15 free questions from the Cinna RE real estate math bank (103 in the app). Tap an answer to check it. The rationale opens right away.
A property generating $2,000 monthly rent closes on the 21st of a 30-day month; the seller already collected the full month's rent. Using actual days remaining, what does the buyer receive?
Answer: B. $666.67
Daily rent is $2,000 / 30 = $66.67; the buyer owns days 21-30 (10 days) = $666.67 credited to the buyer.
Annual taxes of $4,380 are paid in arrears using a 365-day year. Closing is March 1, and the seller is responsible for January 1 through the end of February (59 days). What is the seller's debit?
Answer: A. $708
Daily rate is $4,380 / 365 = $12; 59 days x $12 = $708 owed by the seller to the buyer.
A monthly principal-and-interest factor of $6.00 per $1,000 applies to a $180,000 loan. What is the monthly P&I payment?
Answer: C. $1,080
Multiply the factor by the number of thousands: ($180,000 / 1,000) x $6.00 = 180 x $6.00 = $1,080.
A buyer needs a $190,000 loan and the lender charges 2 points plus a 1% origination fee. What is the total of points and origination fee?
Answer: C. $5,700
Two discount points equal 2% and the origination fee is 1%, totaling 3%: $190,000 x 0.03 = $5,700.
A commercial space is leased at $24 per square foot annually. If the unit is 1,500 square feet, what is the monthly rent?
Answer: A. $3,000
Annual rent = 1,500 x $24 = $36,000; monthly = $36,000 / 12 = $3,000.
A warehouse has a footprint of 80 feet by 50 feet and a ceiling height of 12 feet. What is the total cubic footage of storage space?
Answer: B. 48,000 cu ft
Volume = 80 x 50 x 12 = 48,000 cubic feet.
An investor compares two properties: Property A has an NOI of $40,000 priced at $500,000, and Property B has an NOI of $54,000 priced at $600,000. Based on capitalization rate, which is the better income investment?
Answer: B. Property B, because its cap rate is higher
Property A cap rate = $40,000 / $500,000 = 8%; Property B cap rate = $54,000 / $600,000 = 9%. A higher cap rate means a higher return relative to price, so Property B is the better income investment.
An investor pays $200,000 cash for a rental that produces $16,000 in annual pre-tax cash flow. What is the cash-on-cash return?
Answer: C. 8%
Cash-on-cash return = annual cash flow / cash invested = $16,000 / $200,000 = 0.08, or 8%.
An investor puts $50,000 down on a property and wants a 10% cash-on-cash return. What annual cash flow before taxes must the property produce?
Answer: B. $5,000
Required cash flow = cash invested x desired return = $50,000 x 0.10 = $5,000.
An investor wants an 8% capitalization rate on a property with an NOI of $48,000. What is the maximum price the investor should pay?
Answer: C. $600,000
Value = NOI / cap rate = $48,000 / 0.08 = $600,000.
A property has an NOI of $36,000 and annual debt service (mortgage payments) of $24,000. The investor made a down payment of $120,000. What is the cash-on-cash return?
Answer: B. 10%
Cash flow = NOI - debt service = $36,000 - $24,000 = $12,000; cash-on-cash = $12,000 / $120,000 = 0.10, or 10%.
An investor buys a property for $400,000 using $100,000 of their own cash and a loan for the rest. First-year before-tax cash flow is $9,000. What is the return on the cash invested (cash-on-cash)?
Answer: C. 9%
Cash-on-cash return = cash flow / cash invested = $9,000 / $100,000 = 0.09, or 9%. The loan portion is not counted as the investor's cash.
A property sold for $450,000 at a 7% commission. The listing broker keeps 50% of the total and the rest goes to the cooperating broker. The cooperating broker pays its agent 60%. How much does the cooperating agent earn?
Answer: A. $9,450
Total commission is $31,500; cooperating broker's half is $15,750; the agent's 60% is $9,450.
An apartment building sold for $480,000 with a gross annual income of $80,000. Using the income approach with a GRM, what GRM did this sale establish?
Answer: B. 6
GRM = sale price / gross annual income = $480,000 / $80,000 = 6.
A tenant pays $1,500 monthly rent on the first of the month. The property closes on the 16th of a 30-day month, with rent collected by the seller for the full month. How much rent must the seller credit the buyer?
Answer: A. $750
The buyer owns the property for the last 15 days; daily rent is $1,500 / 30 = $50; 15 days x $50 = $750 credited to the buyer.
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