Real Estate Math Equations
A buyer with a 20-year, $419,000 loan at a 4.25% interest rate has a monthly principal and interest payment totaling $2,594.59. If $1,483.95 is interest, how much is applied toward principal each month?
$1,110.64
A buyer with a 20-year, $419,000 loan at a 4.25% interest rate has a monthly principal and interest payment totaling $2,594.59. If $1,483.95 is interest, how much is applied toward principal each month?
$1,145.83
Your buyer client, Max, just signed a purchase agreement for a $520,000 home. He has a 60% LTV ratio, and his lender's charging a 1.5% loan origination fee. What loan origination fee can Max expect to pay at closing?
$4,680
A borrower has a 30-year, $500,000 loan with an interest rate of 6.25%. His monthly principal and interest payment is $3,078.59. What's the total amount of interest he'll pay over the course of the loan?
$608,292.40
Gary has an 80% LTVR on his new $318,000 townhome with an annual interest rate of 4.125%. What's his interest payment the first month?
$874.50
how to calculate transfer tax in CA
(first 3 figures of price sold) x 1.1 (1.1 per 1000)
LTVR
(loan amount/home value) x 100
Great work! You referred a buyer to a colleague in a neighboring state. The buyer found their dream home for a price of $325,000. A couple of weeks after closing, you receive a card with a check for $3,250 as a thank you from your colleague. At what rate as a percentage did your referral pay off?
1%
Juan secures a fixed rate amortized 30-year loan for $295,000 at 4.25%. If his monthly P&I payment is $1,750, how much interest does he pay in the second month of the loan?
1,042.29 295,000 x .0425 = 12,537.5/12 = 1,044.79 (pays this after the first month) 1,750-1,044.79 = 705.21 295,000 - 705.21=294,294.79 249,294.79 x .0425 =12,507.5296 12,507.5296/12 = 1,042.29
Let's apply the concept of proration to rent. Monthly rent for a property is $2,100. The tenant won't be moving into the property on the first of the month, so the entire rent isn't due. Instead, the lessor prorates the amount of the rent based on the number of days in the month the tenant will occupy the property. Assuming the tenant will occupy the property for 17 days (and also assuming a 30-day month), how much rent is due?
1,190
Let's try a slightly more difficult calculation. This time, seller Ricky's property is assessed real estate taxes of $1,400 for the year. Closing is held on August 15. If Ricky owns the day of closing, what is the amount that Ricky owes for taxes accrued and not yet paid based on the statutory year?
1,400 /12= 116.67 116.67 x 7 =816.69 116.67/30 = 3.89 3.89 x 15= 58.35 816.69 + 58.35= 875.04
Your buyer clients, the Fowlers, obtained an 80% loan on their $600,000 home. At closing, they paid $8,250 for points. How many points did the Fowlers pay to lower their interest rate?
1.72
A seller still owes $45,000 on her mortgage but wants to net $50,000 after the mortgage and 5% commission are paid. What's the minimum the house must sell for to net the seller the desired amount?
100,000
A 20-unit apartment building sells for $5 million. The property can bring in $400,000 in annual gross income. What is the gross income multiplier (GIM)?
12.5
you sold a home for 300,000 and commission was 5%; how much did you get in commission? assume you spit with broker, you get 60%=
15,000 15,000x.6= 9,000
Let's look at a few more scenarios on this and the next couple of slides. Seller Angela's property is assessed real estate taxes of $900 for the year. Closing is held on February 29th (that's right, it's a leap year). What amount does Angela owe for taxes accrued and not yet paid that will appear as a debit for the seller and a credit for the buyer at closing? Use the statutory year and assume that Angela owns the day of closing.
150 You calculate the taxes per month ($900 ÷ 12 = $75), and then calculate the accrued taxes owed and not yet paid by the seller ($75 × 2 months = $150).
You have a property listed at $160,000. The commission rate listed in the listing agreement is 6%, which you will split evenly with the buyer's representative. What does the property sell for if you earn a commission of $4,500?
150,000
A land owner has 300 acres of land. He's parceling the land and selling it for $2 per square foot. James wants to purchase two acres. How much will this cost?
174,240: remember to convert first what they are using the calculation, they want to know price from square foot convert acres to square feet 43,560x2=87,120 87,120x2=174,240
A property that sold for $800,000 is located in a city with a transfer tax of $2.75 per $1,000. What is the amount of the city transfer tax?
2,200
A buyer is purchasing a property for $120,000, which has an assessed value of $130,000. If the tax rate is $1.75 per $100, what will the buyer pay annually in taxes?
2,275 130,000 x .0175
mortgage recording tax rate mortgage recording tax rate for 325,000 is $2.75 per $100 mortgaged. if principal amount of mortgage is 200,000 what is mortgage recording tax amount?
2.75/100=.0275 200,000x.0275=5,500 use PRINCIPAL
If your clients are considering financing $200,000 with a 30-year loan at a 5% interest rate, how much would their principal and interest payment be per month? Plug in the numbers using the amortization chart in your resources see what the payment per month would be. Remember: The monthly payment multiplier is per $1,000 of the mortgage.
200,000/1,000 = 200 5.36822x 200 = 1,073.644 Remember to divide $200,000 by 1,000. Then multiply the factor (5.36822) by 200.
A buyer anticipates a house payment of $1,000 per month, with monthly homeowner association fees of $150. The buyer also has a car payment of $400 per month. If the buyer earns a monthly gross income of $5,000, what's the housing ratio?
23%
housing ratio range to qualify?
25-28%
What if your clients have total monthly debt of $1,000 and a gross income of $3,500 and wants to figure out their debt-to-income ratio?
28.6% DTI
An unimproved lot is advertised as 130,680 square feet. How many acres is this?
3 acres
A property in California sold for $700,000. The property is located in a city that imposes a transfer tax at a rate of $3.30 per $1,000. What is the total amount of transfer tax (between both county and city) for this property?
3,080 700 x 3.3 = 2,310 700 x 1.1= 770 add those numbers
Bob and Mary are financing $160,000 for a new home. Their lender will approve an interest rate of 6%, if Bob and Mary pay two discount points at closing. How much is this?
3,200
debt to income range?
33-36%
You have a buyer who's purchasing a home priced at $385,000 and appraised at $380,000. The bank has a 90/10 loan-to-value ratio and will charge an origination fee of 1% at closing. Calculate the loan origination fee.
3420 used apprasied number always, first find loan amount 385,000x.9 = 346,500 346,500x.01=3,465
A buyer has a 30-year, $750,000 loan with a 5.75% interest rate. How much of the first monthly payment is interest?
3593.75
Maurice received an offer of $480,000 for his home. The commission on the sale is 6%. Maurice's mortgage payoff is $78,500. He has additional closing expenses totaling $2,200. What will Maurice net from the sale of his home, rounded to the nearest whole dollar?
370,500
seller net be with home that just sold for 400,000 and commission is 7%
372,000 400,000x(1-.07)
property value of 225,000 is appreciated at 2% each year, what is the appreciation amount $ after one year? new property value? after 2 years?
4,500 229,500 229,500x.02= 4,590
depreciation value 40,000 valued decrease by 3.5% what will its new value be?
40,000x.035=1,400 40,000-1,400=38,600
You built the formula. Let's play with some numbers now. Your seller wants to net $47,500 after the 5% commission is paid, but before other closing costs are figured in. At what price does the home need to sell for the seller to net this amount?
50,000
A property in California sold for $500,000. What is the transfer tax amount if the property is not subject to city transfer taxes?
500 x 1.1 = 550
Suppose you're gearing up for the next quarter. You really want to push yourself to improve on the results from last quarter. You set a target of $21,000 in total commission for the quarter. Assuming the average total commission rate is 6% for each sale and you'll likely split that evenly with the person representing the other party in the transaction, what is the total value in sales you must reach to hit your target?
700,000
You're working with a buyer who's purchasing a home that appraised at $80,000. The buyer is obtaining a 90% loan, and the lender will charge a one-point origination fee at closing. How much will the loan origination fee be?
720
Purchase price of $600,000 and financing $480,000: calculate LTVR
80/10
A property in California sold for $800,000. What is the county transfer tax that would apply to this transaction?
800 x 1.1 = 880
You have an appointment to meet with Ramon and Willis, a young couple who are in the early stages of the homebuying process. They earn a gross monthly income of $3,600 and a net income of $2,900. The lender the couple is working with is conservative and only funds loans at the low end of the housing debt-to-income ratio. How large of a house payment can Ramon and Willis afford (according to their lender)?
900 use grossly monthly income 3,600 x .25 = 900
ammorization formula (define)
Monthly Payment Calculation Here's the calculation to find the monthly payment using this data: (loan amount ÷ 1,000) × factor = monthly payment paying off of loan over time
A buyer has a 30-year, $750,000 loan with a 5.75% interest rate. How much of the first monthly payment is interest?
Multiply the principal balance by the interest rate: $750,000 x .0575 = $43,125;. Then find the monthly rate by dividing $43,125 by 12 to get $3,593.75. Since the principal balance is less the next month, the interest amount will change too.
What calculation is used to determine the accrued taxes owed by a seller at closing? Assume the closing is held on the last day of the month, the seller owns the day of closing, and you're using a statutory year.
Taxes owed ÷ 12 months = taxes owed per month AND taxes owed per month × number of full months past = accrued taxes owed by the seller at closing
Phoebe's gross monthly income is $4,200, and she has $360 in monthly non-housing debt payments. The lender's qualifying ratios are 28% for the housing ratio and 36% for the total DTI ratio. What's the maximum housing payment she can afford?
The maximum house payment is the lesser of the amounts calculated using both ratios. DTI: $4,200 x .36 = $1,512. $1,512 - $360 = $1,152. Housing ratio: $4,200 x .28 = $1,176. Phoebe's maximum payment is $1,152.
Ramon and Willis have other debt that equals $296 per month. With a gross income of $3,600, and assuming they've found a lender that uses the high end of the total debt-to-income ratio, what's the maximum house payment they can afford?
Total debt-to-income can't exceed 36% of gross income. The couple has gross income of $3,600, so 36% of this is $1,296. To find the housing payment the couple can afford, subtract existing known expenses ($296) from $1,296. 1,000$
statutory year vs calendar year
Using a statutory year: Sometimes these items are prorated based on a 360-day statutory (aka "banker's) year (30 days x 12 months). Using a calendar year: The other method is to prorate based on a 365-day calendar year. Calculations using this method use the exact number of days in each month of the year.
property tax calculation
assessed property value x tax rate = annual property tax
Calculating Annual Debt Service Let's think back to the monthly payment we found using the amortization chart. The monthly payment was estimated to be $1,073.64. What is the debt service?
debt service, simply multiply by 12 12,883.68
how much interest with a home loan for 275,000 and annual interest rate of 4.75%
loan amount x interest rate = annual interest
It's time to crunch some numbers. You're working with buyers who are pre-approved for a loan up to $150,000. If they estimate paying $625 per month toward interest, what interest rate are they assuming?
loan amount x interest rate = annual interest 150,000 x ___= 7,500 (625 x 12) 7500/150,000 5%
loan origination fee
loan amount x loan origination %
formula for points amount typical point %
loan amount x points 1-3%
Calculating Loan Interest
loan balance x interest rate = annual interest
debt-to-income ratio
monthly debt/monthly gross income=DTI
housing ratio
monthly housing expenses/monthly gross income
mortgage recording tax rate
mortgage amount x tax rate = mortgage tax rate
Net to seller calculation
net to seller=sales price x (100%-% commission)
calculation appreciation formula:
original value x appreciation rate = amount of appreciation ($)
depreciation value calculation
original value x value not lost (100-%) = depreciated value OR follow appreciation formula and subtract from original value
e.g. property assessed at 80,000 pays a tax rate of 100 mills, what does the owner pay in taxes? calculate per mill and formula? Annual tax?
per mill = assessed property value/1,000 80,000/1,000=80$ per mill 80 x 100 mills = 8,000 in annual taxes assessed property value x mill rate/1000= annual taxes
calculating commission
sales price x commission rate = commission price
net to seller
set to seller = sales price x (100-% commision rate)
Using the income approach, determine the value of a property that has a net operating income of $15,000 and a cap rate of 15%.
value=operating income/cap rate value=15,000/.15 100,000$
