Mathematics Flashcards
Overview of Mathematics
Convert percent to decimal and decimal to percent
Solve for the Part, The Rate, and the Whole% problems
Determine which variables are given and the method to use to find the answer
Work through a multi-part problem to find a solution
Perform basic math calculations. Essential to the transaction of real estate
Percentage Problems
The answer to a percentage problem is one of 3 variables
- Part of the whole
- The Whole
- Percent Rate of a whole
P= R x W
Part is equal to the Rate multiplied by the Whole.
In percentage problems , 2 of the 3 variables are given.
To answer the problem, identify which 2 variables are present and determine the proper method to solve for the third.
Part
P
\_\_\_\_\_\_\_\_\_\_\_\_\_\_
Whole. |. Rate
W. |. R
When Part is unknown, multiply
Rate x Whole.
When the Part is known, divide
To find R, then divide Part by Whole
To find W then divide Part by Rate
Percentage math tips
1. Multiplying by % of less than 100% , the answer will always be smaller than original number
- Dividing by % of less than 100% , the answer will always be greater than original number!
Finance formulas
Loan to Value Ratio (LTV RATIO)
Typically the sales price or appraised value is known and the loan amount needs to be calculated.
The loan amount is based on LTV ratio.
This ratio, as expressed as a percentage, is the mathematical relationship between the amount the lender will lend and the selling price or appraised value of the property, whichever is less. The resulting percentage is the LTV ratio:
The formula is:
Loan= % x value ( or sales price whichever is less)
LOAN TO VALUE RATIO
Loan
P
\_\_\_\_\_\_\_\_\_\_\_\_\_. Works the same as P= R x W
Value. |. Rate
W. |. R
Loan = Rate x Value
Rate= divide loan by Value
Value= divide loan by Rate
Down payment
Down payment = (100% - LTV%). X Value (sales or appraised value)
Identify the variables:
80%. ®
90,000. (W)
Loan fees (or Points)
Fees
P
_______________
Loan amt|. Points
W. |. R. Loan Fees= points x loan amt
Points= divide fees by loan amt.
Loan Amt = divide fees by points
Identify the variables
INTEREST
USUALLY EXPRESSED AS AN ANNUAL PERCENTAGE WHICH IS CALLED THE INTEREST RATE.
When using formula make sure the interest is annual( one year)
Annual interest ℗ = Rate ® x loan Balance (w)
P= W x R. To find. Annual Interest :multiply whole by rate.
R= to find rate , divide. Annual interest Rate by Loan
W=. To find loan, divide annual interest Nuuanu rate
Interest
Note that interest in the formula is annual interest.
Therefor before solving any interest problem, be sure the interest is for 1year.
If NOT, YOU MUST CONVERT:
If given monthly interest, multiply it by 12
If given quarterly interest, multiply by 4
If given interest for 5 years, DIVIDE IT BY 5
If the problem is to determine the interest for a period of other than a year, solve the problem, to find the annual interest then
Convert the answer accordingly.
If you are told the total interest paid and need to determine the length of time
Solve the problem to determine annual interest
Divide annual interest by total interest to get the numbers of years paid.
You borrow $3750@7.2% interest. If you have paid $405 in interest to date, you’ve had the loan for how long?
In some problems you may be presented with more than 1 percentage.
If so create the formula for each percentage given.
Example: a lender gives a loan of 57% of the value of the lot. The interest rate is10.2% and the first year’s interest is $1505.83.
What is the value of the lot?
Annual interest= rate x loan
To find value, use the loan to value ratio.
Loan= LTVr x value
A finance problem may involve calculating the principal portion of a loan payment.
There is no formula. To calculate principle payment directly.
Example: A monthly payment is $180.00. If the loan balance is $20,000 and the interest rates 9%, what portion of the payment applies to principle?
Annual Interest= 9% of the Loan Balance
Find the annual interest. Divide by 12 to get monthly interest.
Subtract the interest from the monthly payment.
To calculate the principle for next month, start over with the new loan balance.
Another variation of Amortized loans is to determine the total interest. To be paid on a loan.
For example: for $20,000 loan, payments are $180 a month. Interest is 9%. Term is 25 years.
To determine the total interest, just determine the total of all payments made and subtract the original loan amount.
Example: 180 x 12 month x 25 years=. Total interest and subtract it from the original loan amount.
To do by calculator
Enter the mortgage amount
Mortgage terms
Interest rate
Seller’s profits and Costs
Always ask what is the part (P). = Rate (Rate) xWhole (W)
While reading terms like,”profit”, commission, expenses, investment
Seller’s Proft
Profit is expressed as a percentage of its original cost of the property( or amount invested) and the selling price.
To find the dollar amount of profit based on original cost
Profit. =%. Rate x original Cost (or investment W)
Example: a person bought a house for $240000. And sold it for 10% of profit. The dollar amount of profit is?
Seller’s Profit
To find the sales price based on a profit percentage of original cost. Sales Price (p) = (100% added by profit% ) (R) x Original Cost ( or investment). (W)
Sellers Expenses
Net profit is selling property less any expenses I.e. commission, title expenses and loan payoff fees.
To calculate a seller’s net profit , the amount of expenses to deduct from selling pric must be determined.
The formula
Sellers Expenses. (P) = %( R) x Salesprice. (W)
example. a person sold a house for 240000. his closing costs are estimated to be 10% of the sales price
Taxes. The tax levied on real property is a percentage of the assessment value. The assessed value may be a percentage of the market value.
The tax rate is expressed as a percentage or as dollars per hundred or thousands of dollars.
Formula for finding tax and assessed values are:
Tax ( P) = % ( R) x Assessed value (W)
And
Assessed value (P) = % (R) x Market Value. (W)
answering tax questions may require using both formulas, solving one value to use in solving the second
For example: the market value is 200,000. Assessed value is 70% of market value. The tax rate for the area in which the property resides is $15 per $1000 ( or 1.5%)
The math to determine the annual tax due on the property
Formula
Assessed Value= Rate xMarket Value
Formula
Annual Tax=. Rate % x Assessed Value
APPRAISAL FORMULAS
Capitalization: the income approach aka capitalization approach
Value equals price a person pays now for the right to receive income from the property in the future.
To convert future annual net income to present value :
I=. E x V
Income (annual net) = Rate (cap rate) x Value
I is given as net.
ANNUAL NET INCOME
Before proceeding it may be necessary to determine the annual net income.
The following examples use info provided in the question to find:
- Annual gross income
- Effective gross income
- Operating expenses
- Annual net.
Annual Gross Income-equals total mo. Income from all units in building multiplied by 12
- Effective Gross Income: it is unlikely that all units will be continuously be occupied during every month, so effective gross income is used.
To determine effective gross income, subtract the vacancies from the annual gross income.
Example: a building has 40 units that rent for $600 per month. Assume vacancies are 10%, operating expense are 45% of gross income and capitalization rate(cap rate) is 12%.
Known annual gross= 288,000
Find effective gross income
Annual gross income- vacancies= effective gross income
Steps. 100% - 10% vacancies = 90%
90% x 288,000= 259,200
- Operating Expenses may be given as a percentage in the question
Multiply the effective gross income by the rate to find operating expenses
Example: a building has 40 units renting for $600.00 a month. Assume vacancies are 10%, operating expenses are 45% of gross income and the cap rate is 12%.
Known: annual gross income= $288,000
Effective gross income = $259,200
Find Operating Expenses
45% of effective gross income
45% x $259,200 = $116,640. Operating expense
- Annual net Income.
Subtract operating expenses from effective gross income to find annual net income.
Example: building has 40 units at $600. Per month. Assume vacancies at 10%.
Operating expenses are 45% of gross income and cap rate is 12%
Known: annual Gross Income = $288,000
Effective Gross Income = $259,200
Operating Expenses = $116,640.
Find: Annual Net Income
Effective Gross Income -Operating expenses
Step. $259,200 - $116,640. =$142,560. Annual Net Income
Solve: I = R x V
To find Income: multiply Rate and Value
To find rate: divide income by value
To find value: divide income by Rate
Example: building has40 units renting $600./ mo. Assume vacancies are10%, operating expenses are 45% of gross income and the cap rate is 12%.
What is the appraised value of the building?
Steps:income: $242,500
Cap rate: 12%
What is value?
V= I divided by R
V= $142,560 divided by 12% V = $142,500 divided by .12 V= $ 1,188,000
GROSS RENT MULTIPLIER THIS IS THE INCOME APPROACH FOR RESIDENTIAL PROPERTIES.
A gross rent multiplier relates the value of a property to its rent.
The formula for a gross rent multiplier is:
Value (or sales price) = Monthly Gross Rent x Multiplier
This is the exception to the PRWmodel.
Gross rent multiplier the formulas the Whole is equivalent to the Part multiplied by the Rate or W = P x R
To find Value: Multiply Gross Rent and Multiplier
To find Multiplier: Divide Value b Gross Rent
To findGrossRent: Divide Value by Multiplier
Example. A property rented for$500 per month and the multiplier was 150. What is Value of the Property.
Gross rent $500/mo
Multiplier: 150
Value. ?
W= P x R W= $500 x 150 W= $75,000
The Multiplier
is obtained by dividing the sales prices of comps by their rent.
A example: A house sold for $150,000 and rented for $1,000 per month.What is the multiplier?
Sale Price= $150,000
Gross rent: $1,000.
Multiplier ?
R= W divided by P R= $150,000 divided by $1,000 R= 150
A variation of the Gross Income Multiplier used for Ap. Buildings.
The gross income multiplier is based on Annual Income rather than monthly.
Number of units x rent x 12 mos. before proceeding then treat like the formula for
Gross Rent Multiplier
Value = Annual Income x Multiplier
Cost Approach most common for specialty property ie single use factories, churches etc.
Calculating Estimated Value
Replacement Cost - Depreciation = Value of Improvements + Land Value = Property Value
Cost approach
Straight Line Depreciation method by solving for
- Annual. Depreciation by dividing cost by economic life
- Total Depreciation by multiplying annual depreciation by the age
- Currant Value by subtracting the total depreciation from the cost
This may be enough to answer questions, but others may require solving for all three values and possibly calculating these values into the future or the past.
Using a percent (R) instead of a number may ease moving values between the formulas .
- ANNUAL DEPRECIATION= (100% divided by Economic Life) x Cost
The parenthetical 100% will be divided by some #to give (R) as expressed in %.
example: if a building has an economic life of 50 years
Annual depreciation= (100% divided by 50 years) x Cost
2% x Cost
If a building is valued at $250,000 and has an economic life of 40 years, its annual depreciation would be:
100% divided by 40 = 2.5
2.5 convert to .025 x 250,000
$6250.
TOTAL DEPRECIATION
Total Depreciation= (Age x Annual Depreciation%) x Cost
Example: a 10 year old building with a 50 year total economic life would have total depreciation calculated as follows:
Annual Depreciation= (100% divided economic life) x Cost Annual depreciation (100% divided by 50 years) x cost Annual depreciation= 2% x Cost
Total depreciation= (Age x Annual Depreciation) x Cost
Total depreciation= (10 years x 2%) x Cost
Total depreciation= 20% x Cost
CURRENT VALUE FORMULA
CURRENT value= (100% - total depreciation%) x cost
The current value is what is left of the 100% after deducting appreciation.
The previous building has depreciated 20%
Example: a 10 year old building with a 50 year total economic life lif would have total depreciation calculated as follows:
Annual Depreciation= (100% divided by economic life) x cost
Annual Depreciation= (100% divided by 50 years) x cost
Annual depreciation = 2% x cost
Total Depreciation= (age x annual depreciation) x cost
Total depreciation= (10 years x 2%) x cost
Total depreciation= 20%x cost
Current Value= (100% minus total depreciation) x cost
Current value= (100% - 20%) x cost
Current Value= 80% x cost
