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Real Estate School Study Section > Real Estate Math I > Flashcards

Real Estate Math I Flashcards

1
Q

1 acre

A

43,560 square feet

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2
Q

1 square yard

A

9 square feet

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3
Q

Convert feet to inches:

A

multiply the number of feet by 12

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4
Q

Convert inches to feet:

A

divide the number of inches by 12

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5
Q

Convert yards to feet:

A

multiply the number of yards by 3

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6
Q

Convert feet to yards:

A

divide the number of feet by 3

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7
Q

Convert sq. feet to sq. inches:

A

multiple the number of sq. feet by 144

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8
Q

Convert sq. inches to sq. feet:

A

divide the number of square inches by 144

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9
Q

Convert sq. yards to sq. feet:

A

multiply the number of sq. yards by 9

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10
Q

Convert sq. feet to sq. yards:

A

divide the number of sq. feet by 9

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11
Q

Here are the 3 variations of the Made-Paid formula.

A

Made equals Paid times Rate
Paid equals Made divided by Rate
Rate equals Made divided by Paid

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12
Q

Here are the 3 variations of the Made-Paid formula.

A
  • Made = Paid x Rate
  • Paid = Made ÷ Rate
  • Rate = Made ÷ Paid
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13
Q

Effie, a real estate salesperson, found a buyer for a $600,000 house. The
seller agreed to pay a 6% commission on the sale to Effie’s broker. Effie is on
a 50-50 split with her broker. What is the amount of her commission?

A

Known: P (Sales Price, $) and R (Commission Rate %)
P = $600,000
R = 6% or 0.06

Unknown: I (Commission Income, $) What we do not know is the dollar amount of the commission paid to the salesperson Effie. First, the total commission paid to the broker must be calculated, then calculate the amount due Effie.

Formula: I = P x R, or Commission Income = Sales Price x Rate
I = P x R
I = $600,000 x 0.06
I = $36,000 (Total commission income earned by the broker.)
Effie’s commission = ½ of the total commission earned
Effie’s commission = $36,000 ÷ 2
Effie’s commission = $18,000

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14
Q

Paul, a real estate broker, listed a parcel of land for $500,000, with a commission of 10%. A few days later he presented an offer which was 5% less than
the listed price. The seller agreed to accept the price if the broker would reduce his commission by 15%. If Paul agrees to the seller’s proposal, how much will his commission be?

A

Known: P (Sales Price, larger $) and R (Commission Rate, %)
P = $500,000 less 5% ($25,000) = $475,000
R = 10% less 15%
[First calculate 15% of 10% (0.15 x 0.10 = .0150), then subtract it from 10% (.10 - 0.015 = 0.085, or 8.5%]
Unknown: I (Commission Income, smaller $)
What we do not know is the amount of the commission income.
Formula: I = P x R, or Commission Income = Sales Price x Rate
I = P x R
I = $475,000 x 0.085
I = $40,375

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15
Q

(P) Principal:

A

dollar amount of money borrowed, loan amount

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16
Q

(I) Interest:

A

charge for the use of money

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17
Q

(R) Rate:

A

percentage of interest charged

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18
Q

(T) Time:

A

duration of loan

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19
Q

Interest and loan problems involve these three variables:

A 
Paid = P = $ = Principal
Made = I = $ = Interest
Rate = R = % = Interest Rate
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20
Q

When the amount of principal and interest rate (%) are given and you are solving for amount of interest earned (smaller $), use:

A

I = P x R x T (Interest= Principal x Rate x Time)

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21
Q

When the interest income and interest rate are given and you are solving for the principal (larger $), use:

A

P = I ÷ (R x T) [Principal = Interest ÷ (% Rate x Time)]

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22
Q

When the interest income and the principal are given and you are solving for % (interest rate), use:

A

R = I ÷ (P x T) [Rate = Interest ÷ (Principal x Time)

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23
Q

Andrea borrowed $6,000 for one year and paid $520 interest.

What was the interest rate she paid?

A

Known: I (Interest Income), P (Principal), and T (Time)
P = $6,000 (Principal amount of loan)
I = $520 (Interest income bank made on the loan)
T = 1 year
Unknown: I (Interest Rate)
What we do not know is the interest rate Andrea paid.
Formula: R = I ÷ (P x T), or Rate = Income ÷ Principal x Time
R = I ÷ (P x T)
R = $520 ÷ ($6,000 x 1)
R = $520 ÷ $6,000
R = 0.0867 or 8.67%

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24
Q

If one month’s interest is $50 on a five-year,straight interest-only note, and the interest rate on the note is 10% per year, what is the amount of the loan?

A

Known: I (Interest Income), P (Principal), and T (Time)
I = $600 (Interest income bank made on the loan)
($50 per month x 12 months = $600)
R = 10% or 0.10
T = 1 year
Unknown: P (Principal)
What we do not know is the larger $ amount of the loan.
Formula: P = I ÷ (R x T), or Principal = Interest ÷ (Rate x Time)
P = I ÷ (R x T)
P = $600 ÷ (0.10 x 1)
P = $600 ÷ 0.10
P = $6,000

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25
Q

Discounting note problems involve these three variables:

A
  • Made = I = $ = Income (Interest + discount)
  • Paid = P = $ = Amount Paid (Note amount less discount)
  • Rate = R = % = Rate of return on investment
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26
Q

When the amount of money paid and the rate of return (%) are given and you are solving for income or profit (smaller $), use:

A

I = P x R (Income = Amount Paid x Rate

27
Q

When the income and rate of return are given (%) and you are solving for the amount paid (larger $), use:

A

P = I ÷ R (Amount Paid = Income ÷ Rate

28
Q

When the income and the dollar amount invested are given and you are solving for % (rate of profit) use:

A

R = I ÷ P (Rate = Income ÷ Amount Paid)

29
Q

Tex signed a note for $3,000, in favor of (or owed to) a private lender, which is to be paid off in 12 months. He owes the $3,000 plus 9% interest when the note is due. An investor buys the note at a 20% discount. What is the rate of return on the amount invested by the investor?

A

Known: I (Income) and P (Amount Paid)
I = Income (Calculate the interest and the discount)
Interest = $3,000 x 0.09 = $270 (interest owed on due
date).
Discount = $3,000 x 0.20 = $600 (20% discount allowed
investor)
I = $870 ($270 + $600)
P = Amount Paid (Calculate the discount and subtract from the
amount of the note.)
Discount = $3,000 x 0.20 = $600
P = $2,400 ($3,000 - $600)
Unknown: Rate (Rate of Return on amount invested)
What we do not know is the rate (%).
Formula: R = I ÷ P or Rate = profit) ÷ Paid (invested):
Rate = Profit ÷ Amount Invested
Rate = $870 ÷ $2,400
Rate = 36.25%

30
Q
  • Paid = Value of Property
  • Made = Annual Net Income or Loss
  • Rate = Capitalization Rate
A
  • Paid = Value of Property
  • Made = Annual Net Income or Loss
  • Rate = Capitalization Rate
31
Q

Capitalization problems involve these three variables:

A 
Made = I = $ = Net Operating Income (NOI)
Paid = P = $ = Value of Property
Rate = R = % = Capitalization Rate (Cap Rate)
32
Q

When the amount of value of the property and the cap rate (%) are given and you are solving for the NOI (smaller $), use:

A

I = P x R (NOI = Property Value x Cap Rate)

33
Q

When the NOI and capitalization rate are given and you are solving for the value of the property (larger $), use:

A

P = I ÷ R (Property Value = NOI ÷ Cap Rate)

34
Q

When the NOI and the property value are given and you are solving for % (capitalization rate), use:

A

R= I ÷ P (Cap Rate = NOI ÷ Property Value)

35
Q

A duplex brings in $600 per month per unit. Gail and Kevin are interested in buying the property as an investment, and need an investment rate (capitalization rate, or cap rate) of a 10% return. What should Gail and Kevin pay for the duplex?

A

Known: I (NOI) and Rate (Cap Rate)
I = $600 per unit x 2 units = $1,200 net income per month
$1,200 x 12 months = $14,400 annual net income
R = 10% or 0.10
Unknown: P (Value of the Property)
What we do not know is what they should pay for the duplex.
Formula: P = I ÷ R, or Property value = NOI ÷ Cap Rate
P = I ÷ R
P = $14,400 ÷ 0.10
P = $144,000

36
Q

Shirley paid $900,000 for an eight-unit apartment building. The gross income is $800 per month per unit, with expenses of $4,000 annually. What capitalization rate (%) will Shirley make on her investment?

A

As you recall, net operating income, rather than gross income is used to calculate a capitalization rate. Therefore, the first step is to calculate the
gross income and then subtract the annual expenses to arrive at the net operating income.
Gross Income = $800 per month x 8 units = $6,400 per /month x 12
months = $76,800 annual gross income.
Annual Expenses = $4,000
Net Operating Income = $76,800 - $4,000 = $72,800
Known: I (NOI) and P (Property value)
I = $ 72,800
P = $ 900,000
Unknown: R (Cap Rate)
What we do not know is the capitalization rate.
Formula: R = I ÷ P, or Cap Rate = NOI ÷ Property value
R = I ÷ P
R = $72,800 ÷ $900,000
R = .081 or 8.1%

37
Q

Investment problems involve these three variables:

A 
Made = I = $ = Income or profit earned
Paid = P = $ = Amount Paid or invested in the Property
Rate = R = % = Rate of Return or Profit
38
Q

When the amount of money invested and the rate (%) are given and you are solving for $ (smaller dollar amount) use:

A

I = P x R (Income = Amount Paid x Rate of Return)

39
Q

When the income and rate of return are given and you are solving for $ (larger dollar amount) use:

A

P = I ÷ R (Amount Paid = Income ÷ Rate of Return)

40
Q

When the income and the dollar amount invested are given and you are solving for % (percentage of rate of profit) use:

A

R = I ÷ P (Rate of Return = Income ÷ Amount Paid)

41
Q

Steve has a savings account and wants to earn $100 per month in interest. If the account pays 4% interest, how much should Steve keep in the account?

A 
Known: I (Income) and R (Cap Rate)
I 	= $1,200 per year ($100 x 12 months)	
R = 4% or 0.04
Unknown: P (Amount Paid)
The amount of the investment is what we do not know.
Formula: P = I ÷R, or Amount Paid = Income ÷Rate
P = $1,200 ÷ 0.04
P = $30,000
42
Q

Mitch bought a house for $145,000. The house was later sold for $165,000. What is the rate (%) of profit Mitch made on this sale?

A 
Known: P (Amount Paid) and I (Income)
P = $145,000
I = $20,000 ($165,000 – $145,000)
Unknown: R (Rate)
The rate of profit is not known.
Formula: R = I ÷ P, Rate = Income ÷ Amount Paid
R = $20,000 ÷ $145,000
R = 13.8 or 13.8%
43
Q
  • Paid = Purchase Price or Cost
  • Made = Selling Price
  • Rate = Profit or Loss Rate
A
  • Paid = Purchase Price or Cost
  • Made = Selling Price
  • Rate = Profit or Loss Rate
44
Q

Profit or Loss on Sales involves these three variables:

A 
Made = I = $ = Increase in value
Paid = P = $ = Purchase price or original cost of Property
Rate = R = % = Rate of Return (profit or loss)
45
Q

When the purchase price and the rate of return (%) are given and you are solving for the sales price (increase in value), use:

A

I = P x R (Increase = Purchase Price x Rate)

46
Q

When the sales price (increase in value) and rate of return are given and you are solving for the original purchase price, use:

A

P = I ÷ R (Purchase Price = Increase ÷ Rate)

47
Q

When the sales price (increase in value) and the original purchase price are given and you are solving for % (rate of return), use:

A

R = I ÷ P (Rate = Increase ÷ Purchase Price)

48
Q

Review – Calculating the Rate of Profit or Loss

A

When a profit is made add the % to 100%
(15% profit: 100% + 15% = 115% rate or 1.15)

When a loss occurs subtract the % from 100%
(20% loss: 100% - 20% = 80% or 0.80)

49
Q

Maureen sold a rural cabin for $30,000, which allowed her to make a 20% profit. What did she pay for the property?

A

Known: I (Increase) and R (% Rate of profit)
I = $30,000 (Increase earned on the sale of the property. The amount actually earned is the smaller $ because it is the difference between the selling price and the original purchase price.)
R = 100% + 20% = 120% = 1.20
Unknown: P (Purchase Price)
What we do not know is the larger $ amount that she paid for the property.
Formula: P = I ÷ R, or Purchase price = Increase ÷ Rate
P = $30,000 ÷ 1.20
P = $25,000
The circle concept for Practice Problem #10.
• Paid = Purchase Price or Cost
• Made = Selling Price
• Rate = Profit or Loss Rate
If a profit is made add the % to 100%
We have determined that she paid $25,000 for the property and sold it for $30,000, which is an increase in value of $5,000 (the smaller $ amount). Is $5,000 a 20% profit? We can determine this by using the formula: R = I ÷ P. We know the increase in value is $5,000 and that she paid $25,000 for the property, so we divide $5,000 by $25,000 to get the rate of profit, which is 0.20 or 20%.
You may be asked to find the selling price or amount of a loan when the seller receives a net amount.

50
Q

A farmer put his land on the market, wanting to net a certain amount. The real estate agent who found a buyer gave the farmer a check for $90,000, after
deducting a 10% commission. What was the selling price of the farm?

A

Known – I (Net Income) and R (Commission Rate)
I = $90,000 (Income made from sale)
R = 100% – 10% = 90% or 0.90 (Commission rate)
Unknown – P (Selling Price)
What we do not know is the selling price of the farm.
Formula: P = I ÷ R, or Selling Price = Income ÷ Rate
P = I ÷ R
P = $ 90,000 ÷ 0.90
P = $100,000 (Selling Price)

51
Q

Review - Proration

The Proration Process:

A
  1. Determine the number of days to be prorated.
  2. Calculate the cost per day.
  3. Multiply the number of days by the cost per day.
  4. Decide whether the item should be a credit or a debit to the seller or to the buyer.
  5. Expenses that have been paid to some time after escrow closes, credit the seller and debit the buyer.
  6. Expenses that will be due after the close of escrow, debit the seller and credit the buyer.
52
Q

Common Expenses that usually are prorated:

A
  • Property taxes
  • Interest on assumed loans
  • Fire and hazard insurance
  • Rents
53
Q

Lynn sold her home on September 1, 2010. She has an existing loan of $200,000 on the house. The interest on the loan is 8%. Terry took over Lynn’s loan with interest paid to August 15, 2010. Terry also assumed an
existing three-year fire insurance policy for $360 per year, paid by Lynn until November 15, 2011. Lynn also owes property taxes of $1,900 for the year.

A

Calculate the following:
• Prorate interest, and who is credited or debited
• Prorate insurance, and who is credited or debited
• Prorate tax, and who is credited or debited
1. Prorate the interest:
August 15 to September 1 = 15 days
$200,000 x 8% = $16,000 annual interest
$ 16,000 ÷ 360 days in year = $44.44 per day
15 days x $44.44 per day = $666.60 interest
Credit the buyer and debit the seller.
2. Prorate the insurance:
September 1, 2010, through November 15, 2011 = 435 days
$360 ÷ 360 = $1.00 per day
435 days x $1.00 = $435
Credit the seller and debit the buyer.
3. Prorate the property taxes:
July 1 to September 1 = 60 days
$1,900 ÷ 360 = $5.27 per day
60 days x $5.27 = $316.66
Debit the seller and credit the buyer.

54
Q

Review - Basic Area Formulas
The Area of a Square = Length x Width
The Area of a Rectangle = Length x Width
The Area of a Right Triangle = Altitude x Base ÷ 2

A

Review - Basic Area Formulas
The Area of a Square = Length x Width
The Area of a Rectangle = Length x Width
The Area of a Right Triangle = Altitude x Base ÷ 2

55
Q

Felix owned four acres of land with a front footage of 500 feet along the street.
What is the depth of the land?

A 
Known – Area and Width
Area = 4 acres or 174,240 sq. ft. (43,560 sq. ft. per acre x 4 acres)
Width = 500 feet
Unknown – Length
What we do not know is the length (depth) of the parcel.
Formula – Length = Area ÷ Width
Length = 174,240 sq. ft. ÷ 500 feet
Length = 348.48 feet
56
Q

Property tax payments are due on December 31 for the fiscal year. Property taxes are $4,800 per year. The property is sold on April 30. What is the proration?

A

The seller owns the property for 120 days (Jan = 31; Feb= 28, March = 31; April = 30) while the buyer owns the property for the rest of the year, which is 245 days..
The seller needs to compensate the buyer, as he will pay the entire year’s tax bill on December 31.

$4,800/365 = $13.15 tax per day $13.15 x 120 days = $1,578 seller to buyer proration

57
Q

The property tax payment is due on November 1 for the fiscal year. Property taxes are $6,400 per year. The closing is November 10. What is the proration?

A

The seller just paid the tax bill for the entire year, including the 10 months + 10 days he owned the property, and the rest of the year, that the buyer will own the property through to December 31 when the tax year ends. November has 30 days. The buyer owns the property 20 of those days, plus the 31 in December, for a total of 51 days in the tax year. The buyer needs to compensate the seller.
$6,400/365 = $17.53 tax per day
$17.53 X 51 days = $894.03 buyer to seller tax proration

58
Q

Accrued Interest:

A

Accrued interest payments occur at the closing when the seller has a mortgage payment that was paid on the first day of the month and the closing occurs during the month with the buyer assuming the loan. For example, the interest payment for the month is $900 paid in advance and the closing is on the 20th of the
month. The buyer owes the seller 10 days of interest. The amount of the proration is $900 divided by 30 days = $30 per day times 10 days yielding $300 as the proration.

59
Q

Proration of payments “in advance”

A

Insurance: Property insurance is paid in advance. However, in most cases the buyer obtains his or her own property insurance and proration of insurance payment is not an issue at closing. If the buyer accepts or assumes the seller’s property insurance, the proration process involves reimbursing the seller for the prepaid insurance premiums. The proration is for any 365 day period. So, one must determine the starting and ending dates of the policy, and calculate how many days of the policy period the seller has used while owning the property, and how many the buyer will use until the end of the policy period. Then the buyer must reimburse the seller for the pre-paid insurance amount that the buyer will use.

60
Q

Proration of payments “in advance”

You have a closing July 26. The buyer will be assuming the seller’s homeowner’s insurance policy, on which coverage began October 20. The annual premium is
$2,690. What is the insurance proration?

A

The seller will receive a refund for $626.44. The insurance bill is paid in advance for 365 days starting Oct 20, and ending Oct 19 the following year. Buyer will use the remainder of the policy period after closing day July 26. That is 5 days in July, plus August, Sept, and 19 days in Oct, or a total of 85 days.

Proration calculation is $2,690/ 365 days X 85 days = $626.44

61
Q

Rent:

A

Rents are also paid in advance and typically on a monthly basis. The owner of an income property receives rent payments on the first of the month every month during the fiscal year. If the owner received $5,000 in monthly rents for the apartments or retail space and then sells the property on the 12th day of the month, proration must take place for the income, so that it is divided between the buyer and the seller according to their ownership dates. The seller must compensate the buyer. For example, the owner/seller owns the property for 12 days in April while the buyer
owns the property for 18 days or a total of 30 days in the month of April. The seller must provide 18 days of rental income to the buyer.

$5,000 times (18/30) = $3,000

62
Q

Pre-paid Interest:

A

Pre-paid interest occurs at the closing when the buyer/borrower must pay for the use of the new loan amount from the closing date to the end of the
month. If the closing is on March 15 the first mortgage payment is generally scheduled for May 1. This timing makes sense when you realize that mortgage
payments are customarily paid in arrears in Georgia. The May 1 payment covers April. The borrower owes the interest for March 15 to March 30; this is the pre-paid interest. If the loan amount is $100,000 at 5% per annum, the interest payment is $5000 for the first year. The pre-paid interest is $5000 divided by 360 equaling
$13.89 per day times 15 days yielding $208.33 for the pre-paid interest.

63
Q

Transfer Tax

A

At the closing the property ownership transfers from the seller to the buyer, from the grantor to the grantee. The county taxes this transfer. The formula for the transfer tax is:
(Sales Price – Assumed Debt) times 0.1% This formula simplifies to: (Sales Price – Assumed Debt) / 1000 =
Transfer Tax

64
Q

Sale Price x Commission Rate = Commission $
Commission $  Commission Rate = Sale Price
Commission $  Sale Price = Commission Rate

A

Sale Price x Commission Rate = Commission $
Commission $  Commission Rate = Sale Price
Commission $  Sale Price = Commission Rate

Real Estate School Study Section (23 decks)

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