Math Questions
A seller received $800,000 for a 5.5 acre rectangular parcel alongside a road frontage. The property is 400 feet deep. What was the price per front foot of the property? $1,335.67 $2,000 $363.64 $598.95
$1,335.67 First, find the square footage (5.5 × 43,560 = 239,580). You're given one dimension of the rectangle, so find the other: 239,580 ÷ 400 = 598.95 front feet. To find the price per front foot, $800,000 ÷ 598.95 = $1,335.67 per front foot.
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? $17,915.50 $16,000 $14,875.50 $15,000.00
$15,000.00 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
Cheryl and Roberto just signed a contract for Cheryl to buy Roberto's house for $235,000. Roberto owes $48,750 on his current mortgage, he's going to replace the old furnace ($800), he's agreed to pay 3% toward closing costs, and he'll pay a 6% commission to his agent. How much in whole dollars will he have left to put down on the condo he wants to buy? $164,300 $164,771 $167,696 $168, 688
$164,300 Roberto's closing costs will be $7,050 ($235,000 x 0.03) and commission will be $14,100 ($235,000 x 0.06). If you subtract all the costs given ($7,050, $14,100, plus the $800 furnace, and the $48,750 mortgage payoff) from the $235,000 price, you end up with $164,300.
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? $2,000 $25,000 $20,000 $30,000
$20,000 100% + 15% = 115% $23,000 divided by 1.15 = $20,000
Using the capitalization formula, what is the value if the net operating income is $20,000 and the rate of capitalization is 10%?
$200,000 .10 = 20,000 / value .10 x value = 20,000 20,000 / .1 = 200,000
Lorena and Julio purchased a home for $205,950. Their loan amount was $164,760, and the assessed value is now $200,500. Their tax rate is 1.5%. How much will their monthly taxes be? $111.04 $191.37 $250.62 $86.49
$250.62
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? $256,666 / $36,666 $244,444 / $36,666 $256,666 / $44,444 $244,444 / $44,444
$256,666 / $36,666 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 While it's not recommended to pay more than the appraised value of a home, it can be done as long as the buyer doesn't mind coming up with extra cash.
A seller wants to break even after the broker's commission of 5% and loan balance of $300,000 are paid. At what price must the house sell? $150,000 $300,000 $315,789 $450,000
$315,789
How much would a lot that is 400 feet wide by 500 feet long cost at $900 per acre? $2,200 $3,060 $4,132 $4,500
$4,132
If an investment valued at $350,000 returns 12 percent annually, then what is the amount of income produced by this investment? $42,000 $39,200 $3,920 $4,200
$42,000 $350,000 x 12% = $42,000
A buyer is purchasing a property for $500,000. His lender's loan-to-value ratio is 90%. How much is the buyer financing?
$450,000 500,000 x .9 = 450,000
Lenore makes a 95% offer on a townhouse that's listed at $285,000 and includes an earnest money deposit for 10% of her offer, which the seller accepts. She brings to closing a cashier's check for $35,025 comprising the balance of her 20% down payment and closing costs. What's the amount of her total down payment? $35,025 $54,150 $57,000 $62,100
$54,150 Lenore's offer is $270,750 which is 95% of the list price ($285,000 x .95 = $270,750 ). Her total down payment is 20% of her accepted offer of $270,750, which is $54,150 (or $270,750 x .2).
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: $5200. $7400. $9300. $8600.
$8600. $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
Loan to Ratio
(loan amount / value ) x 100
The Smithwicks, your buyer clients, obtained a 90% loan on their new $400,000 home. At closing, they paid $6,150 for points at closing. How many points did they pay? .017 .02 1.71 1.8
1.71 A point is 1% of the loan amount. The Smithwicks' loan is $360,000 ($400,000 x .90), and they paid $6,150 for points at closing. Divide the cost into points by the loan amount to get the number of points they paid: ($6,150 ÷ 360,000 = 0.0170833, or 1.71). Also, remember to round off calculations.
The reciprocal of 8% is: 12.5 .125 1250 125
12.5 8% is equivalent to .08 .08 is equal to the fraction 8⁄100 The opposite of 8⁄100 is 100⁄8 100 divided by 8 = 12.5
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? $358 $21.50 $172 $258
172 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.
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? 20 months 12 months 18 months 16 months
18 months 9% of $7,000 is $630 interest per year $945 divided by $630 equals 1.5 years (1.5 years = 18 months).
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: $180,000 $200,000 $215,000 $155,000
180,000 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.
Sebastien's four-story home includes a 400-square-foot unfinished bonus room on the top floor, an upper level with 850 square feet, a main level with 1,450 square feet (which includes a garage that's 500 square feet), and a finished basement that's 900 square feet. The MLS system in Sebastien's area includes below-grade square footage. What square footage will be reported on his MLS listing? 2,200 2,700 3,600 4,100
2,700 Sebastien should exclude the unfinished bonus room and the garage and add the remaining area (850 + (1,450 - 500) + 900).
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? $202,700.12 $211,170.21 $198,500 $210,410
211,170.21 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
A buyer anticipates a house payment of $1,000 per month, with monthly homeowner association fees of $150. The buyer also has a car payment of $400 per month. If the buyer earns a monthly gross income of $5,000, what's the housing ratio? 20% 23% 28% 31%
23% The housing ratio is 23%: ($1,000 + $150) / $5,000 = .23 x 100 = 23%.
A borrower has a 30-year, $500,000 loan with an interest rate of 6.25%. His monthly principal and interest payment is $3,078.59. What's the total amount of interest he'll pay over the course of the loan?
30 x 12 = 360 360 x 3,078.59 = $1,108,292.40 1,108,292.40 - 500,000 = 608,292.40 608,292.40
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: 5% 24% 35% 10%
35% 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%
$140 is 3.5% of what amount? $4,440 $440 $4,100 $4,000
4,000 $140/.035 = $4,000
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? $4,506,789 $6,545,722 $5,243,167 $4,604,167
4,604,167 $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
Alan and Kate want to build a 5,000-square-foot ranch-style home on two acres of land they just bought. Once the house is built, how many acres of undeveloped land will remain?
43560 x 2 = 87,120 87120 - 5000 = 82128 82128 / 43560 = 1.89
A local buyer is purchasing a property for $120,000. What will the seller pay in transfer tax if the rate is $.37 per $100? $370 $3,700 $4,400 $444
444
Your client, a builder, is considering buying three adjacent lots. They each have the same depth: 275 feet. Lot A is 35,750 s.f., Lot B 53,900 s.f., and Lot C is 33,000 s.f. If your client buys all three lots, what total street frontage will he have? 446 feet 462 feet 464 feet 466 feet
446 feet
Amy is purchasing a $500,000 property, financing $400,000. Assuming a mortgage recording tax rate of $0.115 per $100, what's the mortgage recording tax amount? $460 $4,600 $750 $7,500
460
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: $576.00 $57.60 $67.50 $675.00
576.00 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
Jared has a 70/30 split with his brokerage firm, and his firm has a 50/50 split with cooperating brokerages. Last month, he was paid $12,239.50 in commissions from his home sales, which totaled $538,000. Assuming every transaction for the month was shared with a cooperating brokerage, what is Jared's brokerage's commission rate? 2.3% 3.8% 6.5% 7.6%
6.5 Jared was paid $12,239.50, which is 70% of the amount paid to his broker as commission. That makes his firm's commission $12,239.50 ÷ .70 = $17,485. Multiply that by two for the total commission the firm grossed, since it's shared 50/50 with a cooperating brokerage (the brokerage that brings the buyer to the sale), giving you $34,970. Then divide by the total sales amount for the brokerage's commission rate: $34,970 ÷ $538,000 = 0.065, or 6.5%.
Glenn is purchasing a home for $400,000. The property appraised at $415,000 and Glenn is financing $300,000. What's the loan-to-value ratio? 72% 75% 82% 96%
75% Lenders use the lesser of the sales price or appraised value. This results in an LTV ratio of 75% ($300,000 ÷ $400,000).
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: $75,000 $90,000 $80,000 $60,000
75,000 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.
Jones purchased a home for $80,000 using a down payment of 21.25% of the purchase price, and financing the balance on a 30-year amortized loan with interest at 10.25% per annum. The lender requires monthly impounds for property taxes of $800 per year and casualty insurance costing $978 for a three year policy. Assuming that the first monthly payment on the principal is $119, the total amount Jones will have to pay the first month will be approximately: $751 $242 $921 $634
751 First, find the down payment:$80,000 x .2125 (the same as 21.25%) = $17,000 down payment Next, find the loan amount:$80,000 - $17,000 = $63,000 loan Then find the annual interest:$63,000 x 10.25% = $6,457.50 interest per year Divide by 12 to find the monthly interest:$6,457 ÷ 12 (months) = $538.125 interest per month Now find the monthly taxes and insurance :Taxes: $800 ÷ 12 (months) = $66.67 month Insurance: $978 ÷ 36 months = $27.17 per month Now, add the principal (given in the problem), interest, taxes and insurance to find the first month's payment:$119.00 + $538.125 + $66.67 + $27.17 = $750.95, which is approximately $751.
A unit of measure for lumber, equaling 144 or 12" x 12" x 1"
Board foot unit of volume of lumber equal to 144 cubic inches
A real estate transaction has a closing date of May 20. The seller, who's responsible for closing costs up to but not including the day of closing, has already paid annual property taxes of $1,949. How will the closing statement reflect the proration for the seller? Use a calendar year proration, and round to the nearest dollar. Credited $1,207 Credited $742 Debited $1,207 Debited $742
Credited $1,207 The seller is required to cover the property taxes for January 1 through May 19, which is 139 days. The seller will be credited $1,207, because $1,949 ÷ 365 = $5.34, and $5.34 × 226 days (the number of days the buyer will own the property and have to cover property taxes) = $1,206.84. That's $1,207 when rounded to the nearest whole dollar.
capitalization formula
net operating income / market value
A small duplex sold for $550,000. Each unit can gross $2,500 in monthly rent for the owner, and there are no additional income sources from the property. What's the GRM?
price / rent 2 units so total rent of 5,000 (2500 x 2 ) 550,000 / 5000 = 110
