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Gold Coast schools math
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Gravity
Terms in this set (115)
6 miles by 6 miles
The dimensions of a township
36 square miles
the number of square miles inn a township
1 mile by 1 mile
(1 mile square)
The dimensions of a section
640 acres
The number of acres in each section
640 acres
_______________
4. = 160 acres
the number of acres in the south east (SE) 1/4 of a section
640 acres
_______________
2. = 320 acres
the number of acres in the west (W) 1/2 of a section
640 acres divided 4 divided 4 = 40 acres
the number of acres in the southwest (SW) 1/4 of the northwest (NE) 1/4 of a section
640 acres divided 4 divided 2 divided 4 = 20 acres
the number of acres in the southwest (SW) 1/4 of the Northeast (NE) 1/2 of the Northwest (NW) 1/4 of a section
tract 1:
640 acres divided 4 divided 2 = 80acres
tract 2:
640 acres divided 4 divided 4 = 40 acres
total =120 acres
the number of acres in two contiguous tracts with the following legal description:
S 1/2 of the NE 1/4 and the NE 1/4 of the SE 1/4 of Section 10,
T26S, R18E
1 acres = 43,560 square feet
The number of square feet in an acre
2 acres
X 43,560 sq. ft.
______________________
87,120 sq. ft.
The number of square feet in a two-acre lot
2 acres
X 43,560 Sq. Ft.
______________________
= 87,120 Sq. Ft.
87,120 sq. ft.
________________
240 ft. = 363 ft.
the depth of a two-acre lot with a front foot measurement of 240 ft
($240,000 x 0.06)
_______________________
2. = $7,200
The commission due to the selling broker with a 6% commission on a $240,000 sale, split 50/50 with the buyer's broker
$217,000
0.07
X 0.60
_______________
$9,114
The commission on a $217,000 sale due to a sales associate when the broker charges a 7% commission and the sales associate receives 60% of the broker's commission
($100,000 x .05)
+ ($75,000 x .06)
+ ($25,000 x .07)
_______________________
$5,000
$5,000
+ $4,500
+ $1,750
____________
$11,250
(this is a sliding scale commission)
The commission due to a broker on a $200,000 sale when the broker charges 5% on the first $100,000, 6% on the next $75,000 and 7% on the balance
- total = $196,000 + $4,000 = $200,000
- 100% - 6% = 94%
- listing price = $200,000 divided 0.94 = $212,766
(this is a net listing)
The listing price needed when the owner requires a net of $196,000 the estimated closing costs are $4,000 and the broker's commission is 6%
loan amount
x 1% (or 0.01)
The formula for determining the amount paid at closing by a borrower for one discount point
Loan amount
x 3% (or 0.03)
The formula for determining the amount paid at closing by a borrower for 3 discount points
Loan amount
x 2.5% (or 0.025)
The formula for determining the amount paid at closing by a borrower for 2 1/2 discount points
$100,000
x. 0.03
______________
$3,000
the dollar amount charged for a 3 loan origination points on a home that sold for $150,000 with a $100,000 loan
$100,000
x 0,025
____________
$2,500
you can also think of it as:
$2,000 (for 2 points)
+ $500 (for 1/2 points)
_____________________________
$2,500
The dollar amount charged for 2 1/2 loan origination points on a home that sold for $150,000 with a $100,000 loan
$100,000
x 0.0275
____________
$2,750
The dollar amount charged for 2 3/4 loan origination points on a home that sold for $140,000 with a $100,000 loan
Loan amount
x 2% (or 0.02)
the formula for determining the amount paid at closing by a borrower for 2 discount points (up from charge to decrease the monthly interest rate)
$200,000
x 0.02
____________
$4,000
The dollar amount charged with 2 discount points on a $200,000 loan
$200,000
x 0.02
______________
$4,000 (for discount)
$200,000
- $4,000
__________
$196,000 (paid by lender)
(Borrower loan amount remains $200,000)
The dollar amount that the lender will credit (pay) the buyer at closing to lower the interest rate for 4 1/2% to 4 1/2% for a $200,000 loan with 2 discount points
For each point paid upfront tot he lender, the effective rate of interest increases approximately 1/8%
The mathematical rule of thumb for estimating the effective yield- the interest rate actually received by the lender after any points paid
- 4 points x 1/8% = 4/8% (or 1/2%)
- 5.75% Discounted rate + 1/2%
estimated increase in rate due to points paid = 6 1/4% effective rate paid by the borrower
The effective yield for a loan with a 2-point loan origination fee and a 2-point discount charged to reduce the interest rate from 5% to 5 3/4%
monthly PITI
__________________
monthly gross income
the formula for determining the housing expense ratio
$720 Monthly PITI
divided $3,000 income = 0.24 or 24%
The housing expense ratio for a borrower with an expected monthly PITI payment of $720 and a stable monthly income of $3000
(monthly PITI + other monthly obligations)
divided monthly gross income
the formula for determining the total obligations ratio
($720 PITI + $480 Other obligations) divided $3,000 monthly income = 40%
The total obligations ratio for a borrower with a monthly PITI payment of $720, a monthly income of $3,000 and other monthly debt totaling $480
Loan amount divided purchase price (or appraised value)
The formula for determining the loan-to-value (LTV) ratio
$100,000
- $15,000
______________
$85,000 loan amount
$85,000 loan divided $100,000 = 0.85 or 85% LTV
The LTV ratio of the purchase of a $100,000 home with a down payment of $15,000
$120,000
- $24,000
______________
$96,000 loan
$96,000 divided $120,000 = 0.80 or 80% LTV
The LTV ratio for the purchase of a $120,000 home with a down payment of $24,000
$180,000 x 0.965 Max LTV ratio = $173,700 Max FHA loan amount
FHA loans plus closing cost must not exceed 96.5% of the home's value
The maximum loan amount (including closing costs) for an FHA loan on a $180,000 home
$180,000 x 0.965 Max LTV ratio = $173,700 Max FHA loan amount
$180,000 - $173,700 loan = $6,300 Minimum down payment
The minimum down payment required on an FHA loan for a $180,000 home
$154,00 x 0.965 Max LTV ratio = $148,610 rounded down to $148,600 Max loan
FHA loans are underwritten in $50 increments, rounded down
The maximum loan amount (including closing costs) for an FHA loan on a $154,000 home
I = P x R x T
Interest (I) = Principal (P) x Rate (R) x Time (T), where time is fraction of a year
The formula for calculating the interest portion for a fixed rate, level payment, amortized loan
I = P x R x T
Interest (I) = $10,000 (P) x 0.08 (R) x 1/12 (T) (multiplying by 1/12 is the same as divided by 12)
Interest = ($10,000 x 0.08) divided 12 = $66.67
The amount of interest paid with the 1st monthly payment on a $10,000 level payment loan at a rate of 8%
I = P x R x T
Interest = ($15,000 x 0.05) x 1/12 or
Interest = ($15,000 x 0.05) divided 12 = $62.50
The amount of interest paid with the 1st monthly payment on a $15,000 level payment loan at a rate of 5%
1 = P x R x T
Interest = ($10,000 x 0.08) divided 12 = $66.67
Principal part of the payment = $121.33 - $66.67 = $54.66
The principal amount paid with the 1st payment on a $10,000 level payment loan at a rate of 8% with monthly payments of $121.33
interest = ($10,000 x 0.08) divided 12 = $66.67
Principal = $121.33 - $66.67 = $54.66
New balance = $10,000 - $54.66 = $9,945.34
the new loan balance after the first monthly payment on a $10,000 level payment loan at a rate of 8% with monthly payments of $121.33
P = I divided (R x T)
Memory aide: write as shown and cross out the item you dont know
i
___________
P x R x T
the formula for determining the principal (P) if you know the amount of interest (I), the rate (R), and the time (T)
P= I
______
R x T
Principal (P) = $200 (I) divided (0.08 (R) x 0.5 (T)) = $2,000; six months is half of a year or 0.5
The principal amount for an interest only level payment term loan, at a rate of 8% for six months, with a monthly interest payment of $200
R = I
__________
P x T
The formula for determining the rate (R) if you know the amount of interest (I), the principal (P), and the time (T)
R = I
____________
P x T
Rate (R) = $810 (I) divided ($12,000 (P) x 0.75 (T)) = 0.09 or 9%
The interest rate on a $12,000 interest only, level payment term with interest due of $810 after nine months
T =. I
____________
P x R
The formula for determining the Time (T) if you know the amount of interest (I) the Principal (P) and the rate (R)
T =. I
_________
P x R
Time (T) = $600 (I) divided ($20,000 (P) x 0.12 (R)) = 0.25 of 1/4 of a year, which is 3 months
The amount of time that a $20,000 interest only, level payment loan with an interest rate of 12% with $600 in interest due has been outstanding
Fully indexed note rate =
5% index rate
+ 2% Margin
_______________
7%
The fully indexed note rate on an adjustable rate mortgage (ARM)win an index rate of 5% and a margin of 2%
APR = 5% + (2 pints x 1/8) = 5 1/4%
The estimated annual percentage rate (APR) that must be disclosed for a loan with an interest rate of 5% where two points will be paid
Seller days = 10
buyer days = 31 - 10 =21
The prorated number of seller and buyer days in the month of July if the seller owns the day of closing and the closing is on July 10th
Seller days = 16
Buyer days = 30 - 16 = 14
The prorated number of seller and buyer days in the month of September if the buyer owns the day of closing and the closing is on September 17
Daily rent = $540 divided 30 days = $18
buyer days = 30 - 20 = 10
Seller's share of the rent = $18 x 10 days = $180
(debit seller, credit buyer)
The seller's portion of the $540 rent collected from the tenant on the 1st of the month when closing is on the 20th of September and the day of closing belongs to the seller
Daily rent = $750 divided 30 days = $25
Buyer days = 30 - 7 = 23
Seller's share of the rent = $25 x 23 days = $575
(debit seller, credit buyer)
The seller's portion of the $750 rent collected from the tenant on the 1st of the month when closing is on November 8th and the buyer owns the day of closing
Daily interest = $300 divided 30 days = $10
Buyer days = 30 - 5 = 25
Prepaid interest = $10 x 25 days = $250
(debit buyer, under buyer's expenses)
The amount of prepaid interest on a new mortgage that the buyer must pay at closing when the monthly interest amount is $300 and the closing day, April 5, belongs to the seller
Daily interest = $465 divided 31 days = $15
Buyer days = 31 - 21 = 10
Prepaid interest = $15 x 10 days = $150
(debit buyer, under buyer's expenses)
The amount of prepaid interest on a new mortgage that the buyer must pay at closing when the monthly interest amount is $465 and the closing day, July 22, Belongs to the buyer
Daily interest = $372 divided 31 days = $12
Seller days = 12
Seller's interest = $12 x 12 days = $144
(debit seller, credit buyer)
The prorated amount of interest on an assumed mortgage that the seller must pay at closing when the January interest is $372 and the closing day, January 13 belongs to the buyer
Daily interest =
$330 divided 30 days = $11
Seller days = 2
Seller's interest = $11 x 2 days = $22
(debit seller, credit buyer)
The prorated amount of interest on an assumed mortgage that the seller must pay at closing when the June interest is $330 and the closing day, June 2 belongs tot he seller
Seller days = 31 (Jan) + 28 (Feb) + 11 (mar) = 70
Seller's share = ($2,500 divided 365 days) x 70 = $479.45
(debit seller, credit buyer)
The prorated amount of the unpaid property tax that the seller must pay at closing when the annual tax bill is $2,500 and the closing day, March 11 is allocated to the seller
Seller days = 31 (jan) + 28 (Feb) + 31 (Apr) + 5 (May) = 125
Seller's share = ($2,000 divided 365 days) x 125 = $684.93
(debit seller, credit buyer)
The prorated amount of the unpaid property tax that the seller must pay at closing when the annual tax bill is $2,000 and the closing day, May 6 is allocated to the buyer
Buyer days in December = 31 - 5 = 26
Buyer's share = ($3,000 divided 365 days) x 26 = $213.70
(debit buyer, credit seller)
The prorated amount of the $3,000 annual property tax already paid by the seller that the buyer must pay at closing when the closing day, December 5 is allocated to the seller
Tax units = $120,000 divided $100 = 1,200
tax on deed = 1,200 x $0.70 tax rate = $840
The amount of the state documentary stamp tax on the deed for a property in Brevard Country that sold for $120,000
Tax units = $265,550 divided $100 = 2,655.50 rounded up to 2,656 Tax Units
Tax on deed = 2,656 x $0.70 tax rate = $1,859.20
The amount of the state documentary stamp tax on the deed paid by the seller for a property in Palm Beach County that sold for $265,550
Tax units = $188,000 divided $100 = 1,880
Tax on note = 1,880 x $0.35 tax rate = $658
The amount of the state documentary stamp tax paid by the buyer on a new $188,000 mortgage
Tax units = $75,490 divided $100 = 754.9 rounded up to 755 tax units
Tax on note = 755 x $0.35 tax rate = $264.25
The amount of the state documentary stamp tax paid by the buyer on a new $75,490 mortgage
Assumed loan tax units:
$20,000 divided $100 = 200
New loan tax units:
$75,000 divided $100 = 750
Tax on notes = (200 + 750) x $0.35 = $332.50
The amount of the state documentary stamp tax paid by the buyer with $20,000 assumed loan and a $75,000 new mortgage
Intangible tax = $160,000 x 0.002 tax rate = $320
The amount of state intangible tax paid by the buyer on a new $160,000 mortgage
Intangible tax = ($120,000 + $25,550) x 0.002 tax rate = $291.10
The amount of state intangible tax paid by the buyer on a new first mortgage of $120,000 and a second mortgage of $25,550
Effective age divided Total economic life = Rate (%) of accrued depreciation
The formula used with the economic age-life method for estimating the rate of accrued depreciation over the total life of the building
Rate of accrued depreciation x Reproduction cost of the building = title accrued depreciation ($)
The formula for estimating the dollar amount of accrued depreciation over the life of the building
Accrued depreciation rate = 15 Effective age divided 50 total economic life = 0.3, of 30%
The accrued deprecation rate of a building with a total economic life of 50 years and an estimated effective age of 15 years
Accrued depreciation rate = 15 years divided 50 years = 0.3 accrued depreciation = $150,000 x 0.3 = $45,000
The amount of accrued depreciation after 15 years for a building with an estimated $150,000 reproduction cost, a total economic life of 50 years, and an effective age of 15 years
Accrued depreciation rate = 15 divided 50 = 0.3 yearly depreciation rate = 0.3 divided 15 years = 0.02 or 2%
the yearly depreciation rate of a building with a total economic life of 50 years an an estimated effective age of 15 years.
Accrued depreciation rate = 5 years divided 40 years = 0.125 or 12.5%
The accrued depreciation rate of a building with a total economic life of 40 years and an estimated effective age of 5 years
Accrued depreciation rate = 5 divided 40 = 0.125 accrued depreciation = $120,000 x 0.125 = $15,000
The amount of accrued depreciation after 5 years for a building with an estimated $120,000 reproduction cost, a total economic life of 40 years, and an effective age of 5 years
Accrued depreciation rate = 5 divided 40 = 0.125 yearly depreciation rate = 0.125 divided 5 years = 0.025 or 2.5%
The yearly depreciation rate of a building with a total economic life of 40 years and an estimated effective age of 5 years
EGI = Potential gross income (PGI) - Vacancy and Collection loss (V&C) + other income (OI); other income may come from sources such as carport rentals or vending machines
The formula for calculating the effective gross income (EGI) which is the actual amount the owner can expect to receive from operation of the property for one year into the future
EGI= $100,000 (PGI) - $12,000 (V&C) + $4,000 (OI) = $92,000
The effective gross income (EGI) for an income producing property with $100,000 potential gross income (PGI), $10,000 in vacancy losses and $5,000 additional income
NOI = Effective gross income (EGI) - operating expenses (OE), where OE = Fixed expenses (FE) + Variable expenses (VE) + Reserves for replacements
The formula for estimating the net operating income (NOI) with the direct capitalization technique
NOI = $92,000 EGI - ($9,000 FE + $6,000 VE + $5,000 R) OE = $72,000
The net operating income (NOI) for an income producing property with $92,000 effective gross income (EGI) $9,000 in taxes and insurance, $6,000 in maintenance and management fees and $5,000 in reserves
Value = NOI divided Capitalization rate
The math steps used with the direct capitalization technique to estimate value from the NOI and capitalization rate
- NOI (I) = Rate (R) x Value (V)
- Value (V) = NOI (I) divided Rate (R)
- Rate (R) = NOI (I) divided value (V)
the three forms of the IRV Formula used to determine Income (I), Capitalization rate (R) or estimated value (V)
I = 0.12 (R) x $300,000 (V) = $36,000
The net operating income for a $300,000 property with a capitalization rate of 12%
I
_________
R x. V
V=$15,000 (I) divided 0.10 (R) = $150,000 Memory aid: Write as follows and cross out what you're looking for
The estimated value of a property with a forecasted net income of $15,000 and an overall capitalization rate of 10%
I
_________
R x V
R= $16,200 (I) divided $180,000 (V) = 0.09 or 9%
The capitalization rate for a $180,000 property with a forecasted $16,2000 net operating income
Gross Rent multiplier (GRM) = comparable sales price divided gross monthly rent
The formula used to estimate the value for rental properties based on the monthly gross rental income
GRM = 92,000
____________ = 115
800
The gross rent multiplier for a rental property that recently sold for $92,000 and rented for $800 per month
Monthly income = $109,250 divided 115 = $950
The estimated amount of monthly rental income that should be produced for a property that sold for $109,250 with market evidence indicating a gross rent multiplier (GRM) of 115
Value = $875 x 115 = $100,625
The estimated value of a property that rents for $875 per month with recent market evidence indicating a GRM of 115
Gross income multiplier (GIM) = comparable sales price divided Annual gross rental income
The formula used to estimate the value of rental properties based on the annual gross rental income
Annual gross rental income = $650 x 12 months = $7,800 GIM = $78,000 divided $7,800 = 10
The gross income multiplier for a property that sold for $78,000 and rented for $650 per month
Annual income = $92,000 divided 10 = $9,200
The estimated amount of annual rental income that should be produced for a property that sold for $92,000 with market evidence indicating a gross income multiplier (GIM) of 10
value = $8,500 x 10 = $85,000
The estimated value of a property with an annual gross rental income of $8,500 with recent market evidence indicating a GIM of 10
Operating expense ratio = Operating expenses (OE) divided Effective gross income (EGI)
The ratio that expresses the relationship between the expense incurred in operating the property with the amount the inventory actually receives
Operating expense ratio = $25,000 OE divided $58,000 EGI = 0.431 or about 43%
The operating expense ration for an investment property with $25,000 in operating expenses, an effective gross income of $58,000 and a net operating income of $33,000
Loan-to-value (LTV) ratio = Loan amount divided property value
The ratio that measures financial risk in an investment by comparing the loan amount to the price, or value of the property; the percentage of the property value that is debt
LTV = $188,000 Loan divided $235,000 value = 0.8 or 8%
The loan - to- value (LTV) ratio for a $188,000 loan on a $235,000 property
Loan = $200,000 value x 0.8 LTV = $160,000
The loan amount that would produce an 80% LTV ratio on a property valued at $200,000
Profit or loss % = amount made divided amount paid
The formula used to calculate profit or loss on the amount originally invested
Amount made = $180,000 $120,000 amount paid = $60,000 profit % = $60,000 Made divided $120,000 paid = 0.5, or 50%
The percentage of profit made on a property that was originally purchased for $120,000 and sold for $180,000
0.016
The decimal value for 16 mils
Total number of mils = 6 + 5 + 4 = 15 = 0.015
The total number of mills in decimal when the county tax rate is 6 mills, the city tax rate is 5 mills, and the school tax rate is 4 mills
$50,000 of assessed value, separated into basic (first) and 2nd exemptions
The maximum homestead tax exemption amount
For properties with an assessed value up to $50,000 the basic exemption is the assessed value up to $25,000
The amount of the basic (first) homestead tax exemption
For properties with an assessed value created than $50,000 the 2nd exemption is the amount of assessed value over $50,000 up to a maximum of $25,000
The amount of the 2nd homestead tax exemption
Total exemption = $25,000 (basic exemption) + $10,000 (2nd exemption for amount over $50,000) = $25,000
The amount of homestead exemption for a qualifying homeowner whose primary residence is assessed at $60,000
Total exemption = $25,000 (basic exemption) + $25,000 ( 2nd exemption) = $50,000 (maximum)
The amount of homestead exemption for a qualifying homeowner whose primary residence is assessed at $76,000
Total tax liability = $85,000 x 0.015 = $1,275
The total tax liability without any exemptions for a property with an assessed value of $85,000 with a total tax rate of 15 mills (county, city, and school)
Deduction for basic exemption = $25,000 x 0.015 = $375
The tax deduction for the 1st (basic) exemption for a property assessed at $85,000 with a total tax rate of 15 mills (counts, city and school)
Deduction for 2nd exemption = $25,000 x 0.011 (county and city only) = $275
The tax deduction for the 2nd exemption for a property assessed at $85,000 when the millage rates for the county 6 mills, the city is 5 mills, and school is 4 mills
Total tax liability = $85,000 x 0.015 = $1,275
Tax levy = $1,275 - $375 - $275 = $625
The total tax levy after the 1st (basic) exemption of $375 and 2nd exemption of $275 when the total tax rate is 15 mills (county, city, and school)
Cost = 110 front feet x 12 = $1,320 city's share = $1,320 x 0.25 = $440 owners share (both sides of the street) = $1,320 - $330 (city share) = $990 each owners cost = $990 divided 2 = $495
The special assessment owed by a homeowner for road repairs along their property when the lot has 100 front feet, the estimated cost per foot is $12 and the city will pay 25% of the expense
Married couples filling jointly: up to $500,000 single homeowners or married couple filing separately: up to $250,000
The amount specified by the taxpayer relief act that may be excluded from gain on the sale of property used as the principal residence for at least two of the pervious five years
sq. ft. available per acre = 43,560 sq. ft. x 0.75 = 32,670 sq. ft.
The number of square feet available for development when zoning ordinances require the developer to reserve 25% leaving 75% for development of a 100 acre tract of land
Lots per acre = 32,670 sq. ft. divided 8,500 sq. ft. per lot = 3.84 lots allowed = 3.84 lots per acre x 100 acres = 384
The number of 8,5000 sq. ft. lots can be developed on 100 acres when only 32,670 sq. ft. per acre can be developed
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