Unit 24: Real Estate Mathematics

A 100-foot-by-125-foot lot sold for $125,000. What was the price per front foot?

A) $1,250

B) $10

C) $556

D) $1,000

A) $1,250

$125,000 sales price ÷ 100 front feet = $1,250 per front foot

If the savings and loan gives you a 90% loan on a house valued at $88,500, how much additional cash must you produce as a down payment if you have already paid $4,500 in earnest money?

A) $4,350

B) $3,500

C) $4,000

D) $8,850

A) $4,350

100% value − 90% LTV = 10% down payment

$88,500 × 10% (0.10) = $8,850 down payment

$8,850 down payment − $4,500 earnest money = $4,350 due at closing

What would you pay for a building producing $11,250 annual net income and showing a minimum rate of return of 9%?

A) $101,250

B) $122,625

C) $125,000

D) $123,626

C) $125,000

$11,250 annual net income ÷ 9% (0.09) = $125,000 price

Your monthly rent is $525. What is your rent as a percentage of an annual income of $21,000?

A) 25%

B) 30%

C) 33%

D) 40%

B) 30%

$525 monthly rent × 12 months = $6,300 annual rent

$6,300 annual rent ÷ $21,000 annual income = 0.30 or 30%

Two sponsoring brokers evenly split the 6% commission on a $73,000 home. The selling broker was paid 70% of his sponsoring broker’s share. The listing broker was paid 30% of her sponsoring broker’s share. How much did the listing broker receive?

A) $1,314

B) $1,533

C) $4,380

D) $657

D) $657

$73,000 sales price × 6% (0.06) = $4,380 full commission

$4,380 full commission ÷ 2 sponsoring brokers = $2,190 sponsoring broker’s share of the commission

$2,190 sponsoring broker’s share of the commission × 30% (0.30) = $657 listing broker’s commission

Find the number of square feet in a lot with a frontage of 75 feet 6 inches and a depth of 140 feet 9 inches.

A) 216.25

B) 10,652.04

C) 25,510.81

D) 10,626.63

D) 10,626.63

6” ÷ 12 = 0.5’ + 75’ = 75.5’ frontage

9” ÷ 12 = 0.75’ + 140’ = 140.75’ depth 140.75’ × 75.5’ = 10,626.63 square feet

You attempt to appraise a 28-unit apartment house, employing the income approach. Each unit rents for $775 per month, an amount that seems consistent with similar rental units in the vicinity. For the past five years, the annual expenses of operation have averaged $82,460. The complex has maintained a consistent vacancy rate of 5%. A potential investor is only interested if the return is 9.5%. What value would you arrive at using these variables?

A) $868,000

B) $1,873,100

C) $2,741,100

D) $1,736,000

D) $1,736,000

$775 monthly rent × 28 units × 12 months = $260,400 annual scheduled gross income

$260,400 annual scheduled gross income − 5% vacancy rate = $247,380 annual effective gross income

$247,380 annual effective gross income − $82,460 annual expenses = $164,920 annual net operating income

$164,920 annual net income ÷ 9.5% (0.095) = $1,736,000 value

The buyer has agreed to pay $175,000 in sales price, 2.5 loan discount points, and a 1% origination fee. If the buyer receives a 90% loan-to-value ratio, how much will the buyer owe at closing for points and the origination fee?

A) $5,512.50

B) $1,575.00

C) $3,937.50

D) $6,125.00

A) $5,512.50

2.5 points loan discount + 1 point origination fee = 3.5 points

$175,000 loan × 90% or (0.90) = $157,500 sales price

$157,500 loan × 3.5% (0.035) = $5,512.50 for points and origination fee

Calculate eight months’ interest on a $5,000 interest-only loan at 9.5%.

A) $39.58

B) $316.67

C) $237.50

D) $475.00

B) $316.67

$5,000 loan × 9.5% (0.095) = $475 annual interest

$475 annual interest ÷ 12 months × 8 months = $316.67 interest

An office building produces $68,580 annual net operating income. What price would you pay for this property to show a minimum return of 12% on your investment?

A) $489,857

B) $685,800

C) $571,500

D) $768,096

C) $571,500

$68,580 annual net operating income ÷ 12% (0.12) = $571,500 price

A man earns $20,000 per year and can qualify for a monthly PITI payment equal to 25% of his monthly salary. If the annual tax and insurance is $678.24, what loan amount will he will qualify for if the monthly PI payment factor is $10.29 per $1,000 of loan amount?

A) $35,000

B) $40,500

C) $43,000

D) $66,000

A) $35,000

$20,000 annual salary ÷ 12 months = $1,666.67 monthly salary; $1,666.67 monthly salary × 25% = $416.67 monthly PITI payment

$678.24 annual taxes and insurance ÷ 12 months = $56.52 monthly taxes and insurance

$416.67 monthly PITI payment − $56.52 monthly TI = $360.15 monthly PI payment

$360.15 monthly PI payment ÷ $10.29 × $1,000 = $35,000 loan

What percentage of profit would you make if you paid $10,500 for a lot, built a home on the lot that cost $93,000, and then sold the lot and house together for $134,550?

A) 30%

B) 13%

C) 23%

D) 45%

A) 30%

$10,500 cost of lot + $93,000 cost of home = $103,500 total cost

$134,550 sales price − $103,500 total cost = $31,050 profit

$31,050 profit ÷ $103,500 total cost = 0.3 or 30%

A buyer pays $2,500 each for four parcels of land. He subdivides them into six parcels and sells each of the six parcels for $1,950. What was the buyer’s percentage of profit?

A) 14.5%

B) 52%

C) 17%

D) 78%

C) 17%

$2,500 cost × 4 parcels = $10,000 total cost

$1,950 sales price × 6 parcels = $11,700 sales price

$11,700 sales price − $10,000 cost = $1,700 profit

$1,700 profit ÷ $10,000 cost = 0.17 or 17% profit

A woman earns an annual income of $60,000, and her husband earns $2,400 per month. How much can the couple pay monthly for their total housing payment if the lender uses a 28% qualifying ratio?

A) $2,072

B) $672

C) $1,400

D) $2,352

A) $2,072

$60,000 annual salary ÷ 12 months = $5,000 wife’s monthly salary + 2,400 husband’s monthly salary = $7,400 total monthly salary

$7,400 total monthly salary × 28% (0.28) = $2,072 monthly payment

A buyer is granted a 90% loan of $340,500. How much will her monthly principal and interest payment be, using a loan payment factor of $7.16 per $1,000 of loan?

A) $2,194.18

B) $3,064.50

C) $2,437.98

D) $4,755.59

C) $2,437.98

$340,500 loan ÷ $1,000 × $7.16 = $2,437.98 monthly principal and interest payment