section 5 part 5 math

An investment made semi-annual interest payments of $1,750 which are based on a 7% interest rate. What did the investor pay for this investment?

$1,750 X 2 = $3,500 annual income. $3,500 divided by .07 = $50,000. The correct answer is: $50,000.

An owner receives $102 per month for each of 10 apartments. His annual expenses are $1,440. If his rate of return is 10%, what is the value of the property?

$102 X 10 apartments X 12 months = $12,240 annual gross income. $12,240 - 1,440 annual expenses = $10,800 net income. $10,800 net income / .10 rate of return = $108,000. The correct answer is: $108,000

An $80,000 property has a gross income of $10,000 a year. Management fees are $700 annually, and utility costs are $92 per month. What is the approximate rate of return?

All computations must be converted to an annual basis $92 X 12 = $1,104 utilities, annually. Annual management fees $700 + $1,104 (utilities) = $1,804 annual expense. $10,000 (annual income) - $1,804 (annual expense) = $8,196 net annual income. $8,196 (net income) / 80,000 (value) = .10245 = 10.25% rate of return. The correct answer is: 10.25%

An office building producing a gross annual income of $45,000 is purchased for $225,000. If the only expense is an 11.5% interest payment on a $200,000 term loan, what is the owner's rate of return on equity?

$200,000 x .115 = $23,000 annual interest expense. $45,000 (income) - $23,000 (expense) = $22,000 net income. $225,000 (value) - $200,000 (debt) = $25,000 equity. $22,000 (income) / $25,000 equity = 0.88 or 88% return on equity. The correct answer is: 88.0%

If a person bought a house for $180,000 and the value increased by 5% each year for three years, what would be the value of that house after the 3 years?

$180,000 X1.05 X 1.05 X 1.05 = $208,372.50. The correct answer is: $208,372.50.

An investor purchased a home for $350,000 and paid all cash. After expenses, the investor netted $1,950 per month by renting out the house. What rate of return did the investor earn on this investment?

Rates of return must be computed on an annual basis, so first find the annual income. $1,950 X 12 = $23,400. To find the rate of return, divide the income by the amount invested (I / V = R). $23,400 divided by $350,000 = .0668 = 0.6.7%. The correct answer is: 6.7%.

If an owner receives $225 weekly gross income from each of 16 apartments and pays $3,120 in monthly expenses. What is the rate of return on the investment of $1,200,000?

$225 rent per apartment x 16 (# of apartments) = $3,600 weekly income. $3,600 weekly rent x 52 weeks = $187,200 annual income. $3,120 monthly expenses x 12 months = $37,440 annual expense. $187,200 gross income - $37,440 expenses = $149,760 net income. $149,760 / $1,200,000 = .1248 or 12.5%. The correct answer is: 12.5%

A 50-unit apartment complex rents for an average of $1,800 per unit per month. The vacancy factor is 6%. Operating expenses run 55% of effective gross income. What would be the value of this apartment complex when using an 11% capitalization rate?

Potential Gross Income of $1,080,000 (50 X $1,800 X 12) - Less Vacancies of $64,800 ($1,080,000 X .06) = Effective Gross Income of $1,015,200 ($1,080,000 - 64,800) - Operating Expenses of $558,360 ($1,015,200 X .55) = Net Operating Income of $458,840 ($1,015,200 - $558,360). $458,840 divided by .11 = $4,153,000 (rounded). The correct answer is: $4,153,000.

An owner receives $37,500 per year net income on an investment of $495,000. What is the owner's capitalization rate?

Solution: Income / value = % return $37,500 / $495,000 = .0757575 or 7.6%. The correct answer is: 7.6%

An investor purchased a property for $300,000, taking out a $250,000 loan. The property generates $30,000 of annual income. The only expense is an interest-only payment of 7% interest on the loan. What is the investor's return on equity?

$250,000 X .07 = $17,500 expenses. $30,000 gross income - $17,500 interest = $12,500 net income. $300,000 cost - $250,000 loan = $50,000 equity. $12,500 divided by $50,000 return on equity = .25 = 25%. The correct answer is: 25%.

An investor pays $340,000 for an eight-unit apartment building. Each unit rents for $1,500 per month. Annual expenses are $96,000. What is the investor's approximate rate of return?

$1,500 X 8 units X 12 months = $144,000 Gross Income. $144,00 - $96,000 Expenses = $48,000 Net Income. $48,000 / $340,000 = 14.12% Rate of Return or 14%. The correct answer is: 14%

Each unit in a 20-unit apartment building rents for $750 per month. There is a 0% vacancy rate. The landlord increases the rent 5% and creates a 5% vacancy rate. What effect does this have on the monthly gross income of the building?

Occupancy Rate Before: 20 units (100%) with $750 Rent. Occupancy Rate After: 19 units (95%) with $787.50 Rent ($750 x .05% = $37.5. $750 + $37.5 = $787.50). 20 units x $750 = $15,000. 19 units x $787.50 = $14,962.5. $15,000 - $14,962 = $37.50 net change. $37.50 / $15,000 = .0025 or.25%. The correct answer is: Income is decreased by .25% or $37.50

Sally bought a piece of property that was currently being rented at $990 per month. Comparable properties in the area are operating on a GRM of 116. Based on the comparable, what is the value of Sally's property?

The formula is GRM = value / rent. In this problem the GRM is 116 and the rent is $990. Therefore the value = $990 * 116 = $114,840. The correct answer is: $114,840

A property was purchased for $115,000 and has appreciated 8% each year over the value the previous year for the last five years. What is its present value?

Year 1: 115,000 x 1.08 = 124,200.00. Year 2: 124,200 x 1.08 = 134,136.00. Year 3: 134,136 x 1.08 = 144,866.88. Year 4: 144,866.88 x 1.08 = 156,456.23. Year 5: 156,456.23 x 1.08 = 168,972.72. Present Value = $168,973. The correct answer is: $168,973

An investor bought a 20-unit apartment complex for $700,000. The units rent for an average of $1,250 per month. The annual operating expenses are $220,000. What is the investor's rate of return?

$1,500 X 20 units X 12 months = $300,000. Gross Income $300,000 - $220,000 Expenses = $80,000 Net Income. $80,000 / $700,000 = 0.1143 Rate of Return or 11.4%. The correct answer is: 11.4%.

An investor is considering the purchase of a duplex. He plans to pay all cash. If he believes he can net $1,500 per unit per month after expenses, he can pay up to what amount for the duplex if he wants to receive an 8% rate of return on his investment?

$1,500 monthly rent X 2 units X 12 months = $36,000 annual net income. $36,000 divided by .08 = $450,000 maximum price. The correct answer is: $450,000.

An apartment has gross annual income of $25,000. Operating expenses average $1,250 per month. The property is valued at $125,000. What is the rate of return?

Gross income: $25,000 - expenses - 15,000 ($1,250 X 12) = net income of $10,000. $10,000 divided by $125,000 = .08 = 8% The correct answer is: 8%.

An apartment house owner receives $4,800 per year net income from his investment of $60,000. What is his annual rate of return on this investment?

I / V = R. $4,800 / $60,000 = .08 or 8%. The correct answer is: 8.0%

An investor is considering the purchase of an apartment complex with 15 units. If each unit nets $275 per month in income, what would be the value of this property using a 12% capitalization rate?

15 units X $275 per month X 12 months = $49,500 net income. $49,500 divided by .12 = $412,500 value. The correct answer is: $412,500.

An owner receives $175 per week of gross income from each of 10 apartments and pays $2,400 in monthly expenses. What is the rate of return on the investment of $600,000?

10 units X $175 per week X 52 weeks = $91,000 gross income. $2,400 X 12 = $28,800 annual expenses. $91,000 - 28,800 = $62,200 net operating income. $62,200 divided by $600,000 value = .104 (rounded) = 10.4% rate of return. The correct answer is: 10.4%.

A rental home recently sold for $342,000. It rents for $1,800 per month. A nearby home rents for $1,500 per month. What would you expect this nearby home to be worth?

$342,000 divided by $1,800 = 190 gross rent multiplier. $1,500 X 190 = $285,000. The correct answer is: $285,000.

An investment earns semi-annual interest of $360, and the interest rate is 9% per year. How much money is invested?

$360 semi-annual interest X 2 = $720 annual interest $720 annual interest / .09 = $8,000 invested. The correct answer is: $8,000

A jewelry store in a mall pays base rent each month of $1,000. It also pays 3% of sales in excess of $500,000 per year. If the store paid a total of $33,000 last year in rent, what were its sales for last year?

Base rent = $1,000 X 12 = $12,000. $33,000 - $12,000 = $21,000 rent on sales over $500,000. $21,000 divided by .03 = $700,000 in excess of $500,000. $700,000 + $500,000 = $1,200,000 total sales. The correct answer is: $1,200,000.

A shop owner agrees to $1,350 per month base rent plus 2% of annual gross sales over $80,000. Last year the owner paid a total of $22,000 for rent. What were the gross sales of the shop?

Base rent = $1,350 per mo. x 12 = $16,200. Total rent = $22,000 - $16,200 = $5,800 for excess sales. $5,800 / .02 = $290,000 in sales over $80,000. $80,000 + $290,000 = $370,000 annual gross sales. The correct answer is: $370,000