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Answers and Explanations

NOTE: Questions 6, 9, and 10 are different for ZIP codes 85209 and 85212. Make sure to note the question and answer for the ZIP code you live in.

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AREA
Bob and Sandy bought a home. The backyard already has a pool and a
small grass area, but the rest is dirt. The measurements for each are as
follows: Pool = 18’ x 35’ Small grass area = 12’ x 10’.
1. How many square feet is the pool? 18 x 35=630 square feet
2. How many square feet is the grass area? 12 x 10 = 120 square feet
The pool and the grass area are in a 30’x80’ yard space.
3. How big is the total yard area? 30 x 80 = 2,400 square feet
4. How much of the yard is covered by the pool and the grass? 630 + 120 = 750 square feet
5. How much of the yard is uncovered and unlandscaped? 2400 – 750 = 1,650 square feet

BONUS: If they want to put in landscaping rock 2” deep, how many
cubic feet of rock is needed for that space?

Cubic feet = width x length x height (or depth.) We have our area, which is width x height, so we need to multiple that times our depth/height of the rock. Before we do that, however, we need to convert inches to feet. We know there are 12 inches in a foot, so we’ll calculate 2 ÷ 12, which is .166667.

Thus, 1,650 x .16667 = 275 cubic feet of rock

PERCENTAGE INCREASE

85209:
Tony Stark just bought his house for $300,000. Houses in the 85209 zip
code are increasing in value at 11% annually.
6. If this stays true, how much will Tony’s house be worth in
a year?

First, divide the appreciation rate (the rate at which the value is growing annually) by 100 to convert it to a decimal, and then add 1. Thus, we begin with 1.11.

Next, multiply the home value by 1.11. $300,000 x 1.11 = $333,000.

85212:
Tony Stark just bought his house for $300,000. Houses in the 85209 zip
code are increasing in value at 11% annually.
6. If this stays true, how much will Tony’s house be worth in
a year?

First, divide the appreciation rate (the rate at which the value is growing annually) by 100 to convert it to a decimal, and then add 1. Thus, we begin with 1.11.

Next, multiply the home value by 1.11. $300,000 x 1.11 = $333,000.

Vocabulary: Real Estate Professionals use the term appreciation when
describing an increase in home values. A good way to remember this is to
know that sellers appreciate the fact that their home value increased.

INTEREST RATES
Interest rates are at historic lows. Calculate how much interest would
need to be paid, assuming each borrower paid the $300,000 loan over a
period of 30 years.

A simple interest formula is: interest = principal x rate x years.

Vocabulary:
principal: the sum of money that is lent or invested on which interest is paid.
rate: the proportion of a loan that is charged as interest to the borrower annually.

7. Elsa has an interest rate of 3% for 30 years for her $300,000
home. How much interest will Elsa have to pay over the 30 year
period, and how much will she pay back in total?

interest=principal x rate x years. Thus, $300,000 x .03 x 30 = Interest: $270,000

Total Paid Back is Principal + Interest: $300,000 + $270,000 = $570,000

8. Anna has an interest rate of 4% for 30 years for her $300,000
home. How much interest will Anna have to pay over the 30 year
period, and how much will she pay back in total?

interest=principal x rate x years. Thus, $300,000 x .04 x 30 = $360,000

Total Paid Back is Principal + Interest: $300,000 + $360,000 = $660,000

BONUS: How much did Elsa save with a lower interest rate than
Anna?

$360,000 – $270,000 = $90,000. Elsa saves $90,000 with a lower interest rate.

AVERAGE (MEAN) AND MEDIAN – 85209
Using the Augusta Ranch neighborhood on page 5, calculate the mean
(average) price and the median price for the neighborhood.

9. The average price in Augusta Ranch is $349,862.50.
The total of the above properties is $2,798,900. There are 8 properties in the list. $2,798,900 ÷ 8 = 349,862.50

10. The median price in Augusta Ranch is $305,000.
To calculate the median price, find the number halfway into the set. As there is an even number in the data set, the median is found by taking the average/mean of the two middle most numbers. $275,000+$335,000 = $610,000. $610,000 ÷ 2 = $305,000.

AVERAGE (MEAN) AND MEDIAN (85212)
Using the Eastmark neighborhood on page 5, calculate the mean
(average) price and the median price for the neighborhood.

9. The average price in Eastmark is $435,675.

10. The total of the above properties is $3,485,400. There are 8 properties in the list. $3,485,400 ÷ 8 = 435,675

The median price in Eastmark is $407,500.
To calculate the median price, find the number halfway into the set. As there is an even number in the data set, the median is found by taking the average/mean of the two middle most numbers. $395,000+$420,000 = $815,000. $815,000 ÷ 2 = $407,500.

Vocabulary:
average: the typical value in a set of data, calculated by dividing the sum of the
values in the set by the number of values.
median: the middle value of a series arranged in order of magnitude. For example, the median number of the series 2, 4, 6, 8, 12, 25, 37 is 8.

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