REE VA & Math Questions and
Solutions | Grade A+
A property is being appraised using the income capitalization approach. Annually, it has an
estimated gross income of $48,000, vacancy and credit losses of $3,600, and operating
expenses of $15,000. Using a capitalization rate of 8%, what is the property's value (rounded
up to the nearest $1,000)?
✔️: $368,000
A sale transaction on rental property closes on December 10th. The landlord received the
December rent of $4,400 on December 1. Assuming the closing day is the seller's, and that
the 360-day method is used for prorating, how much will the seller owe the buyer?
✔️: $4,400 ÷ 30 days = $146.66 per day; $146.66 x 10 = $1,467, $4,400 - $1,467 = $2,933
If a buyer purchases 25% of a lot in the spring and then purchases 50% more later in the fall,
what percentage of the lot is still available for purchase?
✔️: 25%
Explanation:
25% + 50% = 75%. 100% - 75% = 25%.
,A building generates $103,000 in effective rental income and $900 in vending machine
income. The same complex has $40,700 in operating expenses and $36,000 in debt service
payments. What is the pre-tax cash flow of the complex?
✔️: $27,200
$103,000 effective rental income + $900 vending machine income = $103,900; $103,000 -
$40,700 expenses -= $63,200 NOI; $63,200 NOI - $36,000 debt service = $27,200 pre-tax
cash flow
Two parcels of land priced at $1,200 per acre were purchased. One parcel was 15 acres in
size and the other was 1 mile square in size. How much did these two parcels cost together?
✔️: $786,000
A property currently valued at $450,000 is expected to appreciate 8% each year for the next 3
years. What will be its appreciated value at the end of this period?
✔️: $566,870
$450,000 x 1.08 x 1.08 x 1.08 = $566,870. The 1.08 comes from adding the 8% appreciation
to 100% for 108%. Then convert that to a decimal, 1.08 and multiply as needed.
, $450,000 x 1.08 x 1.08 x 1.08 = $566,870. The 1.08 comes from adding the 8% appreciation
to 100% for 108%. Then convert that to a decimal, 1.08 and multiply as needed.
✔️: $5,187 x 2 sides = $10,374 total commission; $10,374 ÷ 0.065 = $159,600 sales price
If one discount point costs the borrower 1% of the loan amount, and increases the lender's
yield by 1/8th of one percent, how many discount points must be purchased to lower the
interest rate by 1%?
✔️: 1/8th = 0.125; 1.0 ÷ 0.125 = 8
A five-sided lot has the following dimensions: side A = 44', side B = 67', side C = 91', side D
= 18', and side E = 55'. What is the perimeter of the lot?
✔️: 275 feet
44' + 67' + 91' + 18' + 55' = 275'
An FHA-insured loan in the amount of $57,500 at a 6 ½% interest rate for 30 years was
closed on March 17. The first monthly payment is not due until May 1. If the interest is paid
monthly in arrears, how much pre-paid interest does the buyer owe at closing? (Use a 360-
day year)
✔️: $145.32
Solutions | Grade A+
A property is being appraised using the income capitalization approach. Annually, it has an
estimated gross income of $48,000, vacancy and credit losses of $3,600, and operating
expenses of $15,000. Using a capitalization rate of 8%, what is the property's value (rounded
up to the nearest $1,000)?
✔️: $368,000
A sale transaction on rental property closes on December 10th. The landlord received the
December rent of $4,400 on December 1. Assuming the closing day is the seller's, and that
the 360-day method is used for prorating, how much will the seller owe the buyer?
✔️: $4,400 ÷ 30 days = $146.66 per day; $146.66 x 10 = $1,467, $4,400 - $1,467 = $2,933
If a buyer purchases 25% of a lot in the spring and then purchases 50% more later in the fall,
what percentage of the lot is still available for purchase?
✔️: 25%
Explanation:
25% + 50% = 75%. 100% - 75% = 25%.
,A building generates $103,000 in effective rental income and $900 in vending machine
income. The same complex has $40,700 in operating expenses and $36,000 in debt service
payments. What is the pre-tax cash flow of the complex?
✔️: $27,200
$103,000 effective rental income + $900 vending machine income = $103,900; $103,000 -
$40,700 expenses -= $63,200 NOI; $63,200 NOI - $36,000 debt service = $27,200 pre-tax
cash flow
Two parcels of land priced at $1,200 per acre were purchased. One parcel was 15 acres in
size and the other was 1 mile square in size. How much did these two parcels cost together?
✔️: $786,000
A property currently valued at $450,000 is expected to appreciate 8% each year for the next 3
years. What will be its appreciated value at the end of this period?
✔️: $566,870
$450,000 x 1.08 x 1.08 x 1.08 = $566,870. The 1.08 comes from adding the 8% appreciation
to 100% for 108%. Then convert that to a decimal, 1.08 and multiply as needed.
, $450,000 x 1.08 x 1.08 x 1.08 = $566,870. The 1.08 comes from adding the 8% appreciation
to 100% for 108%. Then convert that to a decimal, 1.08 and multiply as needed.
✔️: $5,187 x 2 sides = $10,374 total commission; $10,374 ÷ 0.065 = $159,600 sales price
If one discount point costs the borrower 1% of the loan amount, and increases the lender's
yield by 1/8th of one percent, how many discount points must be purchased to lower the
interest rate by 1%?
✔️: 1/8th = 0.125; 1.0 ÷ 0.125 = 8
A five-sided lot has the following dimensions: side A = 44', side B = 67', side C = 91', side D
= 18', and side E = 55'. What is the perimeter of the lot?
✔️: 275 feet
44' + 67' + 91' + 18' + 55' = 275'
An FHA-insured loan in the amount of $57,500 at a 6 ½% interest rate for 30 years was
closed on March 17. The first monthly payment is not due until May 1. If the interest is paid
monthly in arrears, how much pre-paid interest does the buyer owe at closing? (Use a 360-
day year)
✔️: $145.32
