Lesson 17 cumulative quiz

A convenience store grosses $555,000 annually. Its operating expense ratio is 83%. If the appraiser assigns a 7% capitalization rate, what is the estimated value of the property?

$1,347,857 Explanation: The first step is to calculate the property's annual net income. If the operating expense ratio is 83%, that means that the remaining 17% of the gross income is the owner's net income (100% - 83% = 17%). Now plug that information into the basic percentage formula. P = % x W P = .17 x $555,000 P = $94,350 Now that you know the net income, you have enough information to use the capitalization formula. You know the income and the capitalization rate, so you need to isolate the property's market value. I = R x V I ÷ R = V $94,350 ÷ .07 = V $1,347,857.14 = V

A fire insurance policy began on April 1. It cost $1,900.80 for three years of coverage. The insurer canceled the policy on December 16 of the same year it was issued. If you use a 360-day year, which of the following figures is closest to the premium for the unused portion of the policy?

$1,452.00 Explanation: If the policy began on April 1 and ended on December 16, it was valid for approximately 8.5 months. First, calculate the yearly premium for the insurance ($1,900.80 ÷ 3 years = $633.60). Then calculate the per diem rate ($633.60 ÷ 360 days = $1.76). Determine the number of days the policy was in effect: 8 full months (April through November) is 240 days. 240 days + 15 days in December = 255 days. Next, multiply the number of days by the per diem rate ($1.76 x 255 days = $448.80). Bear in mind, though, that we're looking for the unused portion, not the used portion, so subtract that amount from the total premium for the policy ($1,900.80 - $448.80 = $1,452).

An appraiser determines the property's net operating income is $125,350. If she applies a capitalization rate of 8%, what is the market value of the property?

$1,566,875 Explanation: Use the capitalization formula to solve this problem. (Note, however, that the capitalization formula is just a variation on the basic percentage formula.) Income = Rate x Market Value You know the income and the rate, so you need to isolate the value. I ÷ R = V $125,350 ÷ .08 = V $1,566,875 = V

A buyer is required in the deposit receipt to place in escrow four months' prorated shares of property taxes and hazard insurance. The applicable tax rate is $1.50 per $100 of assessed value; the assessed value of the property is $400,000. The premium for a three-year hazard insurance policy is $1,800. How much must the buyer place in escrow?

$2,200 Explanation: First, calculate the annual property tax payment ($400,000 ÷ 100= $4,000) ($4,000 x 1.5 = $6,000). Find the monthly share of the annual taxes ($6,000 ÷ 12 = $500) and multiply by the number of months ($500 x 4 = $2,000). Now calculate the monthly share of the three-year insurance policy ($1,800 ÷ 36 = $50) and multiply the monthly share by the number of months ($50 x 4 = $200). Add the tax and insurance payments together for the total amount placed in escrow ($2,000 + $200 = $2,200).

The broker's commission is 7% of the sales price. What is the commission if the property sells for $8.50 per square foot and its dimensions are 200' x 175'?

$20,825 Explanation: The first step is to calculate the area of the property. Use the area formula. A = B x H A = 200 x 175 A = 35,000 Now multiply 35,000 square feet by $8.50 per square foot to find the sales price. 35,000 x $8.50 = $297,500 Finally, use the percentage formula to calculate the amount of the commission. P = % x W P = .07 x $297,500 P = $20,825

Smith bought a home six years ago for $210,000. He wants to sell the property for a 25% profit after paying a 7% commission and $1,750 in settlement costs. What would he have to sell the home for?

$284,140 Explanation: The first step in a seller's net problem like this one is to calculate what the seller's desired net is. Here, the seller's desired net is 25% more than the home's original price, or 125% of the original price. P = % x W P = 1.25 x $210,000 P = $262,500 (desired net) However, you still need to factor in the other costs. The second step is to add all costs other than the commission. $262,500 + $1,750 settlement costs = $264,250 The next step is to subtract the commission rate from 100%. The reasoning is that if Smith wants to net $262,500, that is only a portion of what he will actually have to sell the home for if he also has to pay the agent's commission. 100% - 7% = 93% Finally, use the percentage formula to calculate the entire sales price for the home. You already know the "part" (in other words, the portion of the total sales price that Smith keeps) and the rate, so you need to isolate the "whole" sales price. P = % x W P ÷ % = W $264,250 ÷ .93 = W $284,139.78 = W

A property recently sold for $390,000. How much will the annual property taxes be if the tax rate is $0.95 per $100 of assessed valuation?

$3,705 Explanation: Since the problem does not state otherwise, you can assume that the assessed value is 100% of the market value (as it would be if the property were in California). The first step is to divide the sales price by 100 to determine the number of $100 increments. $390,000 ÷ 100 = 3,900 Next, multiply that figure by the tax rate to determine the amount of the annual taxes. 3,900 x $0.95 = $3,705.00

A 10-year-old property was recently appraised for $257,000. It has depreciated 25% since it was new. What was it originally worth?

$342,667 Explanation: The first step is to subtract the rate of depreciation from 100%. 100% - 25% = 75% This shows that the property is worth 75% of what it was originally worth. Now you can use the basic percentage formula to solve the problem. You know the "part" (its recently appraised value) and the percentage, so you need to isolate the "whole," which is its original value. P = % x W P ÷ % = W $257,000 ÷ .75 = W $342,666.67 = W

Able makes $1,200 quarterly interest payments on a term loan. If the interest rate is 9.5%, what is the amount of the loan?

$50,526 Explanation: Because the problem gives quarterly interest payments, the first step is to convert that to one annual interest payment. Because there are four quarters in a year, multiply the quarterly amount by 4. $1,200 x 4 = $4,800 Now you have enough information to solve the problem, using the basic percentage formula. You know the "part" (the interest payment) and the rate, so you need to isolate the total loan amount. P = % x W P ÷ % = W $4,800 ÷ .095 = W $50,526.32 = W

Jones borrowed $45,000 to purchase some office furniture. He agreed to pay 9.5% interest plus the amount borrowed at the conclusion of 20 months. What was the amount of the payment?

$52,125 Explanation: The first step is to calculate how much the annual interest payment is. You know the principal amount and the interest rate, so plug those into the basic percentage formula. P = % x W P = .095 x $45,000 P = $4,275 Now that you know the annual interest, you need to find out how much the monthly interest is. Since there are 12 months per year, divide the annual interest by 12. $4,275 ÷ 12 = $356.25 Multiply that amount by 20, since interest accrues for 20 months. $356.25 x 20 = $7,125 Add the total amount of interest to the amount of the principal to arrive at the total repayment amount. $7,125 + $45,000 = $52,125

A home is presently appraised at $550,000. Calvin bought it new four years ago. Since then it has depreciated 16%. The home was originally worth approximately:

$654,760 Explanation: This problem involves depreciation, which can be tricky. Remember that the house isn't worth 16% of what it was worth four years ago. Instead, you have to subtract that 16% from 100%. In other words, the house is now worth 84% of what it used to be worth.Now you can apply the Then and Now (Value After) formula, which is just a variation on the basic percentage formula. You know the "part" (its current value, which is only part of the original value) and the percentage of depreciation, and you need to isolate the "whole" value of the home (in other words, the "then" value, or the value before). P = % x W P ÷ % = W $550,000 ÷ .84 = W $654,761.90 = W

A mortgage loan is 80% of the sales price. The loan's interest rate is 9%, and the borrower makes semi-annual interest payments of $24,750. What is the sales price?

$687,500 Explanation: The first step is to figure out what the annual interest payment is. The question only gives semi-annual interest payments, meaning there are two per year. Simply multiply the payment ($24,750) by 2 to determine that the annual interest on the loan is $49,500. Next, plug this information into the basic percentage formula. You know the "part" (the interest) and the rate, so you need to isolate the value of the "whole" (the principal). P = % x W P ÷ % = W $49,500 ÷ .09 = W $550,000 = W Finally, you need to calculate the value of the house. Again, you can use the percentage formula. And again, you know the "part" (the loan amount) and the percentage, so you need to isolate the "whole" (the value of the house). P = % x W P ÷ % = W $550,000 ÷ .80 = W $687,500 = W

Johnson, a salesperson for ABC Realty, sold a home listed by ACME Realty for $604,000. The companies split the 6% commission 50/50, and Johnson's share of her company's commission was 40%. What was the amount of Johnson's commission?

$7,248 Explanation: The first step is to calculate the total commission amount. Use the basic percentage formula. P = % x W P = .06 x $604,000 P = $36,240 Next, you need to find how much ABC Realty's 50% share of the commission comes to. P = % x W P = .5 x $36,240 P = $18,120 Finally, you need to find how much Johnson's 40% share of ABC Realty's share is. P = % x W P = .4 x $18,120 P = $7,248

The asking price is $345,000. The property sells for $330,000. The commission is 6%. 60% of the commission goes to the broker and 40% goes to the salesperson. How much did the salesperson receive?

$7,920 Explanation: This is a percentage question that must be solved in two steps. First, calculate what the total commission was, by finding 6% of the $330,000 sales price. P = % x W P = .06 x $330,000 P = $19,800 Next, calculate what the salesperson's share of the commission was, by finding 40% of the total commission. P = % x W P = .4 x $19,800 P = $7,920

The salesperson earned a 6% commission on the first $500,000 of the sales price and 3% on that portion of the sales price that exceeded $500,000. The commission was $36,600. What was the sales price?

$720,000 Explanation: This problem has to be broken into two segments. The first step is to calculate the amount of the part of the commission that was earned at the 6% rate. Use the percentage formula. P = % x W P = .06 x $500,000 P = $30,000 Now you know that $30,000 of the $36,600 was earned at the 6% rate. Subtract $30,000 from $36,600; the remaining $6,600 of the commission was earned at the 3% rate. Use the percentage formula again, this time switching it around to isolate the unknown quantity, which now is the remaining portion of the sales price. P ÷ % = W $6,600 ÷ .03 = W $220,000 = W Finally, add the $220,000 to the $500,000, for a total sales price of $720,000.

A lender charges a borrower 3 points. How much money will the borrower have to have at closing if the sales price is $445,000 and the lender is requiring a 20% downpayment?

$99,680 Explanation: The first step is to find the loan amount. You know that the percentage of the downpayment is 20%, so subtract that from 100% and you'll find that the loan amount is 80% of the property's sales price. Now you can use the percentage formula to find the loan amount. P = % x W P = .80 x $445,000 P = $356,000 Remember that a point is equivalent to one percent of the loan amount. Therefore, three points is 3% of the loan amount. You can find the value of those points using the percentage formula. P = % x W P = .03 x $356,000 P = $10,680 However, you still need to find the amount of the downpayment. You know it's 20% of the sales price, so you can find that using the percentage formula too. P = % x W P = .20 x $445,000 = $89,000 Finally, add the downpayment and the points together to find the amount of cash required at closing. $10,680 + $89,000 = $99,680

Cortezar purchases a property for $255,000 and puts 20% down. The monthly interest payments are $1,742.50. What is the annual rate of interest?

10.25% Explanation: The first step is to calculate the loan amount. If Cortezar puts 20% down, then the loan amount is 80% of the property's value. P = % x W P = .80 x $255,000 P = $204,000 Note that the interest is expressed in terms of monthly payments. You'll need to multiply by 12 to find the annual interest. $1,742.50 x 12 = $20,910 Now you have enough information to calculate the annual rate of interest. You know the "part" (the amount of interest) and the "whole" (the principal), so you need to isolate the percentage rate. P = % x W P ÷ W = % $20,910 ÷ $204,000 = .1025 Expressed as a percentage, that's 10.25%.

A salesperson sells an apartment building for $2,500,000. She earns a commission of $122,500. If she was paid a 7% commission on the first $1,000,000 of the sales price, what was her rate of commission on the remainder of the sales price?

3.5% Explanation: The first step is to find out how much the salesperson made as a commission for the first $1,000,000 of the sales price. This can be calculated using the basic percentage formula. P = % x W P = .07 x $1,000,000 P = $70,000 Now subtract that $70,000 from the total commission ($122,500), and you'll find that the remaining portion of her commission was $52,500. Subtract the $1,000,000 from the total $2,500,000 sales price of the building, and you'll determine that the $52,500 portion of the commission was earned for the remaining $1,500,000 of the sales price. Now you have enough information to use the percentage formula to find the rate. You have the "part" (the commission) and the "whole" (the sales price), so you have to isolate the percentage. P = % x W P ÷ W = % $52,500 ÷ $1,500,000 = % .035 = % Expressed as a percentage, that's 3.5%.

From the point of beginning, a property's boundaries run 900 feet in a southerly direction; then due east for 1,250 feet; then in a northerly direction 300 feet; then back to the point of beginning. How many square feet are in the described parcel?

750,000 Explanation: It's helpful to draw a picture of this property. The resulting odd shape, however, will have to be broken down into two separate shapes to solve the problem. There should be a large triangle, running 600 feet along its west side and 1,250 feet along its south side, sitting above a long, narrow rectangle, 300 feet long along its western and eastern sides and 1,250 feet along its northern and southern sides. Calculate the area of the rectangle first, by multiplying its length by its width. A = B x H A = 1,250 x 300 A = 375,000 Now calculate the area of the triangle, by multiplying its length by its width by one-half. A = 1/2 x B x H A = 1/2 x 600 x 1,250 A = 375,000 Finally, add the two areas together (375,000 + 375,000 = 750,000).

A borrower obtains a home equity loan in the amount of $99,000, with semi-annual interest payments of $4,331.25. What is the loan's interest rate?

8.75% Explanation: An interest problem can be solved using the basic percentage formula. However, there's one small twist to this problem: instead of being given the annual amount of interest, you're told the amount of the semi-annual payment. Semi-annual means there are two per year, so multiply $4,331.25 by 2, to find that the annual interest payment is $8,662.50. Next, plug the numbers into the percentage formula. You know the "part" (the interest) and the "whole" (the principal), so you need to isolate the rate. P = % x W P ÷ W = % $8,662.50 ÷ $99,000 = % .0875 = % Expressed as a percentage, that's 8.75%.