License Math Exam
The annual property taxes of $1,700 were paid in arrears by the buyer. If the closing took place on June 4th and the seller paid through the day of closing, how did this appear on the settlement sheet if the 360-day method is used?
$727 DS, CB $1,700 ÷ 12 = $141.67 monthly rate, $141.67 ÷ 30 = $4.72 daily rate; Seller owes 5 months: $141.67 x 5 = $708.35; Seller owes 4 days: $4.72 x 4 = $18.88, $708.35 + $18.88 = $727 DS, CB (Debit seller, credit buyer)
If a square-shaped lot measures 125' on one side, what is the square footage of the lot?
15,625 square feet The formula to calculate square footage is L x W. Since each side of a square is of equal length and each side measures 125', multiply 125' x 125', which equals 15,625 square feet.
A tax rate on a building with a $530,000 taxable value is 4.5 mills per thousand dollars of assessed valuation. What is the annual tax liability?
$2,385 $530,000 ÷ 1,000 = $530, $530 x 4.5 = $2,385
Ralph is buying Terry's house. The buyer's loan amount is $105,580. If the buyer has agreed to pay 3 points at closing, how much will he pay for the points?
$3,167 A discount point or point is a fee charged by the lender to lower the interest. Since 1 point COSTS 1% of the loan amount and the buyer is purchasing 3 points, multiply the loan amount of $105,580 x 3 = $3,167
A home sells for $150,000 and has a mortgage loan balance of $100,000 at closing. If the commission is 5% and other closing costs are $6,000, what is the seller's net?
$36,500 $150,000 x 0.05 = $7,500, $150,00 - $100,000 - $6,000 = $44,000, $44,000 - $7,500 = $36,500
Six years ago a commercial property owner paid $490,000 for her complex which included 10 acres of land valued at $100,000. Using a 40-year straight-line depreciation method, what would be the current value of the apartment complex?
$431,500 $490,000 - $100,000 (land does not depreciate) = $390,000/40 years = $9,750 per year depreciation. $9,750 X 6 years age = $58,500 accumulated depreciation. $390,000 - $58,500 = $331,500 Plus the land = $431,500
A property currently valued at $450,000 is expected to appreciate 8% each year for the next 3 years. What will be its appreciated value at the end of this period?
$566,870 $450,000 x 1.08 x 1.08 x 1.08 = $566,870. The 1.08 comes from adding the 8% appreciation to 100% for 108%. Then convert that to a decimal, 1.08 and multiply as needed.
A seller wants to net $55,614 from the sale of her house after paying a 7% commission. Her minimum sales price will have to be?
$59,800 100% - 7% = 93% going to the seller; $55,614 ÷ 0.93 = $59,800
The current value of a property is $60,000. For real estate tax purposes, the property is assessed at 30 percent of its current value, with an equalization factor of 1.25 applied to the assessed value. If the tax rate is $4 per $100 of assessed valuation, what is the amount of tax due on the property?
$900 $60,000 current value x 0.30 assessment rate = $18,000 assessed value; $18,000 x 1.25 equalization factor = $22,500. Convert $4.00 to a decimal by moving the decimal two spaces to the left. $4.00 becomes 0.04. Multiply $22,500 by 0.04 = $900 annual property taxes.
Stacey owns a lot that has 180 feet of front footage and contains 36,000 square feet. He purchases two identically-sized lots adjacent to each side of his lot. These side lots are each 200 feet deep and each side lot contains 19,000 square feet. What is the total front footage of all three lots?
370 First, calculate the depth of the original lot: 36,000 ÷ 180 = 200; Next, calculate the front footage of the side lots using the area: 19,000 ÷ 200 = 95. Total up the front footage dimensions: 95 + 180 + 95 = 370 total front footage
A house is sold for $105,500 and the commission rate is 6 percent. If the commission is split 60/40 between the selling broker and the listing broker, respectively, and each broker splits his share of the commission evenly with his salesperson, how much will the listing salesperson receive from this sale?
$1,266 $105,500 contract price x 0.06 = $6,330 total commission; $6,330 x 0.40 / 2 = $1,266 listing salesperson's share
If a corporate building has nine office suites that rents for $14,800 per month each, but suffers from a 14% vacancy rate and annual expenses of $21,100, what is the NOI of the building (round to the nearest $100)?
$1,353,500 9 units x $14,800 per month x 12 months x .86 - $21,100 = $1,353,524 ($1,353,500)
If a house sold for $40,000 and the buyer obtained an FHA-insured mortgage loan for $38,600, how much money would be paid in discount points if the lender charged four points?
$1,544 One discount point cost the buyer 1% of the loan. $38,600 loan x 0.01 = $386; $386 x 4 = $1,544.
If the roof a property cost $14,000 and its economic life is 18 years, what would its value be after four years using a straight-line method of depreciation?
$10,889 $14,000 ÷ 18 = $777.77, $777.77 x 4 = $3,111, $14,000 - $3,111 = $10,889
A strip mall generates $215,000 in effective rental income and $3,000 in other income. The same mall has $102,000 in operating expenses and $15,000 as reserves. What is the net operating income of the strip mall?
$101,000 $215,000 effective rental income + $3,000 other income = $218,000 total effective gross income; $218,000 effective gross income - $102,000 operating expense - $15,000 reserves = $101,000 annual net operating income (NOI).
A home seller wants to net $15,000. If he has agreed to pay a 5% commission, the loan payoff is $94,000 and closing costs are $16,000, what must the minimum listing price be? Round to the nearest $100.
$131,600 Sales Price = 100%, Commission = 5%. All deductions from the sales price other than the commission = 95% of the sales price. $94,000 loan payoff + $16,000 closing costs + $15,000 net proceeds = $125,000 deductions other than commission. $125,000 / .95 = $131,578.94 (($131,600). $131,578.94 x .05 = $6,578.94 sales commission. $125,000 + $6,578.94 = $131,578.94 ($131,600)
If a borrower's monthly interest payment on an interest-only loan at an annual interest rate of 7.3% is $877, how much was the loan amount (rounded to the nearest hundred)?
$144,200 First, since all interest computations are calculated annually, multiply $877 x 12 = $10,524; Then, $10,524 ÷ 0.073 = $144,200
An FHA-insured loan in the amount of $57,500 at a 6 ½% interest rate for 30 years was closed on March 17. The first monthly payment is not due until May 1. If the interest is paid monthly in arrears, how much pre-paid interest does the buyer owe at closing? (Use a 360-day year)
$145.32 $57,500 loan x 0.065 = $3,737.50 annual interest; $3,737.50 ÷ 12 = $311.45 monthly interest; $311.45 ÷ 30 = $10.38 daily rate; March 17 through March 30 is 14 actual days; $10.38 x 14 = $145.32
A borrower obtains a 30-year $210,000 amortized loan at a 6% interest rate. If his monthly payment is $1199.10, how much is applied to the principal balance in the first month?
$149.10 $210,000 loan x 0.06 interest rate = $12,600 annual interest; $12,600 ÷ 12 = $1,050 monthly interest; $1199.10 payment - $1,050 monthly interest = $149.10 applied to principal balance.
Assuming that the listing broker and the seller broker in a transaction split their commission equally, what was the sales price of the property if the commission rate was 6 ½ percent the listing broker received $5,187?
$159,600 $5,187 x 2 sides = $10,374 total commission; $10,374 ÷ 0.065 = $159,600 sales price
A sale transaction on rental property closes on December 10th. The landlord received the December rent of $4,400 on December 1. Assuming the closing day is the seller's, and that the 360-day method is used for prorating, how much will the seller owe the buyer?
$2,933 $4,400 ÷ 30 days = $146.66 per day; $146.66 x 10 = $1,467, $4,400 - $1,467 = $2,933
A 198-foot x 330-foot lot sold for $30,000. What was the price per acre?
$20,000 198' x 330' = 65,340 sq/ft; 65,340 sq/ft / 43,560 sq ft = 1.5 acres; $30,000 / 1.5 = $20,000.
A homeowner bought a house one year ago for $250,000. Since then, the homeowner has spent $4,000 to pave the driveway and has added a screen porch at a cost of $3,000. Total depreciation has been $6,000. What is the homeowner's adjusted basis?
$251,000 $250,000 sales price + $4,000 improvement + $3,000 improvement - $6,000 depreciation = $251,000 adjusted basis
A lender determines that a homebuyer can afford to borrow $220,000 on a mortgage loan. The lender requires an 85% loan-to-value ratio. How much can the borrower pay for a property and still qualify for this loan amount (to the nearest $1,000)?
$259,000 $220,000 loan ÷ 0.85 LTV = maximum sales contract price, $258,823.53, which rounds up to $259,000.
A fine jewelry store leased a space at the mall with a base rent of $1,800 a month, plus 4% of all sales over $200,000. If the gross sales were $325,000, what was the total amount of rent paid by Heinz Fine Jewelry at the end of the year?
$26,600 $1,800 monthly rent x 12 = $21,600 annual base rent; $325,000 gross sales - $200,000 = $125,000 over the sales amount.; $125,000 x 0.04 = $5,000; $21,600 base rent + $5,000 extra rent = $26,600 total rent paid
A building generates $103,000 in effective rental income and $900 in vending machine income. The same complex has $40,700 in operating expenses and $36,000 in debt service payments. What is the pre-tax cash flow of the complex?
$27,200 $103,000 effective rental income + $900 vending machine income = $103,900; $103,000 - $40,700 expenses -= $63,200 NOI; $63,200 NOI - $36,000 debt service = $27,200 pre-tax cash flow
Agent Daisy agrees to a 5% commission to list a home at $330,000. The property is sold through another cooperating brokerage with that firm to receive 50% of the total commission on the $330,000 sale. If Daisy receives 55% of her broker's commission and does not bring the buyer. How much does Daisy's broker receive from the sale?
$3,712.50 $330,000 x 0.05 = $16,500 total commission; $16,500 ÷ 2 = $8,250 to each side. Since Daisy only listed the house and did not bring the buyer, her brokerage receives only half, $8,250; If Daisy receives 55% of her broker's commission that means that the broker keeps 45%, $8,250 x 0.45 = $3,712.50.
A buyer secured a $125,000 loan at 4.5% interest rate. To receive a lower interest rate, the buyer was required to buy down three discount points. How much were the discount points?
$3,750.00 One discount point costs 1% of the loan amount. If a buyer bought down three points it would cost $3,750.00. ($125,000 loan amount x .03%= $3,750.00).
Shelly bought a house five years ago for $150,000 and obtained an 80% loan. Now the home is worth $140,000 and her loan balance has been reduced by $12,000. What is Shelly's current equity?
$32,000 $150,000 purchase price x 0.80 LTV = $120,000 loan; $120,000 loan - $12,000 = $108,000 loan balance; $140,000 current value - 108,000 loan balance = $32,000 current equity
A property is being appraised using the income capitalization approach. Annually, it has an estimated gross income of $48,000, vacancy and credit losses of $3,600, and operating expenses of $15,000. Using a capitalization rate of 8%, what is the property's value (rounded up to the nearest $1,000)?
$368,000 $48,000 - $3,600 - $15,000 = $29,400, $29,400 ÷ 0.08 = $367,500 rounded up to $368,000
A sale transaction closes on April 15th. The day of closing belongs to the seller. Real estate taxes for the year, not yet billed, are expected to be $2,110. According to the 365-day method, what is the seller's share of the tax bill?
$607 Jan-Mar = 90 days, 90 + 15 + 105, $2,110 ÷ 365 = $5.78, $5.78 x 105 = $607
A property was listed at $200,000. The buyers made an offer of 90% of the list price which was accepted by the sellers. The home appraised for $185,000 and the buyers were obtained an 85% loan for 30 years at 5%. What is the first month's interest payment?
$637.50 $200,000 list price x 0.90 = $180,000 contract sales price. Since lender always uses the less of the appraised value or the contract sales price, use $180,00 for the remainder of the calculations. $180,000 contract sales price x 0.85 LTV = $153,000 loan. $153,000 loan x 0.05 interest rate = $7,650 annual interest. $7,650 ÷ 12 = $637.50 monthly interest payment for the first month.
Two parcels of land priced at $1,200 per acre were purchased. One parcel was 15 acres in size and the other was 1 mile square in size. How much did these two parcels cost together?
$786,000 First, calculate the total number of acres. If a parcel is 1 mile wide by 1 mile deep, that's a section which is 640 acres. (5,280' x 5,280' = 27,720,000 sq/ft ÷ 43,560 = 640 acres). 640 acres + 15 acres = 655 total acres; 655 acres x $1,200 per acre = $786,000
If a hotel has an annual net operating income of $812,000 at a 9.35% cap rate, what is its current value (to the nearest thousand)?
$8,684,000 $812,000 NOI ÷ 0.0935 cap rate = $8,684,000 current value
What is 0.0475 converted to a percentage?
4.75%
If one discount point costs the borrower 1% of the loan amount, and increases the lender's yield by 1/8th of one percent, how many discount points must be purchased to lower the interest rate by 1%?
8 1/8th = 0.125; 1.0 ÷ 0.125 = 8
Assuming the FHA qualifies borrowers based on a 31% debt ratio, if a borrower's monthly gross income is $4,400, what monthly payment for housing expenses can this person afford based on this ratio?
$1,364 $4,400 monthly gross x 0.31 = $1,364 possible monthly payment.
Land sells for $9,000 an acre. What will 750,000 SF of land sell for? Round to the nearest thousand.
$155,000 1 acre = 43,560 sq/ft, 750,000 sq/ft ÷ 43,560 = 17.218 acres, 17.218 x $9,000 = $155,962 which rounds up to $155,000
Sean, age 37, sold the home he purchased three years ago and now rents an apartment. He had originally purchased his home for $86,500 and sold it for $115,300. What is Sean's capital gain?
$28,800 $115,300 - 86,500 = $28,800
A rented office space has a monthly income of $3,800. A suitable gross income multiplier derived from market data is 11.1. What would the estimated value be? Round to the nearest $1,000.
$506,000 The gross income multiplier is an annual calculation. $3,800 x 12 = $45,600, $45,600 x 11.1 = $506,160, which rounds down to $506,000.
Violet has a FHA loan for $90,000. The lender is requiring a 1% discount point to the lower the interest rate. What amount is the lender charging for the discount point?
$900.00 A discount point or point is a fee charged by the lender to lower the interest. Since 1 point COSTS 1% of the loan amount and the buyer is purchasing 3 points, multiply the loan amount of 90,000 x .01= $900.00
What is 25% converted to a decimal?
0.25
How many acres are there in the N ½ of the NE ¼ and the NE ¼ of the SE ¼ of a section?
120 acres There are two parcels in this question. N ½ of the NE ¼ is 2 x 4 = 8; 640 ÷ 8 = 80 acres; NE ¼ of the SE ¼ is 4 x 4 = 16; 640 ÷ 16 = 40 acres; 80 acres + 40 acres = 120 acres.
If a lot contains 48,000 square feet and is 240' wide, how deep is the lot?
200' 48,000 sq ft ÷ 240' = 200'
What is the volume of a 90' x 20' x 12' house?
21,600 cubic feet The formula for volume is L x W x D. 90' x 20' x 12' = 21,600 cu/ft
If a buyer purchases 25% of a lot in the spring and then purchases 50% more later in the fall, what percentage of the lot is still available for purchase?
25% 25% + 50% = 75%. 100% - 75% = 25%.
A five-sided lot has the following dimensions: side A = 44', side B = 67', side C = 91', side D = 18', and side E = 55'. What is the perimeter of the lot?
275 feet 44' + 67' + 91' + 18' + 55' = 275'
Amy agreed to a contract price of $100,000 for a home and secured a mortgage loan for $80,000. If the appraised value is $110,000, what is the loan to value ratio?
80% The lender will use the lesser of the contract price or the appraised value. $80,000 loan ÷ $100,000 contract price = 0.80, which is an 80% LTV.
An apartment building that sold for $780,000 had a monthly gross income of $8,000. What is its monthly gross rent multiplier?
97.5 $780,000 ÷ $8,000 = 97.5 GRM
What is the number one rule of adjusting properties when using the sales comparison approach to value?
Never adjust the subject property