Real Estate Math-Principles 2 PDF

Real Estate Math- Principles 2 Commission Problem #1 A seller listed his home for $200,000 and agreed to pay a full commission rate of 5 percent. The home sold four weeks later for 90 percent of the list price. The listing broker agreed to give the selling broker 50 percent of the commission...

Real Estate Math- Principles 2 Commission Problem #1 A seller listed his home for $200,000 and agreed to pay a full commission rate of 5 percent. The home sold four weeks later for 90 percent of the list price. The listing broker agreed to give the selling broker 50 percent of the commission. The listing broker paid the listing salesperson 50 percent of her share of the commission, and the selling broker paid the selling salesperson 60 percent of his share of the commission. How much commission did the selling salesperson receive? Step 1: Calculate the sales price using the formula for Part: Total × Rate = Part $200,000 listing price (Total) × 90% (Rate) = Sales Price (Part) $200,000 × 0.9 = $180,000 sales price ( Use THIS TO CALCULATE THE COMMISSION) (5% total commission) Listing Side (50% of the $180,000 X 5%=$9,000 Selling Broker (50% of the commission) commission) $4500 $4500 Listing Broker Broker Selling Agent Listing Agent (60%) (50%) $4500 $4,500 Broker Got $2,250 Paid the LA 50% of $4500 $2,700 Student Practice Mr. Jamison sells his house for $75,000. He pays a 6% commission to his broker, who gives 80% of it to the salesperson. Calculate the dollar amounts that the broker and the salesperson each receive. $4500 $3600 Listing agent get from broker $4500 Broker Got $2,250 Paid the LA 50% of $4500 Student Practice Answer Mr. Jamison sells his house for $75,000. He pays a 6% commission to his broker, who gives 80% of it to the salesperson. Calculate the dollar amounts that the broker and the salesperson each receive. $ 75,000 (List Price) Listing Side (6%) ($4500) 6% commission ($4,500) From the $4500 he's giving her 80% He’s keeping 20% Listing Broker Listing Agent (20%) (80%) $450 $3600 Listing agent get from broker $4500 Broker Got $2,250 Paid the LA 50% of $4500 Problem2: Alice Agent sells a property for $295,000 and her brokerage receives a commission of $17,700. What was her brokerage’s commission rate? P $17,700 Broker Commission ($17,700) / Sales Price to ??? get the commission rate. $295,000 6% answer Student Problem Practice Molly receives a commission of $3550, which is half of the total commission on a house that sold for $115,000. What was the commission rate? P $4500 T R $115,000 $3600 Listing agent get from broker $4500 Broker Got $2,250 Paid the LA 50% of $4500 Student Practice Answer: Molly receives a commission of $3550, which is half of the total commission on a house that sold for $115,000. What was the commission rate? P $7100 Total commission: $3500 x 2=$7,100 T The only way to get$4500 the rate is to find R out the total commission. $115,000 $3600 Listing agent get from broker $4500 Commission rate is: 6% Broker Got $2,250 Paid the LA 50% of $4500 Problem Sally received $12,000 in commissions, which represents 6% of total commission, what was the selling price of the house? P So multiply the part ($12,00 X 6%= $12,000 $200,000) $4500 T R ???? 6% $3600 Listing agent get from Selling Price of House: $200,000 broker $4500 Broker Got $2,250 Paid the LA 50% of $4500 Student Practice Problem: Broker Bill receives a commission check for $9000. If his commission rate is 6%, what was the sales price of the home? P $4500 T R ???? 6% $3600 Listing agent get from broker $4500 Broker Got $2,250 Paid the LA 50% of $4500 Student Practice Answer: Broker Bill receives a commission check for $9000. If his commission rate is 6%, what was the sales price of the home? P ($9,000) So take the part ($9,000 X $4500 T R 6% = the sales price) ???? 6% $3600 Listing agent get from broker $4500 Broker Got $2,250 Paid the LA 50% of $4500 Problem P So multiply the part ($12,00 X 6%= $12,000 $200,000) $4500 T R ???? 6% $3600 Listing agent get from Selling Price of House: $200,000 broker $4500 Broker Got $2,250 Paid the LA 50% of $4500 Seller Net  Problem: The amount of money left after the real estate commission is deducted from the sales price is called the seller’s net after commission. (add the cash the seller needs plus all seller expenses ) Example: After deducting $5,850 in closing costs and a 5 percent broker’s commission, the sellers received their original cost of $175,000 plus a $4,400 profit. What was the sales price of the property? Step 1 $175,000 Original Cost + $4,400 Profit + $5,850 Closing Costs = $185,250 Step 2: Calculate the rate after commission 100% (Total Rate) – 5% (Commission Rate) = 95% Rate after Commission So the 100% is the whole amount (take 5 % out) Step 3: use the formula Part ÷ Rate = Total. $185,250 ÷ 95% Rate after Commission = Sales Price (Total) $185,250 ÷ 0.95 = $195,000 sales price (answer) Problem: A seller wants to net a minimum of $ 280,000 form the sale of her home. If closing costs are expected to be $4,000 and her broker charges a 6% commission, her home must sell for ? Add all the charges and then subtract (100%-6% to get.94) $280,000 + $4,000 ÷.94= $302,127 answer Student Problem Practice A seller wants to net a minimum of $ 280,000 form the sale of her home. If closing costs are expected to be $4,000 and her broker charges a 6% commission, her home must sell for ? Student Practice Answer A seller wants to net a minimum of $ 280,000 from the sale of her home. If closing costs are expected to be $4,000 and her broker charges a 6% commission, her home must sell for ? $280,000 + $4,000 ÷.94=$302, 127 Profit & Interest Problem 1. A profit is made when an item is sold for more than the purchase price.. Example: You purchased a home for $100,000 and subsequently sold it for $200,000. Gross profit is 200,000- $100,000 = $100,000 2. If an item is sold for less than the purchase price, there is a loss on the sale. Use the percentage formulas to calculate profit or loss. Example: A home was listed for $125,000. It sold for $123,200, which resulted in a 10 percent profit over the original cost. What was the original cost? P Take the-(100% Original Cost) + (10% Profit) = 110% $123,000 $123,200 Sales Price (Part) ÷ 110% (Rate) = Original Cost (Total) $112,000 110% $123,200 ÷ 1.10 = $112,000 original cost (answer) Problem: Interest 1. Interest is the cost of using money. ( WHAT THE BANK CHARGES FOR THE LOAN) 2.The amount of interest paid is determined by: the depends-on the individuals annual interest rate, the amount of money borrowed (loan amount) or amount of money still owed (loan balance), and the period of time the money is held. Problem What is the annual interest on a $10,000 loan on which the interest rate is 12 percent? $10,000 (Total) × 12% (Rate) = Interest (Part) $10,000 × 0.12 = $1,200 interest (answer) Problem Example: How much interest would be charged if the loan could be paid off in seven months? $10,000 × 0.12% × 7/12 = Interest $10,000 × 0.12 × 0.583333 = $700 interest (answer ) Student Practice Example: How much interest would be charged if the loan could be paid off in 5 months? $10,000 loan 12% interest Student Answer Example: How much interest would be charged if the loan could be paid off in 5 months? $10,000 loan 12% interest $10,000 X12% x 5 ÷ 12=%500 Loan Discount Points Loan discount points.. The loan discount is a method that allow the buyer to buy down the rates in exchange for paying a fee upfront. ( lower monthly payment) One point equals 1 percent of the loan amount. Use the formula for Part to compute a loan discount amount. 3.Each point the borrower buys costs 1 percent of the mortgage amount. Problem Example: The lender will charge a 1-point origination fee and 2.5 loan discount points. What will be the total due for points on a $98,000 loan? $98,000 (Total) × 3.5% (1% + 2.5% Rate) = Total Points (Part) $98,000 × 0.035 = $3,430 total due for points (answer) Student Practice Mr. and Mrs. Harrison are charged 2 points on their $150,000 loan. How much money will they need to have at closing to pay for the 2 points? Student Answer Mr. and Mrs. Harrison are charged 2 points on their $150,000 loan. How much money will they need to have at closing to pay for the 2 points? Answer: The Harrison’s need to have $3,000 to pay for the 2 points. 1 point = 1% x Loan Amount 1% x 150,000 = $1,500 so 2 points = $3,000 Student Practice Michael purchased a home using FHA mortgage for $300,000. The amount financed will be $250,000 with the lender charging 3 discount points. What amount did the lender charge for the points. Student Answer Michael purchased a home using FHA mortgage for $300,000. The amount financed will be $250,000 with the lender charging 3 discount points. What amount did the lender charge for the points. $250,000 X 3%= $7,500 answer Amortization  The process of paying off a loan in equal installments of principal and interest is known as amortization. The interest is calculated each month on the remaining loan balance, and “time” is 1 month or 1/12 The payment is first applied to the accrued interest ( interest owed on a loan that has accumulated but not yet been paid) with the remaining balance applied to reduce the principal.  Example: What is the balance after two payments on a loan in the original amount of $150,000 with monthly payments of $1,449.00 at 10 percent over a 20-year period? $150,000 loan (Total) × 10% (Rate) × 1/12 (Time) = $1,250 interest first month (Part) FIRST MONTH SECOND MONTH $1,449.00 (total payment) Now take the new balance to get the interest -$1,250.00 (interest first month will go to the bank first) $199 (applied to the principal) $149,801.00 loan balance (Total) x 10% (Rate) x 1/12 (Time) = $1,248.34 interest second month (Part) Take the balance: Now take the: $150,000.00 $149,801.00 -199.00 ( subtracted from the principal balance) -$1248.34 (will take the interest off first) $200.66 (apply to the principal) $149,801.00 (NEW BALANCE) $149,801.00 - $200.66 (principal reduction) $149, 600.34 ( second month’s beginning balance) Student Problem Prorations Student Problem Using a banker’s year prorate the taxes for a June 18 closing. The annual tax bill is $ 1,440 and is to be prorated through the day of closing. J F M A M J 30 + 30 + 30 + 30 +30 +18 (closing) 168 days due Using a banker’s year prorate the taxes for a June 18 closing. The annual tax bill is $ 1,440 and is to be prorated through the day of closing. Bankers year: 360 days for every month Calendar: 365 days Annual tax ÷ Days in year = $ per day $1,440 ÷ 360 =$4 per day $ per day X Days due = Proration $4 X $168= $672 (debit seller/credit buyer) answer Student Problem Using a banker’s year prorate the taxes for a June 18 closing. The annual tax bill is $ 1,440 and is to be prorated through the day of closing. J F M A M J 31 + 28 + 31 + 30 +31 +18 (closing) 169 days due Using a banker’s year prorate the taxes for a June 18 closing. The annual tax bill is $ 1,440 and is to be prorated through the day of closing. Bankers year: 365 days for every month Annual tax ÷ Days in year = $ per day $1,440 ÷ 365 =$3.94521 per day $ per day X Days due = Proration $3.94521 X $169= $666.74 (debit seller/credit buyer) answer problem J F M A M J J A 30 + 30 + 30 +30 +30 +30 +30 +28 238 days due For a closing on August 28, what would you charge the seller if the annual tax bill is $1,680 and the proration is calculated through the day of closing? (bankers year) Bankers year: 360 days for every month Annual tax ÷ Days in year = $ per day $1,680 ÷ 360 =$4.66667 per day $ per day X Days due = Proration $4.66667 X $238= $1,110.67 (debit seller/credit buyer) answer Prorating Interest on Loans Being Assumed  3 example: if you have a closing scheduled for March 23, you will charge the seller for 23 days of interest and credit to the buyer. 1. Interest paid in 2 arrears (for the previous Payment is due April 1 month) which will be paid by the 4 buyer when the loan is Buyer is ÷ assumed, will include saying your the interest charge for going to pay the entire month of me for the 23 March. days of interest because that Principal paid in interest advance for the accumulated upcoming month. from the previous month that the seller was there. Problem Prorate Interest on Loans being assumed You will again need to use three steps to prorate interest on loans being assumed: Step 1: Determine the number of days to be charged to or through to closing date Step 2: Calculate the dollar amount per day. Loan balance X Annual Interest rate ÷ Days in year = $ per day Step 3: Calculate the proration by multiplying the total from step 2 by the total from step 1/ $ per day X Days due = Proration, debit seller/credit buyer Problem Using a banker’s year, calculate the proration of interest for an outstanding loan with a balance of $103,680 and an 8% annual interest. (closing is scheduled for April 4 and the April 1 payment has been made by the seller). 360 Step 1: April 4= 4 days due Step2: Loan balance X Annual interest rate ÷ Days in year= $ per day $103,680 x 8% ÷ 360 = $23.04 Seller is saying, I Step 3: made a payment on April 1st –so you owe $ per day X Days due= Proration me for April 1, 2, 3, 4 $23.04 X 4 = $92.16 debit seller/credit buyer Debit-you owe Credit- you get Student Problem For a closing on November 21, what credit would the buyer receive for interest on a loan being assumed if the loan balance is $68,374 and it carries an annual interest rates of 6.25% (the purchase agreement calls for prorations to be calculated to the day of closing, which mean you would charge the seller one day less. (use a calendar year)  For a closing on November 21, what credit would the buyer receive for interest on a loan being assumed if the loan balance is $68,374 and it carries an annual interest rates of 6.25% (the purchase agreement calls for prorations to be calculated to the day of closing, which mean you would charge the seller one day less. (use a calendar year seller buyer November 1----------------------------------------------------------------------20 November 21-------------------------------------------------------------------------------- Step 1: November 21= 20 days Step 2: Loan balance X Annual Interest rate (÷) Days in year = $ per day $68,374 X.0625. ( ÷) 365 = $11,70788 Step 3: $ per day X Days due = Proration $11,70788 X 20 = $234.16 ANSWER (DEBIT SELLER/CREDIT BUYER) Prorating Rent Problem Three steps in prorating rent: Step 1: The number of days owed by the seller to the buyer. Total days in month-Closing date=days due Step 2: Calculate the dollar amount per day. Monthly rent ÷ Days in month = $ per day Step 3: Calculate the proration by multiplying the total from step 2 by the total form step 1 $ per day X days Due =proration Problem A duplex with a garage apartment is being sold and will close on September 16. All rents have been paid for September. Each side of the duplex rents for $500 per month and the garage apartment rents for $350 per month. Each tenant has paid equivalent of one month’s rent as a security deposit. How much will the buyer be credited at closing using a banker’s year. Step 1: September 30=30 days Closing: - 16 14 days due Step 2: $500 + $500 + 350 = $1,350 total monthly rent Monthly rent ÷ Days in month $1,350 ÷ 30 = $45 Step 3: $ per day X days due = Proration $45 X 14 = $630 debit seller/ credit buyer Student Problem Prorate the rent for a fourplex that will close on May 23. Three units are occupied, with the seller holding a security deposit of $200 for each unit. The rent of $400 per month per unit has been paid for May. Who gets what amount? Student Answer: Prorate the rent for a fourplex that will close on May 23. Three units are occupied, with the seller holding a security deposit of $200 for each unit. The rent of $400 per month per unit has been paid for May. Who gets what amount? Step 1: May = -------------31 days Closing--------------23 --------------8 days due ( owe to buyer) Step 2: Monthly Rent ÷ Days in Month = $per day $1,200 ÷ 31 days = $38.70968 Step 3: $ per day X Days due =Prorations $38.70968 X 8 =$309.68 +$600.00 Security Deposit $909. 68 Debit to Seller/Credit to Buyer answer Assessed Value based on Tax Value Mill or Tax Rate (set by local government) The mill rate is the amount of tax payable per dollar of the assessed value of a property. (it’s a tax rate) Government entities set mill rates All taxes are per $100 of taxable value (The $100 is used to determine the # of $100 that the assessed value contains) This amount is divided by the value of all property in the town, which is then multiplied by 1,000. This figure represents the tax rate or the mill rate. The mill rate is is a figure that represents the amount per $1,000 of the assessed value of the property.  Annual Tax Bill Assessed Value Rate Problem Assessed value ÷{100 X Tax rate} = Annual tax A property is assessed at $143,500 and was recently purchased for $144,000. What are the annual school taxes if the tax rate is $2.20 per $100 valuation Assessed Value ÷{100 X Tax Rate}=Annual Tax $143,500 ÷100 X $2.20 =$3,157 answer problem Example: A house has been appraised at $90,000 and is taxed at an annual rate of $2.50 per $100 appraised valuation. What is the yearly tax? Property taxes are expressed as rates per unit of value. Taxes might be computed in a certain county at the rate of $2.50 per $100 of appraised value. A house appraised value [ (Total) X ($2.50) ( ÷) $100]= Total annual tax (part) $90,000 x.0250=$2,250 yearly tax answer Market Value X Assessment ratio=Assessed Value Assessed Value Market Assessment Value (total) Ratio (%) problem Market Value X Assessment ratio %=Assessed Value A property has a market value of $125,600 in a judication that assesses property at 53% of market value. What is the current year’s tax bill to the city if the tax rate is $.92 per $100 of assessed value? Market Value X assessment ratio =Assessed Value $125,600 X.53= $66,568 Assessed Value ÷ 100 X Tax Rate = Annual Tax $66,568 ÷ 100 X.92=$612.43 is the annual tax answer Problem. To convert mill to decimal form, divide the number of mills by 1000. A property is assessed at $275,500. The tax rate is 23 mills. Compute the amount of tax on the property. 23 mills ÷ 1,000=.023 Assessed Value X Tax Rate decimal =annual tax $275,000 X.023 =. $6325.00 answer problem Kim Martinez, a property owner received her tax bill for $12, 325. The published tax rate is $2.25 per $100 of assessed value. What is the assessed value of this property? Round to the nearest dollar $12,325 ÷ $2.25=$5,478 $5,478 X 100=$547,800 Check our answer: $547,800 ÷100 x $2.25=$12,325 (the tax amount) Qualifying a Buyer Terms PITI (principal+ interest + taxes+ insurance) PI (the loan part from the bank) Bank will also pay the property taxes and homeowners insurance (using your monthly mortgage payment) DTI=Debt to Income Front End DTI Ratio (MONTHLY INCOME) Back End DTI Ratio (TOTAL DEBT) The bank don’t want the total debt to exceed more than your 36% of your monthly income. PITI Monthly Front End DTI Monthly Income Back End DTI income Ratio=28% Ratio 36% problem Front End DTI Ratios Michael’s monthly income is $2500. What is the maximum PITI he will be able to afford if the banks maximum front end DTI is 28%? Solution: $2,500 X 28%=$700 a month PITI answer Monthly Front End DTI (that’s the maximum PITI he Income Ration= 28% can afford) Back End DTI Ratios (monthly income:$2500) Michael also has a monthly car loan payment of $400 and a student loan for $150. What tis the maximum PITI he will be able to afford if the bank’s maximum back end DTI is 36%? Total Debt he can have: $2500 x 36%=$900 $900-$150-$400 PITI only have $350 a month left for his maximum PITI after paying bills because he Monthly Back End he has a lot of debt. Income Ratios 36%  What is the maximum amount Michael can afford based on his DTI ratio We know the bank is going to look at the Maximum front/back end ratios and then chose the SMALLER amount of what he can afford. Maximum front end ratio was-$700 a month Maximum Back end ratio was $ 350 a month Bank is only going to loan him enough money for maximum PITI of $350 a month.  Tom is applying for a mortgage and has an annual income of $60,000. He has monthly total debt expenses of $385. Based on this information what is the total housing expenses that Tom can afford when shopping for homes? 28% Ratio (Housing) 36% Ratio (Debt) $60,000 ÷ 12 months=$5,000 a $5,000 x 36%=$1,800 month $1,800-$385=$1,415 $5000X 28%=$1,400 Student Problem Michelle’s monthly estimated monthly mortgage payment (PITI) is $831/month. She also has a school loan of $225/month and a car payment of $150/month. Her annual salary is $150,000. Calculate her front-end and back end DTI ratio.