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
