Known: I (Income) and R (Cap Rate)

I=$1,200peryear($100x12months)

R = 4% or 0.04

Unknown: P (Amount Paid)

Theamountoftheinvestmentiswhatwedonotknow.

Formula: P = I ÷R, or Amount Paid = Income ÷Rate

P = $1,200 ÷ 0.04

P = $30,000



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Practice Problem #9

Mitch bought a house for $145,000. The house was later sold for $165,000. What is the rate (%) of profit Mitch made on this sale?

Known: P (Amount Paid) and I (Income)

P = $145,000

I= $20,000($165,000–$145,000)

Unknown: R (Rate)

Therateofprofitisnotknown.

Formula: R = I ÷ P, Rate = Income ÷ Amount Paid

R = $20,000 ÷ $145,000

R = 0.138 or 13.8%



AtH Cost and Selling Price Problems

Profit or Loss on Sales involves these three variables:

Made = I = $ = Increase in value

Paid = P = $ = Purchase price or original cost of Property

Rate = R = % = RateofReturn(profitorloss)

Formulas:

1.Whenthepurchasepriceandtherateofreturn(%)aregivenandyouaresolvingforthesalesprice(increaseinvalue), use:

I=PxR(Increase = Purchase Price x Rate)

2.Whenthesalesprice(increaseinvalue)andrateofreturnaregivenand you are solving for the original purchase price, use:

P=I÷R (Purchase Price = Increase ÷ Rate)

3.Whenthesalesprice(increaseinvalue)andtheoriginalpurchasepricearegivenandyouaresolvingfor%(rateofreturn),use:

R=I÷P (Rate = Increase ÷ PurchasePrice)

This type of problem is easy to identify because you will be given a selling priceandbeaskedtocalculate theamountofprofitor thecostbeforeaprofit. Sometimes determining the percentage to use can be confusing. Just remember that if a profit is made, add the % to 100%, and if a loss occurs, subtract the % from 100%.

The circle concept for cost and selling price problems.

• Paid = Purchase Price or Cost• Made = Selling Price• Rate = Profit or Loss Rate If a profit is made add the % to 100%


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Review – Calculating the Rate of Profit or LossWhen a profit is made add the % to 100%

(15%profit:100%+15%=115%or1.15)

When a loss occurs subtract the % from 100%

(20%loss:100%-20%=80%or0.80)

Practice Problem #10

Maureensoldaruralcabinfor$30,000,whichallowedhertomakea20%profit. What did she pay for the property?

Known: I (Increase) and R (% Rate of profit)

I=$30,000(Increaseearnedonthesaleoftheproperty.The amount actually earned is the smaller $ because it is the difference between the selling price and the original purchaseprice.)

R= 100%+20%=120%=1.20

Unknown: P (Purchase Price)

Whatwedonotknowisthelarger$amountthatshepaidfortheproperty.

Formula: P = I ÷ R, or Purchase price = Increase ÷ Rate

P = $30,000 ÷ 1.20

P = $25,000


• Paid = Purchase Price or Cost• Made = Selling Price• Rate = Profit or Loss Rate If a profit is made add the % to 100%


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We have determined that she paid $25,000 for the property and sold it for $30,000,whichisanincreaseinvalueof$5,000(thesmaller$amount).Is$5,000 a 20% profit? We can determine this by using the formula: R = I ÷P.Weknowtheincreaseinvalueis$5,000andthatshepaid$25,000forthe property, so we divide $5,000 by $25,000 to get the rate of profit, which is 0.20 or 20%.

You may be asked to find the selling price or amount of a loan when the seller receives a net amount.


Afarmerputhislandonthemarket,wantingtonetacertainamount.Therealestateagentwhofoundabuyergavethefarmeracheckfor$90,000,afterdeducting a 10% commission. What was the selling price of the farm?

Known – I (Net Income) and R (Commission Rate)

I=$90,000(Incomemadefromsale)

R=100%–10%=90%or0.90(Commissionrate)

Unknown – P (Selling Price)Whatwedonotknowisthesellingpriceofthefarm.

Formula: P = I ÷ R, or Selling Price = Income ÷ Rate

P = I ÷ R

P = $ 90,000 ÷ 0.90

P = $100,000 (Selling Price)



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Proration

When property is bought and sold, there are certain expenses that are charged to each party. It is one of the jobs of escrow to credit and debit the buyer and seller correctly as of the closing date of escrow. Proration is the process of makingafairdistributionofexpenses,throughescrow,atthecloseofthesale.For prorating purposes, use 30 days for a month and 360 days in a year.

Review - Proration

The Proration Process: 1. Determine the number of days to be prorated.

2. Calculate the cost per day.

3. Multiply the number of days by the cost per day.

4. Decide whether the item should be a credit or a debit to the seller or to the buyer.

5. Expenses that have been paid to some time after escrow closes, credit the seller and debit the buyer.

6. Expenses that will be due after the close of escrow, debit the seller and credit the buyer.

Common Expenses that usually are prorated:

• Propertytaxes

• Interestonassumedloans

• Fireandhazardinsurance

• Rents



Lynn sold her home on September 1, 2010. She has an existing loan of $200,000onthehouse.Theinterestontheloanis8%.TerrytookoverLynn’sloanwithinterestpaidtoAugust15,2010.Terryalsoassumedanexisting three-year fire insurance policy for $360 per year, paid by Lynn until November 15, 2011. Lynn also owes property taxes of $1,900 for the year.

Calculate the following:

•Prorateinterest,andwhoiscreditedordebited

•Prorateinsurance,andwhoiscreditedordebited

•Proratetax,andwhoiscreditedordebited

1. Prorate the interest:

August 15 to September 1 = 15 days

$200,000 x 8% = $16,000 annual interest

$ 16,000 ÷ 360 days in year = $44.44 per day

15 days x $44.44 per day = $666.60 interest

Credit the buyer and debit the seller.

2. Prorate the insurance:

September 1, 2010, through November 15, 2011 = 435 days

$360 ÷ 360 = $1.00 per day

435 days x $1.00 = $435

Credit the seller and debit the buyer.

3. Prorate the property taxes:

July 1 to September 1 = 60 days

$1,900 ÷ 360 = $5.27 per day

60 days x $5.27 = $316.66

Debit the seller and credit the buyer.


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documentary transfer tax

Each county, upon the transfer of property, may charge a documentary transfer tax. As you recall, the amount of the transfer tax is stamped in the upper right-hand corner of a recorded deed. The amount of the tax is based on $1.10 per $1,000 or $.55 per $500 of transferred value. When a sale is all cash, or a new loan is obtained by the buyer, the tax is calculated on the entire sales price. When an existing loan is assumed by a buyer, the tax is calculated on the difference between the assumed loan and the sales price.


Denise sold her home for $250,000, with the buyer obtaining a new loan.What is the amount of the documentary tax?

Known – Sales Price and Tax Rate

Sales price = $250,000

The sale involves a new loan so the tax is based on entire sales price

Tax rate = $1.10 per $1,000

Unknown – Amount of Tax DueWhatwedonotknowistheamountofthetaxdue.

Calculation – Tax Due = Sales Price ÷ $1,000 x $1.10

Tax due = $250,000 ÷ $1,000 = $250.00

Tax due = $250.00 x $1.10

Tax due = $275.00


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square Footage and Area calculationsOccasionally youmay be asked to solve problems about square footage. Square footage problems are fairly simple and can be solved easily using these simple formulas.

As you recall, the way to determine the value of a building using the cost method is tomeasure the square footage (buildingsaremeasuredon theoutside).Thencheckwithacontractortodeterminethestandardcosttobuild per square foot. Multiply that cost by the square footage of the building to derive the cost to build new, or the upper limit of value.

Review - Basic Area Formulas

The Area of a Square = Length x WidthThe Area of a Rectangle = Length x WidthThe Area of a Right Triangle = Altitude x Base ÷ 2

The concept for square footage and area calculations.


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Felix owned four acres of land with a front footage of 500 feet along the street. What is the depth of the land?

Known – Area and Width

Area=4acresor174,240sq.ft.(43,560sq.ft.peracrex4acres)

Width = 500 feet

Unknown – Length

Whatwedonotknowisthelength(depth)oftheparcel.

Formula – Length = Area ÷ Width

Length = 174,240 sq. ft. ÷ 500 feet

Length = 348.48 feet

All buildings are not square or rectangular and therefore may be irregular in shape. Always reduce the building to squares, rectangles and triangles, for whichyouknowtheformulatodeterminethesquarefootage.

The concept for Practice Problem #14.



Lydia and Cliff bought a lot, with the intention of building a house on it. They needed to determine how much it would cost them to build the house. They were told by contractors the cost to build was $40 per square foot for a garage and $80 per square foot for a home.

Lydia and Cliff had plans drawn for the house. They used the total square footage of the house and garage to figure the cost to build.

Known–Measurementsofstructureandcostpersquarefoot.

Unknown – The cost to build the house and garageTo find the square footage of the house, divide the diagram into imaginary rectangles and use the formula: Area = Width x Length

1. Calculate the area of the house

Rectangle A = 35' x 30' = 1,050 square feet

Rectangle B = 70' x 30' = 2,100 square feet

Rectangle C = 30' x 35' = 1,050 square feet

Area of house = 4,200 square feet

The concept for Practice Problem #15.


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2. Calculate the area of the garage

Garage = 15' x 30' = 450 square feet

3. Calculate the cost to build the house and garage

House: 4,200 square feet x $80 per square foot = $336,000Garage: 450 square feet x $40 per square foot = $18,000Total cost to build house and garage = $354,000


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Documents

Real Estata Math