Basic Math Principles

Transcription

1 Introduction This 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. 561

2 MATH 562 California Real Estate Principles Learning Objectives After reading this appendix, you should be able to: calculate the selling price of a property. calculate the broker (any sales associate) split of a commission. calculate the original amount of a note. calculate the yield on a discounted trust deed purchase. prorate insurance in escrow. calculate documentary tax. calculate net operating income and property value. calculate a percentage of profit. calculate acreage in multiple parcels. Basic Math Principles Terminology It 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. Decimal 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 The process of making a fair distribution of expenses, 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, 52 weeks 1 month For escrow purposes, 30 days

3 Decimals and Percentages Appendix A Real Estate Math 563 It 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. MATH 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 position 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 Amounts Percentage Decimal Fraction 4 1/2% / /3% /15 10% / /2% /8 16 2/3% /6 25% /4 33 1/3% /3 50% /2 66 2/3% /3 75% /4 100% /1 Converting Percentages to Decimals Looking at a number expressed as a percentage, such as 10% or 20%, the decimal 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 % becomes % becomes % becomes 2.10

4 MATH 564 California Real Estate Principles Converting Decimals to Percentages Reverse the above process to convert a number expressed as a decimal to a percentage; in other words, move the decimal point two places to the right. Example: 0.02 becomes 2.0% 0.57 becomes 57.0% becomes 5.8% 9.02 becomes 902.0% Addition of Decimal Numbers All numbers must be in a vertical column when adding numbers with decimals. Always be sure to line up the decimals vertically. Example: Add , Subtraction of Decimal Numbers In subtracting numbers with decimals, the same process is used, making sure to line up the decimals vertically. Example: 43, Subtract , Multiplication of Decimal Numbers After 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: Multiply Division of Decimal Numbers The 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.

5 Example: = 40, , = 40,000 Appendix A Real Estate Math 565 MATH Quotient 40, ,000 Dividend Measurements 1 foot 12 inches 1 square foot A unit of area equal to 1 foot by 1 foot square (144 square inches) 1 board foot 144 cubic inches (1 foot x 1 foot x 1 inch =144 cu. inches) Square footage Perimeter The number of square feet of livable space in a home 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

6 MATH 566 California Real Estate Principles Basic Real Estate Formulas There are usually only three variables in any real estate problem two things that are known and one that is unknown. One way to solve these types of 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 Use this simple way to solve most real estate math problems and look carefully at the circle until you grasp this easy concept. Made = Paid x Rate Paid = Made Rate Rate = Made Paid The circle concept for basic real estate formulas. Whenever you have a math problem, one of these formulas probably can be used. You will always know two of the quantities and will be asked to find the third. From the information given in the problem, you must decide whether to multiply or divide the two numbers that you know in order to find the unknown third number. When you are asked to find an amount resulting from an interest rate, it usually will be an annual number. Make sure you annualize, or convert any monthly 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) will have to be performed either before or after the above formula can be applied. Use the circle concept as an easy way to solve the math problems included here. Once you know into which section of the circle your information fits, simply perform the math function indicated.

7 Solving Real Estate Problems Appendix A Real Estate Math 567 The 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. MATH 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 smaller of the two amounts. For example, the broker s commission on a property 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 different 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 different percentage rates. Whenever you see a %, it is referring to a rate. For example, commission Rate, interest Rate, capitalization Rate, and Rate of return.

8 MATH 568 California Real Estate Principles Review Solving Real Estate Problems $ $ % MADE PAID RATE I P R Commissions Commission Income Sales Price Commission Rate Loans Interest Principal Interest Rate Appraisal Net operating Income Property value Cap Rate Investment Earned Income Amount Paid Rate of Return Selling Price Increase Purchase Price Rate of Profit Seller s Net Net Income Sales Price Commission Rate Commission Problems Paid = Selling Price of Property Made = Amount of Commission Rate = Commission Rate The circle concept for commission problems. Commission problems involve these three variables: Made = I = $ = Amount of commission Income Paid = P = $ = Selling Price of the property Rate = R = % = Commission Rate Formulas: 1. When the amount of selling price and the commission rate (%) are given and you are solving for the commission paid (smaller $), use: I = P x R (Commission Income = Sales Price x % Rate) 2. When the commission income and commission rate are given and you are solving for sales price (larger $), use: P = I R (Sales Price = Commission Income % Rate) 3. When the commission income and the sales price are given and you are solving for % (commission rate) use: R = I P (% Rate = Commission Income Sales Price)

9 Practice Problem #1 Appendix A Real Estate Math 569 MATH The circle concept for Practice Problem #1. Effie, a real estate salesperson, found a buyer for a $600,000 house. The seller agreed to pay a 6% commission on the sale to Effie s broker. Effie is on a split with her broker. 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, $) What we do not know is the dollar amount of the commission paid to the salesperson Effie. First, the total commission paid to the broker must be calculated, then calculate the amount due 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 (Total commission income earned by the broker.) Effie s commission = ½ of the total commission earned Effie s commission = $36,000 2 Effie s commission = $18,000

10 MATH 570 California Real Estate Principles Practice Problem #2 The circle concept for Practice Problem #2. Paul, a real estate broker, listed a parcel of land for $500,000, with a commission of 10%. A few days later he presented an offer which was 5% less than the listed price. The seller agreed to accept the price if the broker would reduce his commission by 15%. If Paul agrees to the seller s proposal, how much will his commission be? Known: P (Sales Price, larger $) and R (Commission Rate, %) P = $500,000 less 5% ($25,000) = $475,000 R = 10% less 15% [First calculate 15% of 10% (0.15 x 0.10 =.0150), then subtract it from 10% ( = 0.085, or 8.5%] Unknown: I (Commission Income, smaller $) What we do not know is the amount of the commission income. Formula: I = P x R, or Commission Income = Sales Price x Rate I = P x R I = $475,000 x I = $40,375

11 Interest and Loan Problems Appendix A Real Estate Math 571 MATH The 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: dollar amount of money borrowed, loan amount (I) Interest: charge for the use of money (R) Rate: percentage of interest charged (T) Time: duration of loan 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. The circle concept for solving interest and loan problems. Interest and loan problems involve these three variables: Paid = P = $ = Principal Made = I = $ = Interest Rate = R = % = Interest Rate Formulas: 1. When the amount of principal and interest rate (%) are given and you are solving for amount of interest earned (smaller $), use: I = P x R x T (Interest= Principal x Rate x Time)

12 MATH 572 California Real Estate Principles 2. When the interest income and interest rate are given and you are solving for the principal (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 solving for % (interest rate), use: R = I (P x T) [Rate = Interest (Principal x Time)] Practice Problem #3 The circle concept for 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 (Principal amount of loan) I = $520 (Interest income bank made on the loan) T = 1 year Unknown: I (Interest Rate) What we do not know is the interest rate Andrea paid. Formula: R = I (P x T), or Rate = Income Principal x Time R = I (P x T) R = $520 ($6,000 x 1) R = $520 $6,000 R = or 8.67%

13 Practice Problem #4 Appendix A Real Estate Math 573 MATH The circle concept for Practice Problem #4. If one month s interest is $50 on a five-year, straight interest-only note, and the interest rate on the note is 10% per year, what is the amount of the loan? Known: I (Interest Income), P (Principal), and T (Time) I = $600 (Interest income bank made on the loan) ($50 per month x 12 months = $600) R = 10% or 0.10 T = 1 year Unknown: P (Principal) What we do not know is the larger $ amount of the loan. Formula: P = I (R x T), or Principal = Interest (Rate x Time) P = I (R x T) P = $600 (0.10 x 1) P = $ 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 payment of principal (P) and interest (I). If a lender has requested an impound account to collect taxes and Review - Monthly Loan Payment Mnemonic = PITI Principal Interest Taxes Insurance insurance, the borrower will make monthly payments of principal (P), interest (I), property taxes (T), and hazard insurance (I).

14 MATH 574 California Real Estate Principles Discounting Notes As 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. When using the Made/Paid formula for discounting notes remember: (1) Made is the total interest payment plus the discount amount, (2) Paid is the original note amount less the discount amount, and (3) Rate is the rate of return on the investment. Before the rate of return can be determined, the dollar amount of profit made by the investor must be known. Discounting note problems involve these three variables: Made = I = $ = Income (Interest + discount) Paid = P = $ = Amount Paid (Note amount less discount) Rate = R = % = Rate of return on investment The circle formula for discounting notes. Formulas: 1. When the amount of money paid and the rate of return (%) are given and you are solving for income or profit (smaller $), use: I = P x R (Income = Amount Paid x Rate) 2. When the income and rate of return are given (%) and you are solving for the amount paid (larger $), use: P = I R (Amount Paid = Income Rate) 3. When the income and the dollar amount invested are given and you are solving for % (rate of profit) use: R = I P (Rate = Income Amount Paid)

15 Practice Problem #5 Appendix A Real Estate Math 575 MATH The circle formula for Practice Problem #5. Tex signed a note for $3,000, in favor of (or owed to) a private lender, which is 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 (Calculate the interest and the discount) Interest = $3,000 x 0.09 = $270 (interest owed on due date). Discount = $3,000 x 0.20 = $600 (20% discount allowed investor) I = $870 ($270 + $600) P = Amount Paid (Calculate the discount and subtract from the amount of the note.) Discount = $3,000 x 0.20 = $600 P = $2,400 ($3,000 - $600) Unknown: Rate (Rate of Return on amount invested) What we do not know is the rate (%). Formula: R = I P or Rate = profit) Paid (invested): Rate = Profit Amount Invested Rate = $870 $2,400 Rate = 36.25%

16 MATH 576 California Real Estate Principles Capitalization Problems Paid = Value of Property Made = Annual Net Income or Loss Rate = Capitalization Rate The circle concept for capitalization problems. Capitalization problems involve these three variables: Made = I = $ = Net Operating Income (NOI) Paid = P = $ = Value of Property Rate = R = % = Capitalization Rate (Cap Rate) Formulas: 1. When the amount of value of the property and the cap rate (%) are given and you are solving for the NOI (smaller $), use: I = P x R (NOI = Property Value x Cap Rate) 2. When the NOI and capitalization rate are given and you are solving for the value of the property (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 % (capitalization rate), use: R = I P (Cap Rate = NOI Property Value)

17 Practice Problem #6 Appendix A Real Estate Math 577 MATH The circle concept for Practice Problem #6. A duplex brings in $600 per month per unit. Gail and Kevin are interested in buying the property as an investment, and need an investment rate (capitalization rate, or cap rate) of a 10% 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) What we do not know is what they should pay for the duplex. Formula: P = I R, or Property value = NOI Cap Rate P = I R P = $14, P = $144,000

18 MATH 578 California Real Estate Principles Practice Problem #7 Paid = Amount Invested or Investment Made = Income or Profit Earned Rate = Rate of Return or Profit The circle concept for Practice Problem #7. 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) What we do not know is the capitalization rate. Formula: R = I P, or Cap Rate = NOI Property value R = I P R = $72,800 $900,000 R =.081 or 8.1%

19 Investments Appendix A Real Estate Math 579 MATH The circle concept for 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. When the amount of money invested and the rate (%) are given and you are solving for $ (smaller dollar amount) use: I = P x R (Income = Amount Paid x Rate of Return) 2. When the income and rate of return are given and you are solving for $ (larger dollar amount) use: P = I R (Amount Paid = Income Rate of Return) 3. When the income and the dollar amount invested are given and you are solving for % (percentage of rate of profit) use: R = I P (Rate of Return = Income Amount Paid)

20 MATH 580 California Real Estate Principles Practice Problem #8 The circle concept for Practice Problem #8. 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 = $1,200 per year ($100 x 12 months) R = 4% or 0.04 Unknown: P (Amount Paid) The amount of the investment is what we do not know. Formula: P = I R, or Amount Paid = Income Rate P = $1, P = $30,000

21 Practice Problem #9 Appendix A Real Estate Math 581 MATH The circle concept for 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) The rate of profit is not known. Formula: R = I P, Rate = Income Amount Paid R = $20,000 $145,000 R = 13.8 or 13.8%

22 MATH 582 California Real Estate Principles 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% The circle concept for 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 = % = Rate of Return (profit or loss) Formulas: 1. When the purchase price and the rate of return (%) are given and you are solving for the sales price (increase in value), use: I = P x R (Increase = Purchase Price x Rate) 2. When the sales price (increase in value) and rate of return are given and you are solving for the original purchase price, use: P = I R (Purchase Price = Increase Rate) 3. When the sales price (increase in value) and the original purchase price are given and you are solving for % (rate of return), use: R = I P (Rate = Increase Purchase Price) This type of problem is easy to identify because you will be given a selling price and be asked to calculate the amount of profit or the cost before a profit. 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%.

23 Review Calculating the Rate of Profit or Loss When a profit is made add the % to 100% (15% profit: 100% + 15% = 115% rate or 1.15) Appendix A Real Estate Math 583 MATH When a loss occurs subtract the % from 100% (20% loss: 100% - 20% = 80% or 0.80) Practice Problem #10 The circle concept for Practice Problem #10. Maureen sold a rural cabin for $30,000, which allowed her to make a 20% profit. What did she pay for the property? Known: I (Increase) and R (% Rate of profit) I = $30,000 (Increase earned on the sale of the property. The amount actually earned is the smaller $ because it is the difference between the selling price and the original purchase price.) R = 100% + 20% = 120% = 1.20 Unknown: P (Purchase Price) What we do not know is the larger $ amount that she paid for the property. Formula: P = I R, or Purchase price = Increase Rate P = $30, P = $25,000

24 MATH 584 California Real Estate Principles We have determined that she paid $25,000 for the property and sold it for $30,000, which is an increase in value of $5,000 (the smaller $ amount). Is $5,000 a 20% profit? We can determine this by using the formula: R = I P. We know the increase in value is $5,000 and that she paid $25,000 for the 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. Practice Problem #11 The circle concept for Practice Problem #11. A farmer put his land on the market, wanting to net a certain amount. The real estate agent who found a buyer gave the farmer a check for $90,000, after deducting a 10% commission. What was the selling price of the farm? Known I (Net Income) and R (Commission Rate) I = $90,000 (Income made from sale) R = 100% 10% = 90% or 0.90 (Commission rate) Unknown P (Selling Price) What we do not know is the selling price of the farm. Formula: P = I R, or Selling Price = Income Rate P = I R P = $ 90, P = $100,000 (Selling Price)

25 Proration Appendix A Real Estate Math 585 MATH 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 making a fair distribution of expenses, through escrow, at the close of the sale. 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: Property taxes Interest on assumed loans Fire and hazard insurance Rents

26 MATH 586 California Real Estate Principles Practice Problem #12 Lynn sold her home on September 1, She has an existing loan of $200,000 on the house. The interest on the loan is 8%. Terry took over Lynn s loan with interest paid to August 15, Terry also assumed an existing three-year fire insurance policy for $360 per year, paid by Lynn until November 15, Lynn also owes property taxes of $1,900 for the year. Calculate the following: Prorate interest, and who is credited or debited Prorate insurance, and who is credited or debited Prorate tax, and who is credited or debited 1. Prorate the interest: August 15 to September 1 = 15 days $200,000 x 8% = $16,000 annual interest $ 16, days in year = $44.44 per day 15 days x $44.44 per day = $ interest Credit the buyer and debit the seller. 2. Prorate the insurance: September 1, 2010, through November 15, 2011 = 435 days $ = $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, = $5.27 per day 60 days x $5.27 = $ Debit the seller and credit the buyer.

27 Documentary Transfer Tax Appendix A Real Estate Math 587 MATH 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. Practice Problem #13 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 Due What we do not know is the amount of the tax due. Calculation Tax Due = Sales Price $1,000 x $1.10 Tax due = $250,000 $1,000 = $ Tax due = $ x $1.10 Tax due = $275.00

28 MATH 588 California Real Estate Principles Square Footage and Area Calculations Occasionally you may be asked to solve problems about square footage. Square footage problems are fairly simple and can be solved easily using these simple formulas. The concept for square footage and area calculations. As you recall, the way to determine the value of a building using the cost method is to measure the square footage (buildings are measured on the outside). Then check with a contractor to determine the standard cost to build 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 Width The Area of a Rectangle = Length x Width The Area of a Right Triangle = Altitude x Base 2

29 Practice Problem #14 Appendix A Real Estate Math 589 MATH The concept for Practice Problem #14. 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 = 4 acres or 174,240 sq. ft. (43,560 sq. ft. per acre x 4 acres) Width = 500 feet Unknown Length What we do not know is the length (depth) of the parcel. Formula Length = Area Width Length = 174,240 sq. ft. 500 feet Length = 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 which you know the formula to determine the square footage.

30 MATH 590 California Real Estate Principles Practice Problem #15 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. The concept for Practice Problem #15. Known Measurements of structure and cost per square foot. Unknown The cost to build the house and garage To 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 2. Calculate the area of the garage Garage = 15' x 30' = 450 square feet

31 3. Calculate the cost to build the house and garage Appendix A Real Estate Math 591 MATH Building: 4,200 square feet x $80 per square foot = $336,000 Garage: 450 square feet x $40 per square foot = $18,000 Total cost to build house and garage = $354,000

32 MATH 592 California Real Estate Principles