Real Estate Math Exam - Practice Questions

Richard Rock sold his residence which was unencumbered. Total deductions in escrow amounted to $215.30 in addition to a broker's commission of 6% of the selling price. The selling price was the only credit item. Richard Rock received a check for escrow amounting to $15,290. The selling price was most nearly:

$16495

A seller took back a second trust deed and note in the amount of $11,400, payable $240 per month, including interest at 7% per annum. If interest on the note begins July 15 and the first payment is made on August 15, the amount of the first payment that is applied to the principal is:

$173.50 (11400 * .07 = 798 (per yr); 798 / 12 = 66.50 (per mo); 240 - 66.50)

One month's interest on a straight note amounted to $45. At 4.5% per year, what was the face amount of the note?

$12,000 ($45 * 12 = $540 / .045 = 12000)

If a note in the amount of $22,250 specifies monthly payments over a period of 30 years at 6.6% interest per annum, what is the first month's interest payment?

$122.38 (22250*.066 = 1468.50 / 12 = 122.38)

Andrew Blacker 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?

$13,000 (5460/5 = 1092 / .084)

Arnold held a straight note which carried an annual interest rate of 8.4%. If in five years he had received $5460 in interest, the principal amount of the note was:

$13,000 (5460/5 = 1092 / .084)

Kent was the owner of a straight note with an annual interest rate of 8.4%. In 5 years he had received $5460 in interest. The principal amount of the note was most nearly?

$13,000 (5460/5 = 1092 / .084)

A property in probate was offered for sale and an offer of $12,000 was received. If anyone else wishes to bid on the property at the time of the confirmation, the initial minimum overbid must be:

$13,100 (Original bid + 10% of first 10k & 5% of any excess)

After subtracting $140 escrow fees and 6% commission on gross sales price, a seller receives $13,584. What is the selling price?

$14,600 (100%x = 13584 + 140 + 6%x; 94%x = 13854+140; 13724/.96 = 14600)

After subtracting $140 escrow fees and 6% commission on gross sales price, a seller receives $13584. What is the selling price?

$14600 (P = 13584+140+.06P; .94P = 13724)

A house sold for $16,350 which was 9% more than its original cost. What was the original cost?

$15,000 (109%x = 16350; 16350/1.09 = 15000)

A house sold for $16350, which amount was 9% more than the cost of the house. The cost of the house was:

$15,000 (16350/109%)

Mr. John listed his home with Broker Bob for $35,000. The broker was a receive a commission rate of 6%. The broker brought an offer at 10% less than the listed price. The owner agreed to accept the offer if the broker reduced his commission by 20%. If they all agree to these terms, what amount of commission would the broker receive?

$1512 ($35000 * .10 = $3500; $35000 - $3500 = $31500; $31500 * .06 = 1890; $1890 * .20 = $378; 1890 - 378 = 1512)

Humphreys sold his residence which was unencumbered. Total deductions in escrow amounted to $215.30 in addition to a broker's commission of 6% of the selling price. The selling price was the only credit item. Humphreys received a check from escrow amounting to $15290. The selling price was most nearly:

$16,495 (P = 15290+215.30+.06P; .94P = 15505.30; P = 15505.30/.94)

A man borrowed $750 on a straight note at an interest rate of 7.2%. If his total interest payment was $67.50, the length of the loan was:

Fifteen months ($750 * 7.2% = $54; $54 / 12 mo = $4.50 / mo; 67.50/4.50 = 15 months)

Mr. and Mrs. Smith acquired a home in 1977 for $48,000. In 1987 they sold it for $60500 and moved into an apartment unit. During the ten year period of ownership, permanent improvements totaling $12,750 were made to their house. If Mr. Smith's income consists entirely of wages, how would the sale affect his 1987 federal income return?

No affect. (Cost + Additions = 48,000 + 12750 = 60,750. Difference: 60750 - 60500 = -250. Losses are not deductible on the sale of a residence)

Assume a real estate salesman sold a residence for $31,000. If the broker's commission was 6% and the salesman was the receive 45% of the total commission for selling the property, the salesman would receive:

None of the above (Commission is exactly $837)

Assume a real estate salesman sold a residence for $31,000. If the broker's commission was 6% and the salesman was to receive 45% of the total commission for selling the property, the salesman would receive:

None of the above (Commission is exactly $837)

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? The:

Rate of depreciation exceeds 4% per annum.

An owner of a section of land dedicates an easement for a road along the south side of his section. The easement contained 3 acres. The width of the road was approximately

Twenty feet (Section is 1 mile; 3 acres is 43560*3=130680 / 5280 = 24.75)

The number of townships in a tract of land that is 28 miles square is most nearly:

Twenty two (township is 6 miles square and contains 36 sq mi. 28*28 =784 / 36 = 21.77)

A parcel of land 1/4 mile by 1/4 mile is how many acres?

forty acres (5280 / 4 = 1320; 1320^2 / 43560 = 40)

Able purchased a $15,000 home. His down payment amounted to 6 2/3% of the purchase price; the balance was carried as a first trust deed bearing interest at 8.4% per annum. The principal is to be repaid at $50.00 per month. A three-year insurance policy costs $72; the property taxes are $360 per year. Able is required to make a proportionate monthly payment to a loan trust fund for these items. The total amount of the first monthly payment most nearly would be:

$182

A building was insured for $19500 at a rate of .18 per hundred. If the three year policy was 2.5 time the one year rate, what amount per month should be added to the monthly payments to properly cover the insurance cost?

$2.44 (.18*2.5=.45 per 100; 19500*.45/100=87.75 / 36 (months))

An investor owns a 20-unit apartment house. When compared to comparable apartment properties he loses $200 net income a month because his property is located next to a busy freeway. Appraisers are using a 12% capitalization rate for this neighborhood of income properties. The subject property has suffered a loss in value in the amount of:

$20,000 ($200 * 12 = 2400; 2400 / .12)

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?

$20,000 (23,000/1.15)

A homeowner sold his house for 23000. If the selling price represented a 15% profit over what he had originally paid for the house, the original price of the home was:

$20,000 (23000/1.15)

An apartment house property costs $240,000 and this price has been verified to be an accurate estimate of the property value. In comparable circumstances it is also verified that the owner may use a 10% capitalization rate to the purchase price in determining his net income. Should there be a 10% increase in rental income with no increase in the owner's expenses and should the capitalization rate of the property be increased to 12%, what would be the estimated value of the property?

$220,000 (Value x Cap Rate = Income)

Escrow closed May 1st with interest on a $4415 second trust deed paid to June 1st. If the interest rate is 7.2%, the debit to the buyer, if the buyer assumed the loan, would be:

$26.49 (4415 * (.072/12) = 26.49 (one month interest))

Escrow closed May 1 with interest on a $4,415 second trust deed paid to June 1. The interest rate is 7.2% what is the debt to the buyer, if the buyer assumes the loan?

$26.49 (Sellers paid 1 months interest in advance, must be returned to them. $4415*.072/12)

There are five units in a condo. Smith paid $12,600, Jones paid $13,500, Kahn paid $13,750, Poe paid $14,400 and Clark paid $15,250. If there was an $1800 annual maintenance fee and each owner was to pay his proportionate share based upon the ratio of his unit purchase price to the total purchase price of all units, the monthly share of Smith's unit would be:

$27 (Total: $69500; Smith's 12600/69500 = .18 * 1800 = 324 / 12 = 27)

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?

$3,000 ($50000 * .06)

Mr. Brown, licensed broker, took an offer from Mr. Green on land for $6,000 with the following terms: $2,000 down and purchase money trust deed and note for the balance, payable $70 per month including interest at 7.2%. If the offer was accepted by the seller, what is the balance of the loan after the first 3 months payment?

$3,861

A man had an income property which suffered a $300 monthly loss of net income when a freeway was built nearby. At a capitalization rate of 12%, how much did his property lose in value?

$30,000 ($300 * 12 = $3600; 3600/.12)

The Phillips sold her home for $36,850, which represents a 17% profit over the original price. What was the original price?

$31495 (36850/1.17)

If Haeli McDonald paid a commission of 6% of the selling price of a property valued at $54,375, the selling broker would receive:

$3262.50

One month's interest on a 5 year straight note amounted to $225. At a 7.5% per year interest rate, what was the face amount of the note?

$36,000 (12*225=2700; 2700/.075 = 36000)

An individual who receives $225 per month on a money market savings account that pays 7.5% per year, has invested which of the following amounts?

$36,000 (225*12 = 2700 / .075)

A married couple purchased a property for a total price of $18,000, paying $5,000 down and having the seller take 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 at the end of the first year, they were to sell the property at twice its original cost, their original dollar is now worth:

$4.60 (18000*2=36000-13000=23000; 5000/23000)

An investor purchased property for a total price of $72000, paying $20,000 down and financing the balance of $52,000 using a straight note. If the investor eventually sold the property after it had doubled in value and had made no principal payments on the loan, each dollar invested would show a return of:

$4.60 (New selling price is $72000*2 = 144,000; 144000 - 52000 (loan) = 92000 (return); 92000 / 20000)

A husband and wife own a vacation home in the mountains. The annual taxes on the property are $400. Since the total taxes cannot exceed 1% of the full cash value of the property, the "full cash value" of the property would be:

$40,000 (400/1%)

Smith and Allen wish to exchange real property. Smith owns a property valued at $150,000 against which there is a $35,000 trust deed. Allen owns property worth $105,000 on which there is an existing first trust deed of $25,000 and a second trust deed of $20,000. Allen has $15,000 in cash which he is willing to pay towards the exchange. If Smith is willing to accept a second trust deed and note from Allen in order to effect the exchange, the amount of the note would be:

$40,000 (Market Value - Loan = Equity)

Assume that a second trust deed of $1,000 was to be paid in annual installments of $300 plus 6% interest, with a balloon payment of the balance at the end of the third year. The remaining balance of the principal after the second annual installment was paid would be:

$400 (300 * 2 = 600; 1000 - 600 = $400)

Assume that a second trust deed of $1000 was to be paid in annual installments of $300 plus 6% interest, with a balloon payment of the balance at the end of the third year. The remaining balance of the principal after the annual installment had been paid was:

$400 (300 * 2 = 600; 1000 - 600 = $400)

A man enters into a lease agreement on a grocery store with the following terms: $350 minimum monthly rent or 5% of grocery sales, 7% of meat sales, 6% of deli sales, and 8% of produce sales (whichever is greater). The grocery sales were $27000 annually, meat sales $500 per month, deli sales $300 per month and produce sales $3000 annually. What was the annual rent on the store?

$4200 (27000/12=2250*.05=112.50; 500*.07=35; 300*.06=18; 3000/12=250*.08=20; 112.50+35+18+20= 185.50 (less than minimum rent) 350*12 = 4200)

A man bought a home for $31680 and now wishes to sell. He is informed that the cost of selling will amount to 12% of the selling price. He wishes to sell at a price so as not to have a loss. How much would the home have had to appreciate in order to offset the selling costs?

$4320.

The Southern Pacific Railroad Company sold ABS Developers three sections of land that had been divided into 20 acre parcels. 16 sold at $4,000 each and the remainder sold at $5,000 each. Which of the following was most nearly the total amount realized by the seller?

$475,000

An investor was going to have a building constructed which was to cost $150000 and could, when completed, be leased for $2500 per month. The annual operating expenses for the property would be $6000. The amount he could invest in the land to realize a 12% return would be:

$50,000 (2500*12 = 30000; 30000-6000 = 24000; 24000/.12 = 200000; 200000 - 150000)

A prospect is considering the purchase of an income property which has an operating statement showing $94,500 deducted from gross income to arrive at the net income. The deductions amount to 60% of the gross income. If the prospect wants a 12% return on the purchase price of any investments he makes, what should he pay for the property?

$504,000 (94500 = 60% x GI. 94500/.6 = 157,500 (GI) GI - Exp = Net Inc. 157500 - 94500 = 63000. Net income value = Net inc/return rate. 63000/.12 = 525,000)

Lots "A", "B" and "C" sold for a total price of $39,000. If lot "B" was priced at $6,400 more than lot "A", and lot "C" was priced at $7,100 more than lot "B", the price of lot "A" was:

$6,366.67

A bank agreed to lend the owner of a piece of property a sum equal to 66.667% of its appraised valuation. The interest rate charged on the amount borrowed is 5% per annum. The first year's interest amounted to $200. What was the valuation placed upon the property by the bank?

$6000 (200/.05 = 4000 (loan) / 66.66% =6000)

If broker Christianson brought in an offer of 10% less than the listing price of $15,300 and the seller would agree to the price if the broker would accept a 20% reduction of his commission, the broker's commission would amount to:

$660.96 (15300-1530 = 13770; 13770*.06=826.20; 826.20*.80 = 660.96)

A man owns an apartment building with 20,000 square feet of living space and wants to carpet 60% of the area. If the carpet costs $6 a square yard, what is the total cost of the carpeting?

$7,998 (20,000 * .60 = 12000; 12,000/9 = 1,333 * $6 = $7998)

Natalie Johnson owns a $100,000 property based on a 6% capitalization rate. If due to changes in economic conditions investors now require a higher capitalization rate or 8%, what would the value of the property be using the same dollar income?

$75,000 (100000*.06=6000 / .08=75000)

An income property was appraised for $100,000 based on 6% capitalization rate. If an investor used an 8% cap rate, the value of the property would be:

$75000 (100000*.06=6000/.08=75000)

Harris obtained a loan in the amount of $20,000 and paid the mortgage lender four discount points and an origination fee of 2%. If the payments on the loan were $163 per month, including 8% interest and the average balance over a five year period was $18500, the gross amount earned by the lender in the 5 years was most nearly:

$8600 (20000 * .04 = $800 (points); 20000 * .02 = $400 (fee); 18500 * .08 = 1480 (annual int) * 5 = $7400; 7400 + 400 + 800)

A real estate syndicate paid $193600 for a lot on which they planned to build a high rise apartment. If the lot was 200 feet deep and they paid $4.40 per square foot, the cost per front foot was:

$880 (193600/4.4=44000 / 200 = 220 (feet frontage); 193600/220 = 880)

If the interest is paid at a rate of $60 per month and the rate of interest is 8% per year, what is the principal amount of the loan?

$9,000 (12mo * $60 = $720 int/yr; 720/.08 = 9000)

A duplex with a fair market value of $20,000 and an outstanding loan balance of $12,000 was exchanged for a four-plex with a market value of $35,000 and an outstanding $18,000 loan balance. The owner of the duplex would pay in cash or secondary financing

$9,100 (Market Value - Loan = Equity) - Duplex: 20k-12k=8k 4plex: 35k-18k=17k diff: 17k-8k=9k

The fastest way to calculate one month's interest on a real estate loan with an interest rate of 7.2% interest per annum is to multiply the principal balance by

0.006 (7.2%/12)

A rectangular parcel of land measures 220'x330' contains most nearly:

1 2/3 acres (220*330/43560)

A homeowner made a regular monthly payment of $550 on her home loan. Out of the total payment, the lender deducted the interest that was due for the month and applied the remaining balance of $43.85 to the principal. If the outstanding balance of the loan was $56,500, the interest rate on the loan was most nearly:

10.75% (550-43.85=506.15 * 12=6073.80 / 56500=11%)

A rectangular parcel containing 540 square yards which has a frontage of 45' would be how many feet deep?

108' deep. (1 sq yd = 9 sq ft * 540 = 4860 sq ft; A = L * W; 4860 = L * 45; L = 4860/45 = 108)

If a borrower pays $1650 interest per quarter on a straight note of $60,000, the interest rate would be:

11% (1650*4=6600/60000)

Clever executed a promissory note in the amount of $7000. If the note called for the payment of interest only and Clever paid off the entire sum in 90 days together with interest of $210, the interest rate on the note was most nearly:

12% (210*4=840 / 7000)

Eddie Ronquillo sold his home for $17200. If this represents 9% more than what he paid for it, the cost of the home was most nearly:

15800 (17200/1.09=15779.82)

If a building's costs increased 20 percent, the value of the investor's dollar has decreased by:

16 2/3% (Materials bought yesterday for 100 now cost $120. 100/120 = 1/6 = 16.667%)

Mr. Morton paid $945 interest on a straight note loan of $7,000, at a rate of 9%. What was the term of the loan?

18 months (7,000 * .09 = $630 / 12 = 52.50 (per mon); $945 / $52.50 = 18 mo)

An individual borrowed $750 on a straight note at an interest rate of 7.2%. If the total interest payment on the loan was $81, the term of the loan was:

18 months (750*.072=54 / 12=4.5; 81/4.5 =18)

A commercial office building yields an annual net income of $174,000. If an appraiser applied a capitalization rate of 8% to the property, the market value of the property would most nearly be:

2175000 (174000/.08)

Keith Johnson purchased a property at 20% less than the listed price and later sold the property for the original listed price. What was a percentage of profit?

25%

A man bought two 60 foot lots for $18000 each and divided them into three lots which he sold for $15,000 each. What was his percentage of profit?

25% ((18000*2 + 15000*3) / (18000*2))

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 3 lots with equal frontage. If the 3 lots sold for $15,000 each, his rate of profit on his investment was:

25% ((18000*2 + 15000*3) / (18000*2))

A man 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?

25% (List price: $10; Purchase price $8; Profit $2; 2/8 = .25)

What is the monthly return on an income property with a 6.5% return on its value of $46,500?

251.88 (46,500 * .65 = 3022.50 / 12 = 251.88)

The Richard Rock sold his home and had to carry back a second trust deed and note of $5310. If he sold the note for $3823.20 before any payments had been made on the note, the rate of discount amounted to:

28% (5310-3823.20 = 1486.80 / 5310)

Maria Watson sold a residence that was free and clear of all liens and received a check for $30,580. If closing costs of $430.60 had been deducted as well as the broker's 6% commission, the actual selling price would have been most nearly:

32990 (30580+430+.06P = P; 31010.60/.94)

A holder of a second trust deed and straight note with a face amount of $3740 sold it for $2431. This amounted to a discount of:

35% (3740-2431 / 3740)

Eddie Ronquillo sold his house and took back a note for $4200 secure a second deed of trust. He promptly sold the note for $2730. This represents a discount of:

35% (4200 - 2730 / 4200)

Ms. Rodgers sold her house and took back a note for $4200 secured by a second deed of trust. She promptly sold the note for $2730. This represents a discount of:

35% (4200-2730 = 1470 / 4200)

Escrow companies normally base their prorations on an escrow year of

360 days (12 months at 30 days each)

An individual who receives $225 per month on a money market savings account that pays 7.5% per year, has invested which of the following amounts?

36000 (225*12=2700/.075)

Broker Thomas is listing a property owned by Gibson. Gibson has advised Thomas that he wished to realize $37,000 Cash from the sale after paying Thomas a 4% commission and paying $600 in closing costs. To accomplish this and assuming that the property is free and clear, the selling price must be at least:

39167 (37000+600+.04P = 37600/.96)

Which of the following contains the largest area?

4 square miles (1/10 of township is 3.6 sq mi; 5280x10560 is 2 sq mi; 2 sections is 2 sq mi)

What is the annual interest rate on a $16,000 loan when the interest payments are $160 per quarter on the full amount? At least:

4% but less than 5% (160*4=640/16000 = 4%)

In order to earn $208 per month from an investment that yields a 6% return, you would have to invest approximately:

41600 ($208 * 12 = 2496 / .12)

A one acre parcel of land that is square is divided into 4 lots of equal size. If the lots are rectangular, parallel to each other and are 240' deep, the width of each lot is most nearly:

45.4' (43560/240=181.5 / 4 = 45.375')

The total number of lineal feet on one side of a Section is:

5280

An acre is to be divided into four equal lots. If the lots are parallel to each other, rectangular, and 200 feet deep, the width of each lot would most nearly be:

55 feet (1 acre = 43560ft2; 43560/200 = 217.8. 217.8/4 = 54.45)

A board foot of lumber could be obtained from a piece of lumber that is:

6" x 12" x 12" (A board foot is 144 cubic inches)

A rectangular parcel of land measures 1780' x 1780' and contains how many acres?

73 (1780 * 1780 = 3168400 / 43560 = 72.74)

A square parcel of land that is 1780' x 1780' contains most nearly

73 acres (1780*1780=3168400/43560=72.736)

A borrower paid $120 interest on a 90-day straight note. The principal was $6,000. Was was the interest rate?

8% ($120 x 4 = $480; $480/$6,000 = .08)

A man paid $140 in interest for a 90 day period on a $7,000 loan. What was the interest rate on the loan?

8% ($140 * 4 (12 months / 3 months) = $560 / $7000 = 8%)

The interest rate on a straight note in the amount of $27,000 that calls for interest payments of $573.75 each quarter would most nearly be:

8.6% (573.75*4=2295 / 27000 = .85)

How many acres are contained in a parcel of land 1320 by 2640?

80 (1320 * 2640 = 3484800; 3484800 / 43560 = 80)

A building that has interior dimensions of 26' x 30' and has 6" walls would cover how much square footage of land?

837 (L = 26' + 6" + 6" = 27'; W = 30' + 6" + 6" = 31'; 27 * 31 = 837)

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:

9% (150/8 = 18.75/mo; 18.75*12=225; 225/2500)

If $150 interest is paid in 8 months on a straight note loan of $2500, what is the annual rate of interest?

9% (8 mo = 2/3 yr = 150 int; 150/.67 = 227.27 int for 8 mo; 227.27/2500)