Real Estate Math
A buyer offer of $295,000 was accepted, and a loan was negotiated for 80% at 7% interest for 25 years. The closing took place on January 5, and the buyer's first PITI payment is due March 1. Using a 365-day year, with the seller having the day of closing, how much interest would the buyer be charged on the closing statement? A) $1,176.77 B) $226.30 C) $1,652 D) $1,276.67
A) $1,176.77 Step 1: determine the loan amount, $295,000 × .80 = $236,000. Step 2: determine the interest, $236,000 × 7% (.07) = $16,520. Step 3: determine what the buyer owes. The buyer will owe 26 days for January (31 - 5 = 26 days) and none for February as the March payment will pay the interest in arrears for February. Total amount due ÷ Total days × Days owed: $16,520 ÷ 365 × 26 = $1,176.77
If the quarterly interest at 10.5% is $3,150, the principal amount of a loan is A) $120,000. B) $30,000. C) $60,000. D) $90,000.
A) $120,000. To find the principal, divide the annual interest by the percent of interest. In this problem, to find the annual interest, multiply the quarterly amount by 4: 4 × $3,150 = $12,600 (annual interest) $12,600 ÷ 10.5% (.105) = $120,000 (principal amount)
Lot A measured 200' x 300' and sold for $30,000 per acre. Lot B, which is located down the street, measures 150' x 200'. If Lot B sells for the same price per acre as Lot A, what is the price of Lot B? A) $20,661 B) $51,229 C) $41,322 D) $21,780
A) $20,661 The price of Lot B is $30,000 per acre, the same as Lot A. An acre is 43,560 square feet. Lot B is 150' x 200' = 30,000 sq. ft. As 30,000 is less than the 43,560 square feet in an acre, divide 30,000 by 43,560: 30,000 ÷ 43,560 = .6887 acres. The price is $30,000 × .6887 = $20,661.
If the market value of a property is $169,000, it is assessed at 35%, and the tax rate is $4.25 per $100, what are the monthly property taxes? A) $209.49 B) $2,513.88 C) $409.49 D) $2,531.88
A) $209.49 Tax rate = $4.25 ÷ 100 = .0425 Assessed value = $169,000 × 35% (.35) = $59,150 $59,150 × .0425 = $2,513.875 Annual taxes $2,513.875 ÷ 12 = $209.49 Monthly taxes
A builder wants to purchase a parcel of land of 17,500 square feet at $60,000 per acre. What is the cost of the land? A) $24,150 B) $124,000 C) $48,300 D) $62,000
A) $24,150 To find the cost of the parcel, first convert the cost per acre into the cost per square foot: $60,000 per acre ÷ 43,560 square feet (square feet per acre) = $1.38 (rounded) per square foot. Then, multiply the square feet of the parcel by the cost per square foot: $1.38 × 17,500 = $24,150.
If a seller needs to net $50,000 after the sale, how much must he sell his home for if the selling costs include a 7% commission and $1,200 in other expenses? A) $55,054 B) $55,633 C) $54,963 D) $54,700
A) $55,054 $50,000 (net) + $1,200 (costs) = $51,200 $51,200 ÷ .93 [100% - 7% (0.07) commission] = $55,053.763 round to $55,054
The buyers applied for a VA loan to purchase a property for $79,500. The property appraised at $79,000. They agreed to pay a 1% loan origination fee. How much did they pay in origination fees? A) $790 B) $975 C) $970 D) $795
A) $790 $79,000 (100% loan) × 1% (.01) = $790
This month's interest payment is $585.70. If the buyer secured a 90% loan at an 8.75% annual rate of interest, what was the sale price? A) $89,250 B) $80,235 C) $80,325 D) $89,500
A) $89,250 $585.75 × 12 = $7,028.40 Annual interest $7,028.40 ÷ 8.75% (.0875) = $80,324.57 Loan amount $80,324.57 ÷ 90% (.90) = $89,249.52 round to $89,250
If an interest payment of $1,500 is made every three months on a $50,000 loan, what is the interest rate? A) 12% B) 6% C) 9% D) 3%
A) 12% $1,500 × 4 (every 3 months is ¼ of a year) = $6,000 (the annual interest). $6,000 ÷ $50,000 (the loan amount) = 12% (.12)
A property was purchased for $175,000. If the loan was $131,250, what was the loan-to-value ratio? A) 75% B) 70% C) 80% D) 90%
A) 75% $131,250 ÷ $175,000 = 75% (.75)
An owner wants to receive a net of $82,000 after selling her home. She has an existing mortgage of $32,500 and will have selling expenses of $444. If the broker is to receive a 7% commission, what is the lowest offer that she can accept for the property? A) $122,515.08 B) $123,595.70 C) $122,990.08 D) $123,959.70
B) $123,595.70 $82,000 + $32,500 + $444 = $114,944 $114,944 ÷ 93% (.93) = $123,595.70
A broker received a 6% commission from the sale of a property. The broker gave the salesperson $3,500, which was 30% of the firm's commission. What was the selling price of the property?\ A) $75,000 B) $194,450 C) $196,000 D) $83,333
B) $194,450 To find the broker's total commission, divide the salesperson's commission by the percentage of the salesperson's commission: $3,500 ÷ .30 (30%) = $11,667. The broker's commission is 6% of the sales price. To find the sales price, divide the broker's commission by the percentage of the broker's commission: $11,667 ÷ .06 (6%) = $194,450.
A salesperson sells a $150,000 home listed with another brokerage. The listing commission is 6.5% of the selling price, with 35% going to the listing broker and 60% belonging to the cooperating broker. The salesperson and his broker agreed that she would receive 55% of any commission that she generated for the brokerage firm. For this transaction, the salesperson is entitled to receive A) $2,632.50. B) $3,217.50. C) $5,850. D) $3,412.50.
B) $3,217.50. $150,000 (sales price) × 6.5% (.065) = $9,750 (listing commission) $9,750 × 60% (.60) = $5,850 (cooperating broker's commission) $5,850 × 55% (.55) = $3,217.50 (the salesperson's commission)
The market value of a property is $65,000 and is assessed for 45% of its value. If the owner's semiannual tax bill was $511.88, what was the tax rate per $100? A) $1.75 B) $3.50 C) 350 mills D) 175 mills
B) $3.50 $65,000 × 45% (.45) = $29,250 Assessed value $511.88 × 2 = $1,023.75 Annual taxes $1,023.75 ÷ $29,250 = .035 .035 × 100= $3.50
Three years ago, the owner paid $165,000 for her investment property. During her period of ownership, she added a family room valued at $16,500 and $10,000 worth of other improvements. If she sells the property for $240,000 and pays a 7% commission, what capital gains may she exclude?\ A) $48,500 B) $31,700 C) $38,700 D) $25,300
B) $31,700 The answer is $31,700. $240,000 - $16,800 (7%) = $223,200 $165,000 + $16,500 + $10,000 = $191,500 $223,200 - $191,500 = $31,700
A sales associate for XYZ Realty listed and sold a $175,000 home. The seller paid a 6% commission, of which the sales associate received 2% for listing the property and 1.5% for selling the property. How much was the brokerage's share of the commission? A) $10,500 B) $4,375 C) $5,250 D) $6,125
B) $4,375 Total commission = $175,000 × 6% (.06) = $10,500. Sales associate's share = 3.5% (2% + 1.5%) $175,000 × 3.5% (.035) = $6,125. $10,500 - $6,125= $4,375 for the brokerage. Or 6% - 3.5% = 2.5% for the brokerage times the sales price.
A borrower pays $200,000 for a home, makes a down payment of $40,000 and obtains a loan for the balance of the purchase price. The lender charges four discount points for the loan. How much will the borrower pay in discount points? A) $12,800 B) $6,400 C) $8,000 D) $16,000
B) $6,400 A discount point is 1% of the loan amount. Four discount points is 4% of the loan amount, which is $160,000. To find the amount of the discount points, multiply the loan amount by 4%: 4% (.04) x $160,000 = $6,400.
A property manager negotiated a 15-year graduated lease with the following terms: The lessee will pay $550 per month for the first five years, with a $50 a month increase every five years thereafter. If the property manager is paid a 6.75% commission, what will be the total commission paid at the end of the term? A) $7,920 B) $7,290 C) $7,087 D) $7,429
B) $7,290 Step 1: determine total rent paid, see chart. Total Rent Paid $550 × 12 × 5 = $ 33,000 $600 × 12 × 5 = $ 36,000 $650 × 12 × 5 = $ 39,000 $108,000 Step 2: determine the fee, $108,000 × 6.75% (.0675) = $7,290.
A small condo sold for $62,250, which was 75% of the list price. What was the list price? A) $77,812 B) $83,000 C) $81,250 D) $74,700
B) $83,000 $62,250 (sales price) ÷ 75% (.75) = $83,000 (the list price)
An apartment building has a semiannual net income of $48,000 and has been appraised for $1,250,000. What is the cap rate? A) 7.86% B) 7.68% C) 4.38% D) 3.84%
B) 7.68% $48,000 × 2 = $96,000 $96,000 ÷ $1,250,000 = 7.68% (.0768)
What capitalization rate is indicated by a property producing $10,000 annual net operating income (NOI) for which an investor paid $105,263? A) 9% B) 9.5% C) 10% D) 10.5%
B) 9.5% $10,000 (annual NOI) ÷ $105,263 (purchase price) = 9.5% (.095) the capitalization rate
After closing expenses of $550 and a 6% commission was paid, the seller received a check for $149,850. What was the sale price of the property? A) $155,424 B) $150,400 C) $160,000 D) $159,424
C) $160,000 100% - 6% = 94% $149,850 + $550 = $150,400 (needed before commission) $150,400 ÷ 94% (.94) = $160,000.
A buyer purchased two parcels of land. One parcel was two miles square and the other contained 30 acres. If the land cost $2,000 an acre, what was the cost of the land? A) $1,340,000 B) $1,626,000 C) $2,620,000 D) $1,800,000
C) $2,620,000 One square mile is 640 acres, so two square miles is 1,280 acres. The two parcels together contain 1,310 acres (1,280 + 30 = 1,310). To find the cost, multiply the cost per acre by the total acres: 1,310 × $2,000 = $2,620,000.
A homeowner has a property valued at $125,000 that is assessed at 35% of its value. If the local tax rate is 6,400 mills per $100 of the assessed value, what are the monthly taxes? A) $140.33 B) $480.00 C) $233.33 D) $280.00
C) $233.33 Tax rate = 6,400 mills ÷ 1,000 = 6.40 ÷ 100 = .064 Assessed value = $125,000 × 35% (.35) = $43,750 $43,750 × .064 = $2,800 Annual tax $2,800 ÷ 12 = $233.33 Monthly tax
What is the two discount points fee on a $180,000 Veterans Affairs-guaranteed loan? A) $2,700 B) $900 C) $3,600 D) $1,800
C) $3,600 $180,000 loan × 2% (.02) = $3,600 (discount point fee) A point is equal to 1% of the total loan amount. 1% (.01) × $180,000 = $1,800 × 2 (2 points) = $3,600
The lender negotiated a $55,000 loan and charged three discount points. What was the cash outflow of the lender? A) $56,650 B) $53,530 C) $53,350 D) $56,560
C) $53,350 $55,000 - $1,650 (3%) = $53,350
A seller wants to net a profit of $20,000 and agrees to pay a 7% commission. He also has closing expenses of $400 and a mortgage of $32,250. What is the minimum offer he could accept for the property? A) $58,565 B) $59,656 C) $56,613 D) $59,545
C) $56,613 $20,000 (profit) + $32,250 (mortgage) + $400 (closing) = $52,650 (before commissions) 100% - 7% = 93% $52,650 ÷ 93% (.93) = $56,612.90 round to $56,613
A rectangular lot is 275 feet deep, and it contains 2/3 of an acre. What is the length of the lot? A) 106.5 feet B) 158.4 feet C) 105.6 feet D) 290.04 feet
C) 105.6 feet 43,560 ÷ 3 = 14,520 × 2 = 29,040 sq. ft. 29,040 ÷ 275 ft. = 105.60 ft. 43,560 × .6667 (2 ÷ 3 = .6667) = 29,041.45 sq. ft. 29,041.45 ÷ 275' = 105.6052 ft.
A building is valued at $215,000 and contains four apartments that rent for $470 each per month. The owner estimates that the net operating income (NOI) is 65% of the gross rental receipts. What is the capitalization rate? A) 3.7% B) 10.5% C) 6.8% D) 14.2%
C) 6.8% To find the rate, divide the NOI by the value of the building. First, calculate the NOI: $470 (unit rent for one month) × 4 (number of units) = $1,880 × 12 (months in a year) = $22,560 × 65% (.65) (owner's estimate of NOI) = $14,664 (the NOI). $14,664 ÷ $215,000 (building's value) = 6.8% (.068)
A savings and loan agreed to make a $65,000 mortgage at 8% interest for 30 years and charged three points to negotiate the loan. What was the effective yield to the lender? A) 8.35% B) 8.25% C) 8.38% D) 8.735%
C) 8.38% The lender yield per point is 1.25% (.125). .125 × 3 = .375 8% + .38 = 8.38%
The buyer had a 20% down payment on a property she purchased for $89,500. She also must pay a 1% origination fee, $350 for title insurance, and one discount point. How much money will the buyer owe at the closing? A) $20,350 B) $17,423 C) $18,966 D) $19,682
D) $19,682 Step 1: determine the loan amount, $89,500 × 80% (.80) = $71,600. Step 2: determine the down payment, $89,500 - $71,600 = $17,900. Determine the points and origination fee $71,600 × 1% (.01) = $716. Total as shown low. + $17,900 Down payment $716 Discount points $716Origination fee $350Insurance $19,682 Total due at closing
Semiannual property taxes of $450 were paid only for the first half of the year. The property sold on July 11 and closed on September 19 with the seller having the day of closing. If the taxes were prorated and paid between the buyer and seller as of the date of sale, using a 360-day year, what will the seller owe at closing? A) $387.50 B) $252.50 C) $251.50 D) $197.50
D) $197.50 The seller owes July, August and 19 days of September for a total of 79 days. Total due ÷ Total days × Days owed: $450 ÷ 180 × 79 = $197.50
A building is 200 feet wide, 300 feet long, and five stories high (each story 12 feet in height). How much does the building cost at $0.79 per cubic foot? A) $275,982 B) $2,568,880 C) $237,000 D) $2,844,000
D) $2,844,000 A cubic foot is a measurement of volume. To find the volume of the building, multiply width × length × height: 200 × 300 × 12 = 720,000 cubic feet (for each floor). The cost per floor is 720,000 × .79 = $568,880. The building is five stories high, so to find the total cost multiply 5 × $568,880 = $2,844,000.
A developer wants to purchase four acres of land that sells for $2.20 per square foot. What is the cost for the parcel of land? A) $191,664 B) $287,496 C) $574,992 D) $383,328
D) $383,328 To find the cost of the land, first convert the acreage to square feet: 43,540 square feet (per acre) × 4 = 174,240 square feet. Then multiply the total square feet times the price per square foot: 174,240 × $2.20 = $383,328.
If the effective gross annual income generated by an apartment house is $112,000 and operating expenses are $53,700, what capitalization rate is used to obtain an indicated value of $542,325? A) 10.25% B) 10.50% C) 9.75% D) 10.75%
D) 10.75% $112,000 (effective gross income) - $53,700 (expenses) = $58,300 (net operating income) $58,300 ÷ $542,325 (property value) = 10.75% (.1075) (the capitalization rate)
How many cubic yards of concrete must a builder buy to pour a sidewalk that measures 45' × 3.25' and is five inches thick? A) 6.7708 B) 60.9375 C) .4167 D) 2.2571
D) 2.2571 5'' ÷ 12'' = .4167' 45' × 3.25' × .4167' = 60.9423 cubic ft. 60.9423 ÷ 27 = 2.2571 cubic yds.
To compute the return on investment, a property manager would need all of the following figures EXCEPT A) expenses. B) potential gross income. C) debt service. D) cap rate.
D) cap rate. An appraiser uses the cap rate to compute the value, but it is not used to determine the return on investment.
