Math Formulas, & Terms
Loan - to - value ratio (LTV)
Loan amount ÷ sale price (or value) = loan - to - value ratio (LTV)
A seller sold his home and agreed to a June 16, 20XX, closing date. The last day for which interest was paid on the $105,500 remaining balance of the 8%, 30-year conventional mortgage was April 30, 20XX. If the total monthly mortgage payment was $774.14, what amount of prorated mortgage interest would appear on the closing statement as a debit to the seller? (Use the 365-day method of proration and charge the day of closing to the buyer.)
The answer is $1,063.52. Seller owes 31 days in May + 15 days in June = 46 days; $105,500 mortgage balance × .08 = $8,440 ÷ 365 = $23.12 interest per day; $23.12 × 46 days = $1,063.52 debit.
The county property appraiser has assigned an assessed value of $117,500. The property is homesteaded. The county charges the following millage rates: city 10 mills, county 10 mills, and school district 6 mills. Calculate the property taxes.
The answer is $1,905. $117,500 assessed value - $50,000 homestead exemption = $67,500 taxable value; $67,500 × .026 mills = $1,755 taxes due; $25,000 additional exemption × .006 school board mills = $150 additional taxes due; $1,755 + $150 = $1,905 total taxes due.
The broker agreed to pay his sales associate 45% of the total commission. The property sold for $320,000, and the commission rate was 7%. The property was sold "in house." What was the broker's share of the commission?
The answer is $12,320. $22,400 total commission; 100% - .45 sales associate split = .55 broker's split; $22,400 × .55 = $12,320 broker's commission.
A buyer paid a state intangible tax of $248 on a $155,000 home. What was the mortgage loan amount, and how much was the state documentary stamp tax on the note?
The answer is $124,000 loan amount; $434.00 documentary stamp taxes on the note. $248 ÷ .002 rate = $124,000 loan amount; $124,000 note ÷ $100 increments = 1,240 taxable increments; 1,240 × $.35 = $434.00 documentary stamp taxes on note.
A single-family residence is available for listing. A comparable home recently sold for $140,000. Compared with the subject property, the comparable has a superior location ($12,500), is smaller ($8,000), and is three years older ($5,000). What is the subject property's value based solely on the information given?
The answer is $140,500. $140,000 sale price - $12,500 location + $8,000 size + $5,000 age = $140,500 adjusted sale price.
A landlord owns a 1,800-square-foot rental house that she rents for $.70 per square foot per month. If the GRM (monthly) for that property is 120, what is the market value of the property?
The answer is $151,200. 1,800 sq. ft. × $0.70 = $1,260 monthly rent; $1,260 rent × 120 GRM = $151,200 market value.
An apartment building has eight units, each of which rents for $475 per month. A vacancy rate of 10% persists year after year. Total operating expenses average $1,875 per month. If a capitalization rate of 12% is appropriate, what is the market value of the property?
The answer is $154,500. $475 rent × 8 units × 12 months = $45,600 PGI; $45,600 × .10 = $4,560 vacancy loss; $45,600 - $4,560 = $41,040 EGI; $41,040 EGI - ($1,875 × 12 months = $22,500 operating expense) = $18,540 NOI; $18,540 NOI ÷ .12 cap rate = $154,500 market value.
An investor, who owns an eight-unit apartment building, spent $2,400 on improvements. How much should the monthly rent on each apartment be increased if this expense is to be recovered by the owner in just one year?
The answer is $25. $2,400 ÷ 8 apartments ÷ 12 months = $25 rent increase.
A homesteaded property is located in Jacksonville, Florida, in Duval County. The city tax rate is 8.1 mills, the county tax rate is 8.9 mills, and the school district tax rate is 5 mills. The homeowner is a blind widow and has qualified for homestead exemption. The home has been assessed at $199,000. What MUST the homeowner pay in property taxes?
The answer is $3,381. $199,000 assessed value ‒ $25,000 base homestead exemption ‒ $500 survivor exemption ‒ $500 blind exemption = $173,000 taxable value for school taxes; $199,000 assessed value ‒ $50,000 base homestead exemption ‒ $500 survivor exemption ‒ $500 blind exemption = $148,000 taxable value for city and county taxes; $173,000 taxable value × .005 = $865 school taxes; 8.1 mills city + 8.9 mills county = 17 mills = .017; $148,000 taxable value × .017 = $2,516 city and county taxes; $865 + $2,516 = $3,381 total taxes due.
If two brokers split the 7% commission 50/50 on a property that sold for $98,400, how much did each receive?
The answer is $3,444. $98,400 × .07 = $6,888 total commission; $6,888 ÷ 2 = $3,444 each broker's share.
A homeowner originally purchased a new home for $249,000. During the period of ownership, the homeowners spent $21,000 in capital improvements. The homeowners sold the home 15 years later for $325,000. The homeowners paid a brokerage fee of 6% of the sale price and paid out-of-pocket closing costs totaling $3,500. What is the homeowners' capital gain from the sale?
The answer is $32,000. $325,000 × .06 = $19,500 broker commission; $325,000 - $19,500 - $3,500 closing costs = $302,000 amount realized from sale; $249,000 purchase price + $21,000 capital improvements = $270,000 adjusted basis; $302,000 - $270,000 = $32,000 capital gain.
The loan-to-value ratio offered by a local financial institution is 75%. If a buyer wishes to acquire a lot selling for $129,500, the buyer will need to make a down payment of
The answer is $32,375. 100% - 75% = 25% -or- .25 $129,500 sale price × .25 = $32,375 down payment.
An appraiser has assigned the following weights to three adjusted sale prices: Comparable 1: $334,500―45% weight Comparable 2: $327,500―35% weight Comparable 3: $317,900―20% weight What is the reconciled estimated market value of the subject property?
The answer is $328,730. $334,500 × .45 = $150,525; $327,500 × .35 = $114,625 $317,900 × .20 = $63,580; $150,525 + $114,625 + $63,580 = $328,730.
Based on the following, what is the estimated market value of a lot 100' × 110' in the Cove Hill Subdivision? Comparable Sales Data Sale 1: lot 100' × 120' adjacent to subject lot, sold one week ago for $36,720 Sale 2: lot 100' × 100' located four blocks away, sold three months ago for $29,800 Sale 3: lot 110' × 110' located on same street, four lots removed, sold two weeks ago for $36,800 Sale 4: lot 90' × 110' across the street, sold one month ago for $29,700
The answer is $33,220. Sale 1: $36,720 ÷ (100' × 120' = 12,000 sq. ft.) = $3.06 per sq. ft.; Sale 2: $29,800 ÷ (100' × 100' = 10,000 sq. ft.) = $2.98 per sq. ft.; Sale 3: $36,800 ÷ (110' × 110' = 12,100 sq. ft.) = $3.04 per sq. ft.; Sale 4: $29,700 ÷ (90' × 110' = 9,900 sq. ft.) = $3 per sq. ft.; $3.06 + $2.98 + $3.04 + $3 = $12.08 ÷ 4 = $3.02 average; 100' × 110' = 11,000 sq. ft. × $3.02 = $33,220 market value.
If a home that sold for $80,000 had sold for its asking price of $85,000, and the sale commission was 7%, how much additional commission would have been paid in excess of the actual commission?
The answer is $350. $85,000 - $80,000 = excess sale price; $5,000 × .07 rate = $350 excess commission.
An investor bought half of a quarter-section of land for $160,000. She plans to develop the property into a residential subdivision. Local zoning will require all lots in the community to be not less than 100' × 120' in size, and the engineering firm employed by the investor has informed her that approximately 484,800 square feet of the tract will be required for parks, streets, storm sewers, and other development purposes. The engineering firm has also estimated that total development costs and associated expenses will amount to five times the raw land costs. The investor wants to make a profit of 10% based on total costs. How much must the investor average per lot to accomplish her profit objective?
The answer is $4,224. ½ of a ¼ section = 640 ÷ 4 ÷ 2 = 80 acres; 80 acres × 43,560 sq. ft. per acre = 3,484,800 sq. ft.; 3,484,800 - 484,800 = 3,000,000 buildable sq. ft.; 3,000,000 ÷ 12,000 sq. foot lots = 250 lots; $160,000 cost × 5 = $800,000 development cost; $160,000 + $800,000 = $960,000 total cost; $960,000 × 1.10 = $1,056,000 ÷ 250 lots = $4,224 average per lot.
A developer sold a lot for $36,000. This represented a loss of 10%. What was the cost of the lot?
The answer is $40,000. 100% cost - 10% loss = selling price; 90% = $36,000; $36,000 sale price ÷ .90 = $40,000 cost.
A buyer has made an earnest money deposit of $10,150 on a house selling for $94,500. A local lender has agreed to lend 85% of the selling price at 4.5% interest for 30 years. If the buyer's closing costs amount to $1,575, how much more cash must the buyer produce at closing?
The answer is $5,600. $94,500 × .15 = $14,175 down payment; $14,175 + $1,575 closing costs = $15,750; $15,750 total buyer costs - $10,150 earnest money = $5,600 cash at closing.
A licensee has been asked to determine the current market value of a six-year-old building with a reproduction cost of $480,000. When new, the economic life of the structure was estimated to be 40 years. If the site value is known to be $100,000, what is the current market value of the entire property?
The answer is $508,000. $480,000 reproduction cost ÷ 40 years = $12,000 annual depreciation; $12,000 annual depreciation × 6 years = $72,000 accrued; $480,000 - $72,000 depreciation + $100,000 site value = $508,000 market value.
Monthly mortgage payments of $450 have been paid for 15 years. The original mortgage amount was $45,000. After 15 years, 50% of the loan has been paid. What is the total amount of interest paid to date?
The answer is $58,500. 15 years × 12 payments a year = 180 payments to date: $450 × 180 = $81,000 total paid to date; $45,000 mortgage × .50 paid = $22,500 principal paid; $81,000 - $22,500 = $58,500 interest paid to date.
An office building produces an effective gross income of $96,400. Building operating expenses total $36,600, and the monthly mortgage payment is $2,240. What is the building's net operating income?
The answer is $59,800. $96,400 EGI - $36,600 operating expense = $59,800 NOI.
The scheduled date for closing a duplex is June 15. Rent collected on the first of each month is $600 per unit. Day of closing belongs to the buyer. How will the proration be entered on the closing statement?
The answer is $640 debit seller; $640 credit buyer. $600 × 2 units = $1,200 monthly rent; $1,200 ÷ 30 days = $40 per day; $40 × 16 days belong to buyer = $640; Entered on closing statement; $640 debit seller; $640 credit buyer.
What is the cost per acre of a tract of land that sold for $1,306,800 and is described as follows? Beginning at a point on the North side of State Highway 50, exactly 200 feet West of the corner formed by the intersection of the West side of Dillard Street and the North side of State Highway 50; running thence due West 4,000 feet; thence due North 2,000 feet; thence due East 4,000 feet; thence directly to the point of beginning.
The answer is $7,116 per acre. 4,000 ft. × 2,000 ft. = 8,000,000 sq. ft.; 8,000,000 sq. ft. ÷ 43,560 = 183.65 acres; $1,306,800 sale price ÷ 183.65 acres = $7,115.71 per acre, or approx. $7,116.
A house cost $89,500 to build. When new, the building was estimated to have a 50-year useful life. Using straight-line depreciation, what is the accumulated depreciation after four years?
The answer is $7,160. $89,500 cost ÷ 50-year useful life = $1,790 annual depreciation; $1,790 × 4 years = $7,160 accumulated depreciation.
What did a new home cost if the state documentary stamp tax on the deed was $546?
The answer is $78,000. $546 doc stamps ÷ $.70 rate × 100 increments = $78,000 sale price
If a capitalization rate of 10.5% is used, what is the market value of an investment property assuming a net income of $8,424?
The answer is $80,228.57. $8,424 net income ÷ .105 rate = $80,228.57 value.
The sellers are asking $144,000 for their 1,800-square-foot home. The asking price per square foot is
The answer is $80. $144,000 ÷ 1,800 sq. ft. = $80 per sq. ft.
A sales associate measured the exterior of a home and found it to be 40' × 60'. Disregarding other factors, what is the cost per square foot if the house sold for $202,080?
The answer is $84.20. 40' × 60' = 2,400 sq. ft.; $202,080 sale price ÷ 2,400 sq. ft. = $84.20 cost per sq. ft.
A building was sold for $90,000. The buyer paid 10% cash and obtained a loan for the balance. The lending institution charged a 1% loan origination fee. The total cash used by the buyer for this purchase was
The answer is $9,810. $90,000 × .10 = $9,000 down payment; $90,000 - $9,000 down payment = $81,000 loan; $81,000 loan × .01 = $810 loan origination fee; $9,000 + $810 = $9,810 total cash.
A lot is 73 feet wide and 120 feet deep. What fraction of an acre is this lot?
The answer is 1/5. 73 × 120 = 8,760 sq. ft.; 8,760 ÷ 43,560 = .20 or 1/5.
Examination of documentary stamps on recently recorded deeds provided the following sale prices. Data obtained from property managers produced the income figures. Use the information given to determine the correct overall capitalization rate for the comparable apartment properties. (Round all decimals to three numbers before final rounding to two places.) Project 1: $39,400 NOI ÷ $345,000 sale price = Project 2: $45,680 NOI ÷ $464,000 sale price = Project 3: $36,800 NOI ÷ $386,000 sale price = Project 4: $43,790 NOI ÷ $424,000 sale price =
The answer is 10.25%. Project 1: $39,400 NOI ÷ $345,000 sale price = .114; Project 2: $45,680 NOI ÷ $464,000 sale price = .098; Project 3: $36,800 NOI ÷ $386,000 sale price = .095; Project 4: $43,790 NOI ÷ $424,000 sale price = .103; .114 + .098 + .095 + .103 = .41 ÷ 4 = .1025 = 10.25%.
A rental house produces $875 per month in gross income. The house costs $113,750. What is the monthly gross rent multiplier?
The answer is 130. $113,750 ÷ $875 monthly rent = 130 GRM.
A real estate office sold 180 homes this year. This was 20% more sales than last year. How many homes did the office sell last year?
The answer is 150. 100% + 20% more sales = 180 home sales; 120% = 180; 180 ÷ 1.20 = 150 home sales last year.
A developer purchased five lots each measuring 110' × 150'. The lots cost $325 per front foot. The developer subdivided the lots into eight lots and then sold them for $28,000 each. How much profit did the developer make on the deal?
The answer is 25%. 110 front feet × $325 per front foot = $35,750 per lot; $35,750 × 5 lots = $178,750 total cost; 8 lots × $28,000 sale price =$224,000 total received; $224,000 - $178,750 cost = $45,250 made on sale; $45,250 made ÷ $178,750 cost = 25.3 or approximately 25% profit.
A 43,560 square-foot lot is to be subdivided. One-fourth of the lot is made up of a retaining pond, and one-eighth of the lot will be used for a road. How many square feet of usable area are left?
The answer is 27,225 sq. ft. ¼ = 2/8 + 1/8 = 3/8 for pond and road; 8/8 - 3/8 = 5/8 usable area; 5 ÷ 8 = .625; 43,560 sq. ft. × .625 = 27,225 usable sq. ft.
A buyer purchased a mobile home appraised at $60,000 with closing costs of $2,500. The loan is for $50,000. If the seller paid a $2,500 discount, how many points were charged by the lender?
The answer is 5 points. $2,500 discount ÷ $50,000 loan = .05 or 5 points.
If a building has an estimated economic life of 20 years, the percentage loss of economic life per year is
The answer is 5%. 100% ÷ 20 years = 5% loss per year.
A person borrowed $3,500 for a period of time at a rate of 7.5%. She paid $131.25 for the use of the money. How long did the borrower have the money?
The answer is 6 months. $3,500 amount borrowed × .075 rate = $262.50 for 12 months; $131.25 interest paid (part) ÷ $262.50 (whole) = .5 or ½ year or 6 months.
A commercial property leases for $200,000 per year. Miscellaneous income derived from the property totals $12,000 per year. The property recently sold for $1,395,000. What is the GIM?
The answer is 6.6. $200,000 lease income + $12,000 other income = $212,000 total income; $1,395,000 ÷ $212,000 = 6.58 or 6.6 GIM.
The buyers paid a cash down payment of $55,000 and applied for a $145,000 loan. What is the LTV ratio?
The answer is 72.5%. $145,000 loan + $55,000 down payment = $200,000 sale price; $145,000 ÷ $200,000 = .725 or 72.5% LTV.
What is the loan-to-value ratio for a loan amount of $80,000, a property price or value of $100,000, and a net operating income of $18,400?
The answer is 80.0%. $80,000 loan ÷ $100,000 price = .80 or 80% LTV.
A measure of the financial risk associated with lending and borrowing money is the
The answer is loan-to-value ratio. The loan-to-value ratio is a measure of the financial risk associated with lending and borrowing money.
Which property has the highest assessed value? Market value $81,400; assessed at 60% of value Market value $119,600; assessed at 40% of value Market value $49,500; assessed at 100% of value Market value $66,900; assessed at 75% of value
The answer is market value $66,900; assessed at 75% of value. $66,900 value × 75% = $50,175; $49,500 value × 100% = $49,500; $81,400 value × 60% = $48,840; $119,600 value × 40% = $47,840.
In the formula for determining the tax rate for a government taxing unit, the approved budget minus non-property tax revenue is divided by
The answer is total assessed property valuation minus exemptions. The tax rate is calculated based on the following formula: [approved budget - non property tax revenue] ÷ [total assessed value - exemptions].
The borrowers have a combined gross monthly income of $2,350. They have applied for an FHA loan that will require monthly housing expenses of $658. They have other credit obligations of $282 per month. Will they meet the established FHA standards/ratios for housing expenses and total obligations?
The answer is yes, they meet the FHA standards for both ratios. FHA allows up to 31% for housing expense ratio (HER); FHA allows up to 43% for total obligations ratio (TOR); HER = $658 monthly housing expense ÷ $2,350 monthly gross income = 28%; $658 monthly housing expense + $282 other credit obligation = $940; TOR = $940 total monthly obligation ÷ $2,350 monthly gross income = 40%.
Total obligation Ratio (TOR)
Total monthly obligation ÷ monthly gross income = total obligation ratio (TOR) Example: $1944 ÷ $5400 = .36 or 36% total obligation ratio (TOR)
Housing Expense Ratio (HER)
monthly housing expenses ÷ monthly gross income = housing expenses ratio (HER) Example: $1512 ÷ $5400 = .28 or 28% housing expense ratio (HER)
