Real Estate Math
Find the capitalization rate on a building that is worth $430,000, and rents for $1,500 a month.
To solve this, find the yearly rent and divide by the cost of the building:$1,500 x 12 = $18,000 in yearly rent. $18,000 ÷ $430,000 = 4% NOTE - The full answer is 4.186047% (.04186047), but when the answers provided are rounded to a whole number, you'll want to choose the "most correct" answer.
If a man paid $50,000 for a business which gave him a 6% return on his money, how much did he make during the first year that he owned it?
$50,000 x 6% = $3,000
What is the selling price of a property if the seller paid $3500 for taxes due, has a $125,000 mortgage, paid a 6% broker commission, and netted $70,000 on the sale?
To arrive at this answer, start by adding the taxes, mortgage, and profit from the sale:$3500 + $125,000 + $70,000 = $198,500 This number is equal to 94% of the selling price, with the broker's 6% commission equaling the rest (94% + 6% commission = 100% sales price). To find the full selling price, divide $198,500 by .94 (which is the same as 94%) to find the total:$198,500 ÷ .94 = $211,170.21
If Jamie's quarterly interest payments are $150 on a $12,000 loan, then what is her annual interest rate?
To figure out a percentage, divide the interest by the investment. So, $150 x 4 (quarters a year) = $600, and $600/$12,000 = 5%
Joe's duplex has depreciated 3% per year for the 5 years he has owned it. Since the building originally cost $20,000, what is the current value of the duplex?
To figure this out, first figure out the total depreciation:3% x 5 years = 15%Next, multiply that by the original cost:$20,000 x 15% = $3,000Finally, subtract that amount from the original cost to find the current value:$20,000 - $3,000 = $17,000
Calder's Construction Company built a home in a new subdivision. It sold 6 months later for $48,500. This amount reflected a depreciation of 3%. Knowing this, what was the original asking price on the home?
To figure this out, take the sale price and divide it by 97% (or .97), which is the amount remaining after 3% depreciation:$48,500 ÷ .97 = $50,000
Mr. Fixit wanted to remodel his business, so he got a loan of $4,300, at a rate of 6 percent interest. He paid this loan off in 8 months. Knowing this, what was the total amount of interest Mr. Fixit paid?
To figure this problem, first take the loan amount multiplied by the interest rate for the annual interest ($258). Then divide this amount by 12 (as in months per year) to find out the interest paid per month. Multiply that total ($21.50) by 8 (months) for the total interest paid of $172.
Stephen sold his house and took back a note for $4200 secured by a Second Deed of Trust. He promptly sold the note for $2730. This represents a discount of:
To figure this problem, first we need the "discount" (or difference) between the amount of the note and the amount the note was sold for :(original amount of note) - (net received from sale) = (amount of discount)$4200 - $2730 = $1470 Now, divide the discount by the original note amount to find the rate of discount:$1470 ÷ $4200 = .35, or 35%
The Noonan family sold their home and had to carry back a Second Trust Deed and note of $5310.00. If they sold the note for $3823 before any payments had been made on the note, the rate of discount amounted to:
To figure this problem, first we need the "discount" (or difference) between the amount of the note and the amount the note was sold for: (original amount of note) - (net received from sale) = (amount of discount) $5310 - $3823 = $1487 Now, divide the discount by the original note amount to find the rate of discount:$1487 ÷ $5310 = .28, or 28%
What is the cubic footage of a driveway that measures 60 feet long, 8 feet wide, and is 3 inches deep?
To find out the total cubic footage, multiply the length, width and depth. Keep in mind that 3 inches is the same as 1⁄4 of a foot:60 ft. x 8 ft. x 1⁄4 ft. = 120 cubic feet On a calculator, this looks like:60 x 8 ÷ 4 = 120 cubic feet
After subtracting $140.00 escrow fees and 6% commission on gross sales price, a seller receives $13,584.00. What is the selling price?
To find the answer, add the seller's net sales price ($13,584) to the subtracted escrow fees ($140), then divide that by .94 (100% - 6% for the commission), which is the percentage of gross sales the seller gets to keep. $13,584 + $140 = $13,724$13,724 ÷ .94 = $14,600 The selling price is $14,600.
A building has interior dimensions of 26 feet by 30 feet. The walls are 6 inches thick on every side. How much square footage of land does it cover?
To find the total square footage of land covered by a building, you'll need to add the wall thickness from each end (6 inches) of the building to the internal dimension. When you measure the width, there are two walls, when you measure the length there are two walls. Once you have the total length by the total width, multiple them together to find the square footage: 26 ft. (internal dimension) + 6 in. (one wall) + 6 in. (the other wall) = 27 ft. on one side;30 ft. (internal dimension)+ 6 in. (one wall) + 6 in. (the other wall) = 31 ft. on the other.31 ft. x 27 ft. = 837 sq ft.
If Chris's house depreciates at the rate of 2.5% per year for 10 years and has a present value of $12,500, what was the original value of the house?
To solve this problem, first multiply 2.5% by 10 (years) for the total depreciation of 25%. Subtract that from 100% for 75%. Then, take $12,500/.75 = $16,666, which was the home's original value.
John and Sandi Samson, who file a joint income tax return, pay 28 percent income tax on their earnings. If they have an $85,000 mortgage at 8 percent interest, their allowable tax savings would be:
To solve this problem, first multiply the mortgage by the interest to arrive at the annual interest. ($85,000 x .08 = $6,800) Next, multiply this number by the tax bracket to arrive at the savings. $6,800 x 28% = $1,904.
A prospect is considering the purchase of an income property. The property's operating statement shows the deductions subtracted from a total gross income of $94,500. The deductions amount to 60% of the gross income. If the prospect wants a 12% return on the purchase price of any investment he makes, what should he pay for the property?
To solve this problem, start with finding the net income. Expenses equal 60% of the gross income, so the net income is the other 40%. To find the net income, multiply the gross income by .4 (which is the same as 40%):$94,500 x .4 = $37,800 Now, divide the net income ($37,800) by the desired return (12%) to determine the desired purchase price:$37,800 ÷ .12 = $315,000
Sydney Blackwell manages an office building with leases of $60,000 per year. Her management agreement is for 7 years, with fees as follows: 7% the first year; 5% the second and third year; and 3 % the remaining years. What will be Sydney's total management fee?
To solve this problem, you have to figure out the commission for each year, as follows: 7% of $60,000 = $4,200; 5% of $60,000 = $3,000, and that multiplied by 2 years at that rate is $6,000; 3% of $60,000 = $1,800 x 4 (years at that rate) = $7,200. Add these totals to reach the total of $17,400.
Bailey Broker leases a property to Susie Smiley for 5 years. Bailey will receive a 5% commission based on the annual rent. The rent for the property is $3000 per month for the first year, with a $100 increase to the monthly payment each succeeding year. Knowing this, what will Bailey's commission be?
To solve this problem, you must figure out the monthly rent for each of the 5 years, multiply that by 12 to find total rent for the 5-year period, then add those together and multiply that sum by 5% to arrive at the commission. Start by adding the monthly rents for each year:$3000 + $3100 + $3200 + $3300+ $3400 = $16,000 Now, multiply that by 12 to figure the yearly rent for the full 5-year period:$16,000 x 12 = $192,000 Finally, multiply that by 5% to find the commission:$192,000 x .05 = $9,600
An office building earns $850,000 per year, and expenses are 35% of that amount. If the property is capitalized at 12%, what is its approximate value?
To solve this, first find out the amount spent on expenses (remember that 35% can be expressed as .35):$850,000 x .35 = $297,500 Now, subtract that amount from the total:$850,000 - $297,500 = $552,500 To reach the final answer, divide the net revenue by the capitalization rate (remember that 12% can be expressed as .12):$552,500 ÷ .12 = $4,604,167
A broker was paid 6% commission on the first $60,000 of a sale price and 4% for everything above that. What would the sale price be if the total commission was $4,375?
To solve this, first find the commission made by the broker (6% or .06) up to $60,000 and subtract that from the total commission ($4,375), then divide by the remaining commission percentage (4% or .04) to find the amount paid at that rate. Finally, add that number to $60,000 to get the total selling price. .06 x $60,000 = $3,600$4,375 - $3,600 = $775$775 ÷ .04 = $19,375$19,375 + $60,000 = $79,375 The total sale price was $79,375.
A borrower signed a straight note for a term of eight months in the amount of $2500. If she paid $150 in interest on the loan, the interest rate was:
$150 divided by 8 months = $18.75 per month$18.75 X 12 = $225 per year (APR is Annual Percentage Rate, so you must figure the rate for 1 year)$225 divided by $2500 = 9%
If a borrower pays $1650 interest per quarter on a straight note of $60,000, the interest rate would be:
$1650 = interest for 3 months$1650 X 4 = $6600 interest for one year$6600 divided by $60,000 = .11 or 11%NOTE - 1 quarter of a year is equal to 3 months.
An individual who receives $225 per month on a money market savings account that pays 7 1⁄2% per year, has invested which of the following amounts?
$225 X 12 = $2700 per year $2700 divided by 7.5% = $36,000
A building that cost $300,000 to construct 10 years ago has depreciated 25%. The land costs $51,000, so the appraised value is:
$300,000 x 25% (depreciation) = $75,000. Then subtract that from $300,000 for a total of $225,000, and add $51,000 for a total appraised value of $276,000.
Selwyn was the owner of a straight note with an annual interest rate of 8.4%. In 5 years, he had received $5,460 in interest. What was the principal amount of the note?
$5,460 divided by 5 years = $1,092 annual interest$1,092 divided by .084 = $13,000 principal amount
If Skylar's property has a net income of $5,480, and returns 8 percent annually on the investment, then what is her property's value?
The formula for finding a property's value when you have the net operating income and cap rate is: Current Market Value (CMV) = Net Operating Income (NOI) ÷ Cap RateCMV = $5,480 ÷ .08 (8% in decimal form)CMV = $68,500
A house is appraised for $25,000, and shows an assessed value of $20,000. The taxes on the house are $300 annually. What would the tax be on a house that is appraised at $45,000, with an assessed value of $40,000?
To solve this problem, first figure out the levy percentage by dividing the tax amount by the assessed value (of the first house), and then multiply that number by $40,000 (the value of the second house). So, $300/$20,000=.015 mill levy. Then $40,000 x .015 = $600.
$140 is 3.5% of what amount?
Remember to always divide to find the value or rate, so in this case, $140/.035 = $4,000.
A homeowner sold his house for $23,000. This selling price represented a 15% profit over what he had originally paid for the house. What was the original price of the home?
100% + 15% = 115%$23,000 divided by 1.15 = $20,000
If the assessed valuation of a property is $20,000, with a tax rate of $4.00 per $100, what is the annual tax?
Remember that the $4.00 per $100 means that the $20,000 must be divided by 100, giving a total of $200. That, multiplied by $4.00 gives the total tax of $800.
If an investment valued at $350,000 returns 12 percent annually, then what is the amount of income produced by this investment?
Remember, take the value multiplied by the return to equal the income. So, in this case: $350,000 x 12% = $42,000
If the capitalization rate on a building that produces a $20,000 annual income is 10 percent, what is the estimated value of the building?
Remember, the interest rate into the income equals the investment, so you can use this here in a slightly different equation. $20,000/.10 (the rate) = $200,000.
An owner depreciated the improvements based on a cost basis of $160,000 using the straight line method. Improvements are depreciated 37.5% to date and the remaining economic life is estimated to be 15 years. Which of the following is correct?
100% - 37 1⁄2% = 62 1⁄2% remaining to depreciate 62 1⁄2% divided by 15 years = 4.17% per year Rate of depreciation exceeds 4% per annum
An individual borrowed $7,000 on a straight note at 9% interest. If the total interest paid on the note was $945, what was the term of the loan?
9% of $7,000 is $630 interest per year $945 divided by $630 equals 1.5 years (1.5 years = 18 months).
Which of the following is the largest parcel of land?
A two mile square would be a square measuring two miles on each side. It would contain four sections and have an area of 4 square miles.
Pat purchased a brand new piece of income property for $180,000. The listed price was $220,000. Pat considered this a good deal on his part, since he only put $10,000 down and acquired a new first trust deed for the difference. The tax assessed value was indicated at $150,000. Pat's cost basis for income tax purposes would be:
For income tax purposes, the cost basis is generally the actual purchase price of the property. Improvements are added to the cost basis, and depreciation subtracts from it. When a property owner sells a home, the sale price is compared to the property's cost basis to determine if the seller realized any "capital gains", or profit, from the sale that needs to be taxed. $180,000
An investor is going to have a building constructed which would cost $150,000. When completed, it will be leased for $2,500 per month. The annual operating expenses for the property will be $6,000. How much should he invest to realize a 12% return?
First, calculate how much the building would earn per year by renting it out:$2,500 x 12 = $30,000 Next, subtract the projected annual operating expenses:$30,000 - $6,000 = $24,000 Now, divide that number by a 12% capitalization rate to determine the projected asset value:$24,000 ÷ .12 = $200,000 Finally, subtract the construction cost from the asset value to determine the dollar amount of the required investment:$200,000 - $150,000 = $50,000
What are the actual measurements of a property shown as 5-3⁄4 inches long and 4-1⁄2 inches wide, if the scale is 1⁄8 inch = 1 foot?
First, convert your scale to feet. If 1⁄8 in. = 1 foot, then 1 in. = 8 feet (multiply both sides of the equation by 8). Use this to solve the problem.8 x 5 3⁄4 is the same as 8 x 5.75 = 468 x 4 1⁄2 is the same as 8 x 4.5 = 36The area is 46' x 36'.
An investor purchased two lots and paid $18,000 for each one. Since each lot had a 60' frontage he was able to subdivide the combined parcels in three lots with equal front footage. If the three lots sold for $15,000 each, his rate of profit on his investment was:
First, find the selling price of the three lots:3 lots X $15,000 each = $45,000 selling price. Next, find the purchase price:2 lots X $18,000 each = $36,000 purchase price. Now we find the difference between selling price and purchase price:$45,000 selling price - $36,000 purchase price = $9000 profit. Finally, we divide the profit by the purchase price to determine the rate of profit on the investment:$9000 ÷ $36,000 = .25, or 25%
Madison Davidson negotiated for a $30,000 loan with $400 monthly payments and a 9 percent interest charge. What is her first month's interest payment?
First, multiply $30,000 by .09 (same as 9%) to find the total annual interest paid- $2,700. Divide $2,700 by 12 (number of months in a year) to get the interest payment of $225 for the first month.
An income property was appraised for $100,000 based on a 6% capitalization rate. If an investor used an 8% cap rate, the value of the property would be:
First, multiply the appraisal value by the capitalization rate:$100,000 X 6% = $6000 net income Then, divide the net income by the alternate cap rate to find the alternate value:$6000 divided by 8% = $75,000 value.
If $150 interest is paid in 8 months on a straight note loan of $2,500, what is the annual rate of interest?
In 8 months, or 2⁄3 of a year, $150 interest was paid. Divide $150 by 2⁄3 to find the total paid in a year, so $150 ÷ (2⁄3) = $225 interest per year.Divide interest per year by total loan amount to find the interest rate, so $225 ÷ $2500 = .09, or 9% APR.
Sage owned an income property with an adjusted cost basis of $150,000 and a fair market value of $200,000. He exchanged the property for another income property, which has a fair market value of $210,000. Both parties had no loans against them and no adjustment was made for the difference in value. For federal income tax purposes, the new property will have a basis for Sage of:
In a tax deferred exchange transaction, the cost basis of the property transferred becomes the cost basis of the property which is acquired or received. Even though Sage's new property had a higher fair market value, no adjustment was made for the difference in value so the basis for the new property remained the same as the basis for the old property. $150,000
The reciprocal of 8% is:
In math, the reciprocal is the inverse of a number. This means that the product of a number and its reciprocal yields 1. So the reciprocal of 8⁄100 is 100⁄8.8% is equivalent to .08.08 is equal to the fraction 8⁄100The opposite of 8⁄100 is 100⁄8100 divided by 8 = 12.5
A rectangular parcel of land that measures 220' by 330' contains most nearly:
Multiply both sides of the parcel to figure out square footage:220' x 330' = 72,600 square feetNow figure out how many acres that is:1 acre is 43,560 sq. ft., so 72,600 ÷ 43,560 = 1.66 acres Now we know it's an answer that starts with 1, but we need to figure out which fraction equals .66. Fractions equal the top number divided by the bottom number, so: 3 ÷ 5 = .6, 1 ÷ 4 = .25, and 2 ÷ 3 = .6666 The answer that fits "most nearly" is 1 2⁄3 acres.
An acre is to be divided into four equal lots. If the lots are parallel to each other, rectangular, and 200 feet long, the width of each lot would most nearly be:
One acre = 43,560 square feet, divide this by 200 to find the total width of all 4 lots:43,560 sq. ft. ÷ 200 ft. = 217.8 ft. Now divide the total width by number of lots to find the width of each lot:217.8 ft ÷ 4 = 54.45 ft, rounded to 55 ft. (the question asks "would most nearly be" and only provides one "near" answer of 55 feet).
Jones sold his home for $17,200. If this represents 9% more than what he paid for it, the cost of the home was most nearly:
Selling price = cost + 9% or 109%$17,200 divided by 1.09 = $15,779Closest answer is $15,800
Solly bought a home for $31,680 and now wishes to sell. He is informed that the cost of selling will amount to 12% of the selling price. He wants to sell at a high enough price that he doesn't take a loss. How much does the home need to appreciate in value to offset the selling costs?
Solly wants his original home purchase price of $31,680 to be 88% of his desired sales price. Start by finding his desired sales price, which is the original purchase price divided by 88%:$31,680 ÷ .88 = $36,000 Now, subtract Solly's original purchase price from his desired sales price to find out how much the house needs to appreciate in value:$36,000 - $31,680 = $4,320 Alternately, you can multiply $36,000 by 12%, which is the portion of the overall sales price that must be appreciation in value:$36,000 x .12 = $4,320
A house sold for $345,000, which was 9% more than the cost of the house. The original cost of the house was most nearly:
The Original Cost (OC) is Current Cost (CC) divided by Adjusted Cost Ratio (ACR).The Current Cost is $345,000, the Adjusted Cost Ratio is 100% plus or minus the appreciation/depreciation of the house. Because the house is now worth 9% more than OC, the ACR is 109% (or 1.09).OC = CC ÷ ACR, so OC = $345,000 ÷ 1.09$345,000 ÷ 1.09 = $316,513.76, so the answer is "most nearly" $316,514.
Andrew purchased a property at 20% less than the listed price and later sold the property for the original listed price. What was the percentage of profit?
This problem can be figured using any list price, but let's assume that the property was listed at $10,000.20% of that list price is .2 x $10,000 = $2,000.So the purchase price is $10,000 - $2,000 = $8,000.Andrew sold the property for the original list price, so his profit is $10,000 - $8,000 = $2,000.To find the percentage of profit, divide the profit by purchase price: $2,000 ÷ $8,000 = .25, or 25% profit.
A small studio sold for $16,350, which was a 9% appreciation over the original cost of the studio. What was the original cost of the studio?
This problem tells you that the original cost of the studio plus a 9% appreciation equals $16,350: Cost (100%) + Appreciation (9%) = $16,350So here's another way to look at it- the studio sold for 109% of its original cost: 109% = $16,350To find out what 100% of this number is, divide $16,350 by 1.09 (109%):$16,350 ÷ 1.09 = $15,000
An owner of a six-family apartment complex pays the property manager an annual salary equal to 12% of the property's annual gross income. If the annual gross income is $ 140,000, the annual expenses are $65,000 and the capitalization rate is 10%, what is the property manager's annual salary?
This question is full of red herrings. The only figures that count are the gross annual income of $140,000 and the property manager's salary of 12% of GAI, which yields annual compensation of $16,800.
If a home appraised for $93,000, and Mr. Nickel, the borrower, puts 20% down, what would his loan amount be?
To arrive at the loan amount, take the $93,000 appraisal amount and multiply that by 80% (loan needed) for a total loan amount of $74,400.
How much less are the monthly payments on a $36,000 home than on a $40,000 home if a 75% loan is obtained at $8.70 per month per $1000 of value?
To arrive at this amount, start with the difference between the prices of the two homes, which is $4,000. Multiply that amount by 75%:$4,000 x .75 = $3,000Now, divide that by $1000:$3,000 ÷ $1000 = 3Finally, multiply that by $8.70 to get the final difference:3 x $8.70 = $26.10
Sage obtained a loan in the amount of $20,000 and paid the mortgage lender 4 discount points and an origination fee of 2%. If the payments on the loan were $163.00 per month including 8% interest, and the average balance over a 5-year period was $18,500, the gross amount earned by the lender over those 5 years was most nearly:
The lender earned the discount points, origination fee and interest.$20,000 X 4% = $800 in points$20,000 X 2% = $400 in origination fee$18,500 X 8% = $1480 annual interest X 5 years = $7400.Total of these three amounts is $8600.
A married couple purchased a property for a total price of $18,000. The down payment was $5,000 and the seller took back a First Trust Deed in the amount of $13,000. The terms of the $13,000 Trust Deed called for no payments in the first year. If they were to sell the property for twice its original cost at the end of the first year, their original dollar is now worth:
The owners had an initial equity (or investment) of $5000. If the property doubled in value to $36,000, you would deduct the $13,000 loan to find their new equity of $23,000. Divide the current equity by the initial equity to find the increase of dollar value:$23,000 ÷ $5000 = $4.60
Wayne Goodspeed falls in love with a house and buys it for 5% more than the appraised value. He secures a loan for $220,000, which represents the appraised value minus a 10% down payment. What was the purchase price, and how much did Wayne have to come up with in cash?
The purchase price is $256,666. The total amount in cash Wayne needed to come up with is $36,666.To figure the amount, do the following: Step 1, find the appraised value - $220,000 divided by 90% = 244,444.44 Step 2, find the purchase price - $244,444.44 X 105% = $256,666.67 Step 3, find the down payment - $256,666.67 minus $220,000 = $36,666
A property sells for $495,000, which represents a 10% profit for the owner. What was the original cost of the property?
The selling price of a property is 100% of the original cost plus 10% of the original cost (the profit), so the selling price actually equals 110% of the original cost of the property. Convert 110% to decimal form, which is 1.10 (move the decimal 2 places to the left). Finally, divide the sales price by that number to get the answer:$495,000 ÷ 1.10 = $450,000
Freddy Froghammer owns a lot measuring 80 ft. x 120 ft. The city puts in a new street on the front and the side of his house and assesses him 6 cents per square foot based on the area of this lot. His costs are:
To arrive at this answer, figure out the area first:120 x 80 = 9,600 sq. ft. Then multiply that by the assessed amount (6 cents or $.06), and this is what you'll have:9,600 x $.06 = $576.00
If the transfer taxes are payable at the rate of 55 cents per $500 or part thereof, what is the grantor's cost on a $49,750 sale?
When figuring transfer tax, you are generally required by the state to round up to the nearest $500. Round $49,750 up to $50,000 and divide it by $1000. The transfer tax is $.55 per $500, but you can double it to $1.10 per $1000 because it's easier to work with: $50,000 ÷ $1000 = 50 Now multiply that by $1.10, so:50 x $1.10 = $55.00
A house sold for $95,000 with a sales commission rate of 7.5%. The listing broker received 50% of the total commission and the selling broker received 50%. How much would the selling salesperson receive if the selling broker kept 60% and gave 40% to the salesperson?
With total commissions of $7,125, the selling and listing broker each receive $3,562.50. At 40% of the selling broker's share ($3,562.50), the selling salesperson would receive $3,562.50 x .4 = $1,425.
A homeowner sold his house for $230,000. If the selling price represented a 15% profit over what he had originally paid for the house, the original price of the home was:
selling price = cost (100%) + profit (15%) = 115% which is $230,000$230,000 divided by 1.15 = $200,000
