NJ RE Exam Scholar Math

Steve bought a piece of property for 25% less than the listed price. He later sold it for the listed price. His gain was:

33%. Explanation: If the listing price is $100,000, 25% less would be $75,000. Later selling at $100,000 would be a gain of $25,000 divided by $75,000 = .33 (33%).

John has a loan for $18,000 with interest to be paid at the rate of $225 quarterly. What is the interest rate on the loan?

5% but less than 6% Explanation: 225 x 4 = 900 divided by 18,000 = .05 (5%).

A $5,000 investment at 10% interest compounded annually earns how much in three years?

$1,655 Explanation: $5,000 x 10% = $500 (interest for 1st year). $5,000 + $500 = $5,500 x 10% = $550 (interest for the 2nd year). $5,500 + $550 = $6,050 x 10% = $605 (interest for the 3rd year). $500 + $550 + $605 = $1,655 interest earned in 3 years. Remember, compound interest is interest on the principal and prior interest earned.

An owner of a home listed it at a price which would leave him $16,800 after the broker received a 6% commission. If the broker sold the property at the listed price, how much commission would he receive?

$1,072. Explanation: $16,800 divided by 94% = $17,872 - $16,800 = $1,072 commission.

Frank purchased a home for $80,000. He financed the purchase with a 90% conventional fixed-rate loan. The loan fee charged by the lender was 2%. The private mortgage insurance company charged a .50% first-year premium and a .75% renewal premium. What was the loan fee? The first-year premium? The monthly renewal premium?

$1,440; $360; $45 Explanation: Loan fee = $80,000 x 90% x 2% = $1,440. First year premium = $80,000 x 90% x .5% = $360. Monthly renewal = $80,000 x 90% x .75% divided by 12 = $45.

Ted, an intelligent real estate investor wants to purchase a 60-unit apartment building that has an annual net income of $180,000. How much would he be willing to pay for the building if he uses a 12% capitalization rate?

$1,500,000 Explanation: $180,000 divided by 12% = $1,500,000.

Inventory in a store costs $8,500 net. It was sold for 20% profit. However, 10% of the gross profit was lost due to bad credit risks over a period of one year. How much profit did the store owner make that year?

$1,530 Explanation: $8,500 x .20 = $1,700 x .10 = $170. $1,700 - $170 = $1,530.

A buyer is obtaining a conventional loan that requires 29/33 ratios. He earns $75,000 a year, and has a $450 car payment. What is his maximum PITI payment?

$1,612.50 Explanation: $75,000 + 12 = $6,250 monthly income. $6,250 x .29 = $1812.50 front end qualifier. $6,250 x .33 = 2062.50— $450 debt = $1612.50 back end qualifier. The maximum PITI (Principal, Interest, Taxes, and Insurance) is the lower of these two qualifiers.

A loan was made for $14,000 at an interest rate of 6% per year for a 20-year period. The total interest that would be paid over the entire loan period if the monthly payment for this fully amortized loan is $7.17 per $1,000, would be approximately:

$10,000. Explanation: $7.17 per $1,000 x 14 thousands = $100.38 monthly payment;|20 years x 12 months = 240 monthly payments;|$100.38 x 240 = $24,091.20;|$24,091.20 - $14,000 (money borrowed) = $10,091.20 total interest paid.

Steve sold his home which had no loans against it. He received a settlement check from escrow for the amount of $96,400 after paying escrow fees of $1,365.00 plus a 6% real estate broker's commission. What was the selling price?

$104,005 Explanation: $96,400 + $1,365.80 = $97,765.00 net amount after paying commission. $97,765.00 divided by 94% = $104,005.32 selling price.

An apartment's financial statement disclosed the following: Gross income = $20,000; vacancy factor = 9%; operating expenses = $5,000; payments to amortize the existing 1st and 2nd deeds of trust = $300 monthly. Using a 12% capitalization rate, what is the value of the property?

$110,000 Explanation: $20,000 (gross income) - $1,800 (vacancy factor) = $18,200 (effective gross income). $18,200 - $5,000 (operating expenses) = $13,200 (net income). $13,200 divided by .12 (cap. rate) = $110,000. Note: You cannot subtract principal or interest payments on trust deeds. This is not an operating expense.

Mr. White sold an apartment building for $139,000. This was 20% more than what he paid for it. His original cost was approximately:

$115,833. Explanation: Divide $139,000 by 120% to produce an answer of $115,833.33.

Ned just sold his house for 9% less than he paid for it. The selling price was $105,900. What was the original purchase price?

$116,374 Explanation: $105,900 represents 91% of the original price. $105,900 divided by 91% = $116,373.63(original purchase price).

Kevin Holstead, the owner of a commercial building, estimates the depreciation of the physical plant at $15,000, the furniture and fixtures at $8,000, and the machinery at $7,500. If he is in the 40% bracket, his tax savings would be:

$12,200. Explanation: The owner would save 40% of the total depreciation. ($15,000 + $8,000 + $7,500)x 0.40 = $12,200.

A deposit receipt states, "Buyer to assume existing first trust deed of $8,000 at 6-1/2% paid per quarter." If Mr. Pinkham took possession February 15th and the first interest payment was due on March 15th, how much would Mr. Pinkham pay on the next interest date?

$130.00 Explanation: $8,000 x 6-1/2% (0.065) = $520.00 interest/year; $520 divided by 12 (months) = $43.33 interest/month; $43.33 x 3 (1/4 of a year) = $130.00/quarter.

A deposit receipt states, "Buyer to assume existing first trust deed of $9,600 at 5-1/2% paid per quarter." If Mr. Taylor took possession February 15th and the first interest payment was due on March 15th, how much would Mr. Taylor pay on the next interest date?

$132.00 Explanation: $9,600 x 5-1/2% = $528.00 interest per year. $528 divided by 12 (months) = $44 interest per month. $44 x 3 (1/4 of a year) = $132.00 per quarter.

A homeowner has a balance of $149,570.75 remaining on the mortgage. The interest rate is 9.5% and the monthly payment is $1,303.55. After the next two payments, the balance will be:

$149,330.91. Explanation: $149,570.75 x 0.095 ~ 12 = $1,184.10 month interest; $1,303.55- $1,184.10 = $119.45 principal; $149,570.75 -$119.45 = $149,451.30; $149,451.30 x 0.095 ~ 12 = $1,183.16 month interest; $1,303.55$1,183.16 = $120.39 principal; $149,451.30- $120.39 = $149,330.91.

Ms. Williams purchased a house in a run-down condition and spent an amount equal to 10% of the purchase to fix it up and bring it to its present value. The house in now worth $18,700. The cost of the house is equal to the existing loan of the property. The amount of the loan is:

$17,000. Explanation: $18,700 = 100% purchase price + 10% fix-up money. $18,700 divided by 110% = $17,000.

Tom obtains an interest-only purchase money loan for $60,000. The interest rate is 9.5% and the term is 30 years. How much interest will Tom have paid at the end of the 30-year term?

$171,000 Explanation: $60,000 x 9.5% = $5,700 interest per year. $5,700 x 30 years = $171,000 total interest.

Ted borrowed $40,000 from a bank to purchase a lot. He paid 4 points to get the loan. The loan contained a 4% prepayment penalty. His monthly payment was $160.00, including interest at 8% per year. Five years later, John sold this real estate and paid-off the loan. If the loan had an average loan balance of $38,500 during the five years Ted owned the property, what was the bank's gross profit on this loan?

$18,600. Explanation: $40,000 x 4% = $1,600 points. $40,000 x 4% = $1,600 prepayment penalty. $38,500 x 8% = $3,080 interest per year. $3,080 x 5 years = $15,400. $1,600 + $1,600 + $15,400 = $18,600 gross profit by bank.

Investor Bob bought a piece of income property for $185,000. The listed price was $240,000. He put $10,000 down and acquired a new first trust deed for the difference. The tax assessed value was indicated at $160,000. Investor Bob's cost basis for income tax purposes would be:

$185,000. Explanation: Cost basis for income tax purposes (book value) is the price paid for the property.

Mr. Jones, an owner of a packaging firm, purchased a new machine in 1991 and paid $5,500. It was estimated at the time of the purchase to have a total economic life of 10 years and a salvage value of $550. Using the straight line method of depreciation, the book value at the end of 7 years would be:

$2,035. Explanation: Salvage value must be deducted before computing depreciation. $5,500 - $550 = $4,950 divided by 10 = $495 per year x 7 years = $3,465. $5,500 - $3,465 = $2,035 (book value).

Jerry spends 25% of her gross monthly income on her apartment rent of $600. What is her gross monthly income?

$2,400 Explanation: $600 divided by 25% = $2,400.

A man needed money to purchase a new car and had a real estate broker arrange a fully amortized 3-year loan using his home as security. The note was for $2,500 calling for payments of $80.00 per month, including 10% interest. If the borrower received $1,900 cash proceeds from the loan after deducting all expenses, the total amount of principal that must be paid to the lender on the note is:

$2,500. Explanation: Since the borrower signed a note for $2,500, he will be required to pay back this amount of principal plus the interest.

To buy a car, Bob executed a second trust deed and note on his home for $2,600, payable at $66.00 per month, including interest at 8%. When he sold his home, he paid off the entire loan balance of $1,989.50. What was the total face amount of the principal on the loan?

$2,600 Explanation: The face amount of the loan is the amount of the original amount on the note.

The Bakers bought a vacation home with a $90,000 first mortgage. Current conventional rates are 10.5%, 30-year term. The seller agreed to pay three points, which will amount to:

$2,700. Explanation: $90,000 x 3% = $2,700.

Sam paid $310,000 for an income property. His tax bill showed the assessments to be as follows: Land $20,120, improvements $37,200. In arriving at a figure to be used for depreciation for income tax purposes, he used his assessment figures as a basis. Which of the following most nearly reflects the depreciable amount:

$201,500. Explanation: $20,120 (land) + $37,200 (improvement) = $57,320. $37,200 divided by $57,320 = 65% improvement. $310,000 x 65% = $201,500. Land is not depreciable for tax purposes.

How much money would have to be invested at 8% interest to provide an income of $140.00 per month?

$21,000 Explanation: $140 x 12 = $1,680 per year. $1,680 divided by 8% = $21,000.

An apartment building is valued at $275,000 using a 7% capitalization rate. How much would an investor pay for the property if she demanded a 9% capitalization rate?

$213,889 Explanation: $275,000 x 7% = $19,250 annual net income. $19,250 divided by 9% = $213,889.89. Remember, as capitalization rate goes up, the value goes down.

Lynn sold a home for $27,000. She made a 15% profit. What did the home cost?

$23,478 Explanation: $27,000 divided by 115% = $23,478.

Rita Morgan has $86,576 left on her 8.5% mortgage. Her monthly payment is set at $852.56 for principal and interest (she pays her own taxes and insurance). How much of her next payment will go to reduce the principal?

$239.31 Explanation: A year's interest on the present debt would be $7,358.96 ($86,576 x 0.085). A month's interest is $613.25 ($7,358.96 ~ 12). The principal portion of her payment is $239.31 ($852.56 —$613.25).

Broker Bob leased a commercial property for 30 years at a rent of $26,000 per year. His commission was 9% of the first year rent, 7% of the rent for years 2 through 5, 4% of the rent for years 6 through 10, and 2% of the rent for years 11 through 30. Assuming all the commission is paid to him as per this schedule, what is the total commission he will receive?

$25,220 Explanation: $26,000 x 9% = $2,340 (first year commission). $26,000 x 7% = $1,820 (per year 2, 3, 4, 5). $1,820 x 4 = $7,280 (total commission for years 2-5). $26,000 x 4% = $1,040 (per year 6, 7, 8, 9, 10). $1,040 x 5 = $5,200 (total commission for years 6-10). $26,000 x 2% = $520 (per year 11-30). $520 x 20 years = $10,400 (total commission for years 11-30). $2,340 + $7,280 + $5,200 + $10,400 = $25,220 total

Ned, a salesperson working for Broker George, received a 45% share of a 8% commission. His share came to $9,000. What was the selling price of the property?

$250,000 Explanation: $9,000 commission divided by 45% share = $20,000 total commission. $20,000 divided by 8% = $250,000 selling price

How much interest would a $6,000 loan earn in five years at 10% simple interest?

$3,000 Explanation: $6,000 x 10% = $600 per year x 5 years = $3,000.

What percentage profit would an investor make if he purchased two lots for $16,000 each and then divided into three lots and sold them for $14,000 each?

31% Explanation: $16,000 x 2 = $32,000 cost of lots. $14,000 x 3 = $42,000 selling price. $42,000 - $32,000 = $10,000 profit. $10,000 divided by $32,000 = 31.25% profit

An income property has a value of $400,000 and returns a net of 8% to its owner. What would the value of this property be to a new purchaser who wished to receive an 10% return on his money?

$320,000 Explanation: The trick is getting the NET INCOME. The net income is determined by recognizing that the property nets its present owner 8% of $400,000 which is $32,000 (400,000 x 8% = $32,000). Now knowing the net income is $32,000 and the investor wants and 10% return on a property with a $32,000 net, you divide the $32,000 (net income) by 10% (the cap rate) to get $320,000 (the appraised value).

A lender charged the borrower 2 points for making a loan. The lender then sold the loan immediately to an investor at a discount of 4-1/2 percent and received $35,800. What was the original loan amount?

$37,487 Explanation: $35,800 divided by 95.5% = $37,486.91. Note the 2 points have nothing to do with answering this question.

What will the amount of taxes payable be if the property's assessed value is $85,000 and the tax rate is 50 mils in a community where the equalization factor is 120%?

$5,100 Explanation: Calculate the tax by multiplying the assessed value times the equalization factor divided by 1,000 multiplied by the mill rate; $85,000 x 1.20 = $102,000 / 1,000 = 102 x 50 = $5,100.

Bob took a listing providing for a 6% commission on the sales price of $210,000. Sue made an offer at the listed price, but did not complete the transaction. The seller declared a forfeiture of the 5% deposit. A provision in the deposit receipt provides that the broker will receive half of the buyer's deposit in the event of the buyer's default. Under these circumstances, the broker is entitled to:

$5,250. Explanation: $210,000 x 5% = $10,500 divided by 2 = $5,250.

An apartment has total operating expenses of $75,000 a year and income of $750 a month for each of its 15 units. If an investor wants a 12% return on his money, what is the value of this property to him?

$500,000 Explanation: $750 x 15 = $11,250 income per month; $11,250 x 12 = $135,000 income per year; $135,000 income - $75,000 expenses = $60,000 annual net operating income. Convert 12% to a decimal and divide; $60,000 12 = $500,000 value to investor.

Mr. Johnson listed his home with Broker Smith for $165,000 with a commission rate of 6%. Broker Smith brought an offer at 10% less than the listed price. Mr. Johnson said he would accept the offer if the broker reduced his commission by 16-2/3%. If they all agreed to these terms, what amount of commission would Broker Smith receive?

$7,425 Explanation: 16-2/3% is 1/6. 1/6 of 6% is 1% (so total commission is 5%). $165,000 x 90% (100% - 10%) = $148,500 selling price. $148,500 x 5% = $7,425.

The original value of a property was $130,000, with the land valued at $20,000. If the economic life of the improvements were estimated to be 30 years using the straight line approach, what was the book value of the property after 15 years?

$75,000 Explanation: $130,000 - $20,000 = $110,000. $110,000 divided by 30 years = $3,666.67. $3,666.67 x 15 years = $55,000 depreciation. $130,000 - $55,000 = $75,000 book value.

A parcel of land was purchased in 1985 and subdivided into four separate lots. Five years later, each lot sold for $200,000. The adjusted basis for each lot was $10,000. What was the capital gain on these transactions?

$760,000 Explanation: $10,000 x 4 lots = $40,000 adjusted basis. $200,000 x 4 lots = $800,000 total selling price. $800,000 - $40,000 = $760,000 capital gain.

What is the salesman's 40% of a 6% commission on a $32,000 sale?

$768 Explanation: $32,000 x .06 = $1,920 x .40 = $768

Broker Bob listed a home for sale for $200,000. He presented the seller with an offer which was 15% less than the listed price. The seller said he would accept the offer if the Broker Bob agreed to reduce her 6% commission by 16-2/3%. If Broker Bob agreed, how much commission would he receive?

$8,500 Explanation: $200,000 x 15% = $30,000. $200,000 - $30,000 = $170,000 (amount of the offer). 16-2/3% = 1/6 (memorize this). 6% reduced by 1/6 = 5% commission. $170,000 x 5% = $8,500 commission to Broker Bob.

Jane purchased a house for $100,000 with a down payment of 25% of the purchase price. The balance was financed on a 30-year amortized loan with interest at 8% per annum. The lender requires monthly impounds for property taxes of $1,000 per year and casualty insurance costing $788 for a three year policy. Assuming that the first monthly payment on the principal is $217, the total amount the buyer will have to pay the first month will be approximately:

$822. Explanation: $100,000 x 25% = $25,000 cash down payment. $100,000 - $25,000 = $75,000 loan amount. $75,000 x 8% = $6,000 annual interest. $6,000 divided by 12 = $500 monthly interest. $788 divided by 36 = $21.89 monthly insurance. $1,000 divided by 12 = $83.33 monthly taxes. $500 + $21.89 + $83.33 + $217 principal = $822.22 total first month payment.

A buyer wants a 8% return on his investment and he is interested in a retail center that produces a net operating income of $75,000 per year, what would the investor be willing to pay for the center?

$937,500 Explanation: Divide the net income, $75,000 by the capitalization rate, 8% to get $937,500.

How many square feet of cement would be needed for a 7-foot wide continual sidewalk around the outside edge of a 60 foot by 90 foot corner lot?

1,099 square feet Explanation: Note around the outside edge. Don't forget the corner.|90 x 7 = 630;|67 x 7 = 469 + 630 = 1,099 square feet.

The regular monthly payment on a loan, including principal and interest, was $560. All of the payment went toward interest, except for $45. The principal balance on the loan during that month was $55,500. What was the interest rate?

11.14% Explanation: $560 - $45 principal payment = $515 interest payment. $515 x 12 months = $6,180 annual interest. $6,180 divided by $55,500 loan balance = .1114 = 11.14% interest rate.

A man owns a lot with 15,400 square feet. It has a depth of 140 feet. He buys two more lots that are adjacent to his lot, both with a depth of 140 feet. Together, the two new lots contain 4,200 square feet. What is the total front footage of all the lots combined?

140 feet Explanation: 15,400 square feet + 4,200 square feet = 19,600 square feet;|19,600 divided by 140 = 140.

Ted paid $85,000 for a house, putting up a 15% cash down payment and borrowing the balance at 8.5% interest. The loan is payable over 30 years with monthly payments of $560, including principal and interest. If Ted makes the payments as scheduled, the percentage that the original cost of the house increased because of the use of credit is?

152.2% Explanation: $560 x 360 months = $201,600 (loan payments). $85,000 x 15% = $12,750 (down payment). $201,600 + $12,750 = $214,350 (total cost). $214,350 divided by $85,000 x 100 = 252.2%. 252.2% - 100% (original cost) = 152.2% increase.

An individual borrowed $9,000 on a straight note and an interest of 7%. If the total interest paid on the note totaled $840.00, the term of the loan was:

16 months. Explanation: To determine this, you multiply $9,000 times 7%, which equals $630.00 interest per year. Next $630.00 divided by 12 equals $52.50 per month. And finally $840.00 total interest divided by $52.50 equals 16 months.

A $7,000 loan is sold to an investor for $6,500. It is a straight note, due and payable at the end of one year. It bears a 9% interest rate. What percentage return on the principal dollar invested will be made by the investor?

17.38% Explanation: $7,000 x 9% = $630 interest paid on the loan. $7,000 - $6,500 = $500 made by investor as a result of the discount. $630 + $500 = $1,130 total profit made by investor. $1,130 divided by $6,500 = 17.38%.

Jim purchased a property for 20% less than the listed price. Later he sold the property for the original listed price. What percentage profit did he make?

25% Explanation: If a property were listed at $150,000 and it was purchased at 20% discount, the purchase price was $120,000. The property is then sold for the list price, $150,000. $150,000 (selling price) - $120,000 (purchase price) = $30,000 (profit) divided by $120,000 = .25 or 25%.

A man purchases a $8,000 straight note for $6,500. Interest rate on the note is 5%. What was his percentage of profit made on his investment if the note is paid off in one year?

29.2% Explanation: $8,000 x .05 = $400. $8,000 - $6,500 = $1,500. $400 + $1,500 = $1,900 divided by $6,500 = .292 (29.2%).

An owner is planning to build on newly purchased property. Zoning laws state that no improvement may exceed 50 feet in height, architectural guidelines limit improvements to 45 feet in height, and the deed restriction states the maximum height to be 30 feet. What is the tallest building the owner can legally construct?

30 feet Explanation: When there is a conflict in limitations on the development of property, the most restrictive applies.

An apartment building cost $600,000. It brings in a net income of $4,000 per month. The owner is making what percentage of return on the investment?

8% Explanation: $4,000 per month x 12 months equals $48,000 per year (always convert monthly rent to annual rent in the income approach). Net income $48,000 + $600,000 cost (or value) = 8% return on the investment.

John bought a house four years ago for $80,000. He just sold it for $86,900. What was the percent of profit?

8.6% Explanation: $86,900 - $80,000 = $6,900 (profit) divided by $80,000 = .086 (8.6%).

Two appraisers, one using a capitalization rate of 10% and the other one 8%, both agree that the net income of a building was $11,200. The higher capitalization rate made the price of the building:

lower by 20%. Explanation: $11,200 divided by 10% = $112,000. $11,200 divided by 8% = $140,000. $140,000 - $112,000 = $28,000 or 20% lower.

Jim bought a second trust deed and note that had a face amount of $1,800 on which he was allowed a 20% discount. If he received payments of $120 per month, including 8% interest, for 1 year, what was his percentage of return on his investment?

No return was received on the investment Explanation: $1,800 x 20% = $360. $1,800 - $360 = $1,440. $120 x 12 = $1,440 - $1,440 = 0. No return on this investment.

Inventory in a store costs $8,500 net. It was sold for 25% profit. However, 15% of the gross profit was lost due to bad credit risks over a period of one year. How much profit did the store owner make that year?

None of the above Explanation: $8,500 x .25 = $2,125 x .15 = $318.75. $2,125 - $318.75 = $1,806.25.

The Smiths offer to buy the Brown's house for $125,000, with the closing scheduled for June 15. The Browns sign a written acceptance, with the provision that the closing is to be on June 16. At this point, which of the following can occur?

The Smiths can back out of buying the house with no penalty. Explanation: When the Browns made a counteroffer, it constituted a rejection of the original offer. The Smiths are now free and may accept or reject the counteroffer.