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Flashcards in Chapter 1 Math Deck (39):

Total Commission

=Sales price X rate of commission


Commission Rate

=Commission ÷ Price


Property price

=Commission ÷ Commission Rate


Percentage of Profit

= Profit ÷ Original cost


Profit margin

= Profit ÷ Selling price



$ paid in return for use of money, borrowed at rate of interest for specific time. Borrower repays.


Simple interest

$ only for amount of principal borrower owes


Interest formula

= principal x rate x time


Interest formula example

The interest rate on a $2,250 loan for 1 year at 7 percent interest is $157.50.
=$2,250 x .07 x 1 = $157.50


Add on Rate

Interest on total amount of the loan for loan term.
Added to total principal before payments calculated.
Add-on interest almost doubles the simple interest rate.
Calculating interest as a percentage of the original amount of loan (principal), rather than interest on the balance due prior to each payment.
Used for home improvement loans; junior liens.
Borrower pay a higher effective rate of interest each month as the principal balance decreases.


AOI Formula

AOI = LA x I x N,

Add-on interest = loan amount x interest rate x number of payments.

1. Calculate AOI.
2. Add the interest amount to the total loan amount.
3. Divide the new total loan amount by the number of payments to get the monthly payment amount.


AOI Example

Loan of $2,250 at 7 percent for 1 year.

1. $2,250 loan amount x 7% interest x 1 (number of years);
2. $2,250 + $157.50 = $2,407.50
3. $2,407.50 ÷ 12 = $200.62


Add On Interest APR - Effective Rate

APR = 2 x n x I ÷ P(N +1)

APR = 2 x number of payment periods in one year x total financing charges ÷ principal, or amount borrowed x (number of scheduled payments +1)


Add on Rate APR Example

Loan of $2,250 at 7 percent for 1 year.
I = 157.50 (total financing charges)

2 x 12 x $157.50 ÷ ($2,250 (12 + 1) = APR
$3,780 ÷ ($2,250 x 13) = APR
$3,780 ÷ $29,250 = 12.9 percent


Effective Rate/APR

Nominal 7% interest per loan agreement results in borrower paying an effective rate, or APR of 12.9% .


Compound Interest

Computed on the principal amount + accrued interest.
Compound amount = Initial deposit (1 + Interest rate)n


Points 2 types

Cost of obtaining a new real estate loan. One-time service charge to the borrower for making the loan.

Prepaid interest, lender charges them to get additional income on loan.

Paid at closing and are usually equal to 1 percent of the loan amount.


Origination Points

Two (2) points on a $75,000 loan would be $1,500.
($75,000 x .01 x 2 points)


Discount Points (optional)

For lender offsets loss when selling the loan to secondary mortgage market. Raises effective interest rate on loan.

1/8 x Discount Points
Add that amount to interest rate


LTV Ratio

= (Loan amount ÷ Value)

relationship between a property's purchase price and its loan amount.

The higher the LTV, the greater loan amount to equity.
Lenders use it as UNDERWRITING STANDARD in QUALIFYING borrowers for loans.
If too high loan, can exceed property value.


Loan Amount

=LTV ratio x Property Value


Property Value

= Loan Amount ÷ LTV


Amortized Loans

Schedule of monthly payments

1. amount of loan
2. term
3. interest rate


Income Ratio

LIMIT percent of buyer's gross income he can spend on housing cost.

Formula = total house payment ÷ gross monthly income.

Conventional loans = less than 28%
FHA = 31% or less


Borrower's Debt Ratio

Buyer's monthly debt obligations

Formula = total monthly debt ÷ gross monthly income.

Conventional loans = 36% or less
FHA = 43% or less


Area of triangle

½ base x height


Price per square foot

=Sales price of home ÷ area

Example: A parcel of land that is 150' wide and 100 feet deep and sold for $140,000.

150 X 100 = 15,000 square feet
$140,000 ÷ 15,000 = $9.34 per square foot



43,560 square feet



10,000 square meters or approximately 2.47 acres

Example: A parcel of land is 40 acres.
40 ÷ 2.47 = 16.19 hectares



Expenses divided between seller and buyer.

-Mortgage interest


Prorating Paid in Advance

Items paid in advance = buyer will owe money to seller Ex: Rent & Insurance

Debit to Buyer (buyer pays $), Credit to Seller (seller receives $).

EX: Seller paid for insurance for the year and the transaction will close on September 18. The buyer owes seller the portion of the insurance that applies from September 19 to December 31.


Prorating Paid in Arrears

Incurred by seller but hasn't paid for them yet. Ex: Taxes & Utilities

Debit to Seller (seller owes $), Credit to Buyer

Ex buyer receives the sewer bill for the month of September. The charges from September 1-18 belong to the seller, buyer will be paying the bill.


The 12 month/30 day method

calculates the amounts due based on a 360-day year and a 30-day month. The steps of this method are as follows.

1. Identify an item and the amount needing to be prorated.
2. Divide by 12 to get the monthly rate.
3. Divide by 30 to get a daily rate. (Day of closing is seller's responsibility)
4. Multiply the monthly rate by the number of months the seller owned the property before closing to get the months-amount due.
5. Multiply the daily rate by the number of days the seller owned the property in the closing month to get the amount due for the closing month.
6. Add the two amounts to get the prorated amount for the seller.
7. Subtract the seller's prorated amount from the starting amount to get the buyer's prorated amount.


365-day method

1. Identify an item and the amount needing to be prorated.
2. Divide by 365 to get the daily rate. (Divide by 366 in a leap year.)
3. Multiply the daily rate by the number of days the seller owned the property before closing to get the seller's share.
4. Subtract the seller's prorated amount from the starting amount to get the buyer's prorated amount.


Rent example, paid in advance

A closing is set for March 23, and the tenant's rent is $950 per month. The seller owns the day of closing. How much rent credit does the buyer receive using the 365-day method?

1. The number of seller days is 23.
2. The daily rent amount is ($950 ÷ 31) or $30.6452
3. The proration amount is $704.84 ($30.6452 x 23)
4. $950-$704.84 = $245.16.

Credit the buyer and debit the seller $245.16.


Utility example, paid in arrears

Sellers owes that $, but buyer pays a portion of the seller's bill since bill comes at month end.

Power bill $350 in the month of closing, closing is set for February 16th, the seller owns the day of closing, and the 365-day method is used. The proration will be as follows:

Seller days = 16
Daily cost = $350 ÷ 28 = $12.50
Total proration amount = $12.50 x 16 days = $200

Debit the seller and credit the buyer $200


Buyer's loan interest example

Seller is not related to this transaction.

Buyer's new loan is for $200,000 at 5% interest and the day of closing is August 20th. The interest charge will be for the period between closing and the end of the month. If the buyer owns the day of closing, and the method to be used is the 360-day method, how much interest does the buyer owe?

The number of buyer days is 11 (remember, count them with your fingers!)

Daily interest charge is
$200,000 x .05 = $10,000 interest per year
$10,000 ÷ 360 = $27.78 interest per day
$27.78 daily interest x 11 days = $305.58 interest charge to buyer. CREDIT buyer.


Seller's loan interest

Lender provides a payoff number for period between the last full payment and closing date. DEBIT to seller.


Debit & Credit reminder

Debit is taken away from someone; credit is given to someone.