Realtor Math Problems

What will be the amount of tax payable when the property's original assessed value is $185,000 then a 10% horizontal adjustment is made to all assessed values and the tax rate is 40 mills in a community? $4,625 $5,087 $7,400 $8,140

$8140

How many discount points would the lender need to charge if the lender wishes to increase the yield on the loan from 9% to 10.25%? Two points Eight points Six points Ten points

10 Rationale: Each discount point increases the yield .125. The rates have a difference of 1.25 (10.25-9.0). 1.25/.125 = 10 points.

Determine the excise tax to be paid on a house that sells for $268,210 if the buyer makes a $25,000 down payment and the seller takes back a second mortgage for $50,000? $536.42 $537.00 $533.00 $538.00

537 Rationale: The amount of the excise tax is $1 for each $500 of value. The sales price must be rounded up to the nearest $500. $268,210÷$500 = $237

What is the size of a section of real estate? 640 acres 6 miles square 43,560 square feet 460 acres

640 acres Rationale: A section of land contains 640 acres and measures one mile by one mile. 6 miles square Rationale: A township is 6 miles square. 43,560 square feet Rationale: 43,560 is the number of square feet in an acre.

How many acres are contained in the following legal description: the SW1/4 of the NE 1/4 of the NW 1/4 and the SW 1/2 of the NW 1/4? 70 Acres 90 Acres 120 Acres 160 Acres

90- acres

If the monthly interest payment at 6% is $1,050, the principal amount of the loan is: $63,000 $75,600 $126,000 $210,000

Rationale: $1,050 x 12 = $12,600 in annual interest. $12,600/.06 (6%) = $210,000.

A building was sold for $115,000. Down payment was made in the amount of $15,000 and deposited in escrow. The buyer obtained a new loan for the balance of the purchase price. The lender charged two discount points. What was the total amount charged to the buyer for points in this purchase? $2,000 $2,300 $3,000 $14,375

Rationale: $115,000-$15,000 = $100,000 loan amount. $100,000 x 2% = $2,000.

Gary bought a house for $180,000 with an 85% LTV ratio. The term of the loan is 30 years at a 7% rate of interest. It will take a loan factor of 6.65 per 1,000 to amortize the loan. The annual real property taxes are estimated to be $996. The annual premium for the homeowner's policy is estimated to be $480. What is the monthly PITI? $1,017.45 $1,100.45 $1,140.45 $1,320.00

Rationale: $180,000 x 85% = $153,000 loan amount. $153,000 x .00665 (6.65 per 1,000) = $1,017.45 principal and interest. The annual property taxes are $996/12 = $83 monthly taxes. The insurance is $480/12 = $40 monthly insurance. $1017.45 + $83 + $40 = $1,140.45

Last month's debt service payment included $412.50 interest on a $60,000 loan balance. What is the annual rate of interest? 7.5% 7.75% 8.25% 8.5%

Rationale: $412.50 x 12 = $4,950 annual interest. $4,950 divided by $60,000 = .0825 (8.25%).

Several months ago, Bill purchased four lots for $24,000 each. He later divided the lots into six lots and sold each for $20,000. What was Bill's percent of profit (loss)? 20% 25% 80% 125%

Rationale: Bill's total investment was $96,000 (4 lots at $24,000 each). He divided the lots and sold a total of 6 at $20,000 a piece and received $120,000. His total profit was $24,000 ($120,000-$96,000). If he invested $96,000 and made $24,000, then the amount he made of $24,000 divided by his original investment of $96,000 = 25%.

A lender is charging a below market interest rate of 6.5% with 6 discount points. What is the lender's effective rate of interest? 7.25% 7.125% 5.75% 6.25%

Rationale: Each discount point represents a .125 yield. 6 points x .125 = .75. The lender's effective rate of interest is 6.5% + .75% = 7.25%

A lender is charging a borrower 6% fixed interest rate and 4 discount points. What is the yield to the investor? 6¼% 6½% 5½% 5¾%

Rationale: Each point provides a .125 yield to the investor. 4 x .125 = .50 additional yield. 6% + .50 = 6.5%.

An investor sold a property for $590,000. He made a 35% profit on the sale. What did he originally pay for the property? $206,500.50 $437,037.03 $428,500.25 $286,222.41

Rationale: If the investor made a 35% profit, then he got back 135% of his money. $590,000÷1.35 (135%) = $437,037.03

A seller sold his property for $97,000. He made a 321.74% profit. What was the purchase price of the property? $13,000 $23,000 $74,000 $97,000

Rationale: If the investor made a profit of 321.74%, then he got back 421.74% of his money. $97,000÷4.2174 (421.74%) = $22,999.95 (rounded up to $23,000).

If a seller needs to net $50,000 after the sale of a property, what is the minimum acceptable sales price if the selling expenses include a 7% commission and $1,200 in additional expenses? $53,763.44 $54,784.00 $55,053.76 $55,633.25

Rationale: If the seller will net 93% of the total sales price (100%-7%), then $50,000 + $1,200 = $51,200÷.93 = $55,053.76

The seller wants to net $165,000 after paying the broker fee of 6% of the sales price. What is the minimum acceptable gross sales price to the nearest dollar? $169,850 $174,900 $175,532 $178,745

Rationale: If the seller will net 94% of the sales price (100%-6%), then $165,000÷.94 = $175,531.915 (rounded up to $175,532).

The lender is willing to make an 80% loan on the purchase of a home. The home is listed at $190,000. The purchase price is $175,000, and the appraised value of the home is $180,000. How much is the buyer's down payment? $36,000 $40,000 $35,000 $38,000

Rationale: Lenders base the LTV on either the purchase price or the appraised value, whichever is less. The purchase price is $175,000. $175,000 x 20% (required down payment) = $35,000.

Jack bought a home for $125,000 with an ad valorem tax assessed value of $130,000. The following year, a horizontal adjustment of a 15% increase in assessed value occurred. If the new tax rate is $1.678 per $100 of assessed value, what are the annual taxes? $2,097.60 $2,508.61 $2,181.40 $2,412.13

Rationale: Taxes are based on assessed value and horizontal adjustments are across the board adjustments for homeowners. $130,000 + 15% ($19,500) = $149,500 x .01678 ($1.678 per $100) = $2,508.61.

What is the monthly tax liability on a property assessed at $133,000 if the published tax rate is $1.50 per $100 of assessed value? The sales price of the property was $150,500. The vacancy rate in the area is 6%. The market capitalization rate is 8%. $1,995 $166.25 $1,950 $3,234

Rationale: Taxes are based on assessed value. $133,000 x .015 ($1.50 per $100) = $1,995. The problem asks for the monthly tax liability. $1995 ÷12 = $166.25.

The current market value of a property is $135,000. For tax purposes, it is assessed at 60% of market value. The tax rate is $2.45 per $100 of assessed value. What is the annual tax liability? $1,190.40 $1,323.75 $1,984.50 $3,307.25

Rationale: Taxes are based on assessed value. $135,000 (Market Value) x 60% = $81,000 (Assessed Value). $81,000 x .0245 = $1,984.50.

Presume the interest rate on an FHA-insured mortgage loan to be 6.5% with a current monthly interest payment of $846. What would be the current principal? $65,988.39 $147,339.48 $156,184.62 $164,97.82

Rationale: The amount of annual interest is $10,152 ($846 x 12). $10,152/ .065 (6.5%) = $156,184.615 (rounded up to $156,184.62)

What is the amount of the excise taxes charged to a seller who sells a property for $143,250? $287 $242 $300 $378

Rationale: The amount of the excise tax is $1 for each $500 of value. The sales price must be rounded up to the nearest $500. $143,500÷$500 = $287

Bill & Betty received $19,000 from the sale of their house to apply to a new townhome costing $90,000. They assumed an existing mortgage of $49,500 and borrowed $24,000 at 12% to be secured by a second mortgage. The lender charged them a 1/2% assumption fee, a 2% origination fee on the second mortgage and 5.5 points on the new loan. How much was the lender paid in fees? $2,226.00 $3,092.00 $2047.50 $2,470.00

Rationale: The assumption fee is charged on the loan that they assumed. $49,500 x .005 (1/2%) = $247.50. Both the origination fee and the points are paid on the new loan of $24,000. $24,000 x 2% = $480. $24,000 x 5.5% = $1,320. Their total lender fees are $247.50 + $480 + $1,320 = $2,047.50.

A buyer obtained a 30-year fixed rate loan for $72,000 at a 5% annual interest rate. If the monthly debt service payment is $386.64, how much interest rounded to the nearest dollar would the buyer pay over the lifetime of the loan? $31,190 $67,190 $98,380 $108,000

Rationale: The borrower will pay the lender a total of $139,190.40 ($386.64 x 360). Of the $139,190.40 paid, $72,000 was for repayment of the principal. $139,190.40-$72,000 = $67,190.40 (rounded to $67,190).

A developer owns 2 acres and plans to subdivide them into 6 individual lots. If the six lots are all equal in size and each one is 100 feet wide, what is the depth of the lots? 145.20 feet 189.60 feet 249.50 feet 329.25 feet

Rationale: The entire parcel is 2 acres. There are 43,560 square feet in an acre. 43,560x2 = 87,120 square feet. There are six lots, each one is 100 feet side so the frontage of the parcel is 600 feet. 87,120 square feet (total of the parcel)÷600 = 145.20 feet is the depth of the lots.

Smith is interested in purchasing a warehouse for the storage of inventory from his business. If the building which he is considering purchasing is 30 feet high, 28 feet wide and 62 feet long, how many cubic feet of storage space will the building provide? 52,080 cubic feet 177,000 cubic feet 18,000 cubic feet 1,860 cubic feet

Rationale: The formula to calculate volume and cubic feet is length x width x height. 62x28x30 = 52,080 cubic feet.

A home with a market value of $190,000 is located in a city where the assessed value is 80% of market value. The county tax rate last year was 0.75 per $100 and the city tax rate last year was 0.85 per $100. The tax rate increased 10% this year. What is the new property tax on this house? $2,432 $2,675.20 $2,150 $3,344

Rationale: The home has an assessed value of $152,000 ($190,000 x 80%). The previous tax rate was $1.60 per $100. (0.75 + 0.85). The new tax rate is $1.76 per $100. (1.60 +0 .16). A value of $152,000 x .0176 (1.76 per $100) = $2,675.20.

A buyer paid $45,000 for a home. Five years later, she put the home on the market for 20% more than she originally paid. The home eventually sold for 10% less than the asking price. At what price was the home sold? $49,500 $54,000 $44,000 $48,600

Rationale: The home was listed for $54,000 ($45,000 x 120%). If it sold for 10% less than the asking price, then it sold for 90% of the list price. $54,000 x .90 = $48,600.

Andy purchased a new home for $180,000. He paid 20% down and financed the balance at 9% for 30 years. Two discount points are charged. How much money will Andy actually pay at closing for the two discount points? $2,880. $3,600 $1,800 $3,100

Rationale: The loan amount is $144,000 ($180,000 x 80%). $144,000 x 2% discount points = $2,880

Bill and Betty just received $25,000 profit from the sale of their home. They are in the process of buying a new home for $185,500 with an 80% LTV ratio. The lender is charging the normal loan origination fee and is lending the money at 1.5 discount points. Bill and Betty pay an attorney $400 to handle the closing, and they must also pay for the excise tax. How much money will the lender be paid in fees? $1,484 $2,226 $3,710 $41,581

Rationale: The loan origination and discount points are paid on the loan amount. The loan amount is $148,400. $148,400 x 1% origination fee = $1,484. $148,400 x 1.5% discount points = $2,226. $1,484 + $2,226 = $3,710.

A parcel of vacant land 80 feet wide and 200 feet deep was sold for $200 per front foot. How much money would an individual agent receive for a 60% share of the 10% commission earned? $640 $960 $1,600 $2,400

Rationale: The sales price is based on front footage. $200 x 80 = $16,000 sales price. The commission was $1,600 ($16,000 x 10%). Of the $1,600 received by the brokerage, the agent receives $960 ($1,600 x 60%).

What is the assessed value of a house if the tax rate is $1.30 per $100 of value and the owner's annual taxes are $1,599? $12,300 $32,000 $123,000 $132,000

Rationale: The taxes are $1,599÷a rate of .013 ($1.30 per $100) = $123,000.

Two brokers split a 6% commission equally on a $73,000 home. The selling provisional broker, Joe, was paid 70% of his broker's share. The listing provisional broker, Janice, was paid 30% of her broker's share. How much did Janice receive? $657 $1,314 $1,533 $4,380

Rationale: The total commission for the sale was $4,380 ($73,000 x 6%). The brokers split the commission equally so each broker received $2,190 ($4,380÷2). Jan received 30% of her broker's share ($2,190 x 30%) = $657.

A provisional broker sells another firm's listing for $150,000. The commission is 6.5% of the sales price. Of this amount, 55% goes to the listing broker and the remaining 45% belongs to the cooperating broker. If the provisional broker receives 60% of any commission that he generates for the office, he is entitled to receive: $2,632.50 $3217.50 $4,387.50 $5,850

Rationale: The total commission was $9,750 ($150,000 x 6.5%). The provisional broker sold another firm's listing. The cooperating firm (the provisional broker's firm) received $4,387.50 ($9,850 x 45%). The provisional broker received $2,632.50 ($4,387.50 x 60%).

Using the 28/36 ratios, how much annual income must the borrower have to qualify for a $98,000 loan at 8% if the proposed P&I payments will be $719.32, taxes and insurance will be $135 per month, and the borrower's other monthly recurring debts total $500? $28,478.32 $36,613.71 $45,144.00 $58,042.00

Rationale: The total housing obligation is $854.32 ($719.32 + $135.00). $854.32 divided by .28 = $3,051.24 monthly income or $36,613.71 annually. The total debt including the housing is $854.32 plus $500 = $1,354.32. $1,354.32 divided by .36 = $3,762 monthly or $45,144 annually. The borrower must qualify for both ratios, so they will need $45,144 annually.

Using the 28/36 ratios, how much annual income must the borrower have to qualify for a $98,000 loan at 8% for 30 years if the proposed P&I payments will be $719.32, taxes and insurance will be $135 per month and the borrower's other monthly recurring debts total $500? $28,478.32 $36,613.71 $45,144.00 $58,042.00

Rationale: The total housing obligation will be $854.32 ($719.32 + $135.00). If the housing ratio is 28%, they must have $3,051.14 ($854.32 divided by .28) monthly income or $36,613.68 annually. Their total debt will include the housing payment of $854.32 + $500.00 = $1,354.32. $1,354.32 divided by .36 = $3,762 per month or $45,144 ($3,762 x 12) annually. They must qualify for both ratios so they will need $45,144 in annual income.

A rectangular-shaped parcel of land, which measures 400 feet by 600 feet, is divided into two equal lots by a creek that runs from the northeast corner to the southwest corner. What is the approximate acreage of each divided parcel? .55 acres 2.75 acres 3.47 acres 5.51 acres

Rationale: The total of both lots is 400 feet x 600 feet which equals 240,000 square feet. They are equal parcels, so each parcel contains 120,000 square feet (240,000÷2). There are 43,560 square feet in an acre. 120,000 square feet÷43,560 = 2.75 acres.

James earns $46,000 per year and his wife Judy earns $60,000 per year. Recurring obligations include monthly credit card payments of $800 and automobile loan payments of $650. The couple has a monthly grocery bill of approximately $400 and monthly medical expenses that average $200. What is the maximum monthly mortgage payment (principal and interest) that this couple can qualify for using an expense-to-income ratio of 28% of gross income for housing and 36% for housing expenses plus recurring obligations? $2,473.33 $1,729.88 $1,130.00 $2,325.00

Rationale: Their gross monthly income is $8,833 ($46,000 + $60,000 = $106,000 divided by 12). The maximum housing payment is $2,473.33 ($8,833.00 x .28). Their total maximum debt allowance is $3,179.88 ($8,833x.36). From their total debt obligations they must deduct the $800 in credit card payments and the $650 in auto loans. The medical bills and groceries are not counted in recurring debt. $3,179.88-$800-$650 = $1,729.88 remaining for housing. This is the answer because they must meet both ratios.

A broker has an Exclusive Right to Sell Listing Agreement with Fast-Food Market with a $4,000 commission fee. The same broker has a similar listing with Smithy-Hardware Store with a $7,000 commission. Due to changing demographics, the two stores decide to swap locations and ownership of the stores through a 1031 tax deferred exchange. In this case, the broker's commission would be? None, because an exchange of real property is not a sale of the property that results in a commission payment. $4,000, assuming that Fast-Food Market was listed prior to Smithy-Hardware. $7,000, assuming that Smithy-Hardware was listed prior to Fast-Food Market. $11,000 because the broker assisted in the conveyance of real property.

$11,000 because the broker assisted in the conveyance of real property. Rationale: Their is no reason the firm would not be entitled to both commissions. An Exclusive Right to Sell Agreement includes instances where the owner sells or transfers th property with or without the assistance of the brokerage.

Assume annual real estate taxes amount to $1,800 and have been paid in advance for the calendar year by the seller. If closing is set for September 15, which of the following is correct? credit seller $525; debit buyer $1,275 credit seller $1,275; debit buyer $525 credit buyer $525; debit seller $1,275 credit seller $525; debit buyer $525

credit seller $525; debit buyer $525 Rationale: The annual taxes are $1,800. The daily amount is $1,800 divided by 360 = $5 per day. The seller has been in the property for 255 days. (From Jan - Aug - 240 days + 15 days for the month of September = 255). 255 days at $5.00 per day means the seller owes $1,275. The seller has already paid $1,800. $1,800 - $1,275 = $525. The seller will be credited for the $525 and the buyer will be debited that amount at closing.

You are on a listing appointment and the sellers tell you they would like to net $135,000 from the sale of their home. You estimate they will have to pay $950 in miscellaneous settlement costs. You will charge them a 6.5% commission to sell the property. They also have a loan payoff of $53,500. What must the property sell for to ensure they receive their desired net? $145,401.06 $201,604.27 $201,764.25 $202,620.3

rationale: The amount needed to cover the itemized items is $189,450 ($135,000 + $950 + $53,500). The payoff of those items represents 93.5% (100%-6.5%). $189,450÷.935 (93.5%) = $202,620.32.