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12345 [234]
3 years ago
5

Mark takes out a $238,000 mortgage for 30 years. Instead of paying his monthly payment of $1,220.09, he decided to pay $1,420.09

. This leads to Mark paying off the entire mortgage in 22 years and 5 months. Mark calculates the percent of the total loan he pays back in interest with and without the extra payments. What is the difference between Mark's calculated percentages?
Mathematics
1 answer:
Stells [14]3 years ago
8 0

Answer:

24.04%

Step-by-step explanation:

Given that:

Mortgage = $238,000

Number of years = 30

Monthly payment without extra payment= $1220.09

Monthly payment with extra payment = $1420.09

Total amount paid :

Number of months * monthly payment

12 months = 1year

30 years = (30 * 12) = 360 months (without extra payment)

22 years 5 months = (22 * 12) + 5 = 269 months (with extra payment)

Amount paid without extra payment :

$1220.09 * 360 = $439232.4

Percentage of total loan paid as interest :

((439232.4 - 238000) / 238000) * 100%

= 0.8455142 = 84.55%

Amount paid with extra payment :

$1420.09 * 269 = 382004.21

Percentage of total loan paid as interest :

((382004.21 - 238000) / 238000) * 100%

= 0.6050597 = 60.51%

Difference between percentages:

84.55% - 60.51% = 24.04%

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Answer:

  • y = 2x² - 5x + 7

Step-by-step explanation:

For this problem, imagine the standard form, which is:

f(x) = ax² + bx + c = y

Using the table, and adding that y at the end, we can plug in and write out the following equations. (<em>Writing it out is important</em>):

f(-1) = a(-1)² + b(-1) + c = 14

f(0) = a(0)² + b(0) + c = 7

f(1) = a(1)² + b(1) + c = 4

f(2) = a(2)² + b(2) + c = 5

Now if this doesn't look familiar, it's actually a <u>systems of equations</u> using the a, b, and c elements as your three variables! If you simplify the equations:

f(-1) = a - b + c = 14

f(0) = c = 7

f(1) = a + b + c = 4

f(2) = 4a + 2b + c = 5

Something unique just happened. We have already defined what ' c ' is!

<u><em>c = 7</em></u>

Setting that aside, if you remove the f(x) portion of the equations, you're left with:

a - b + c = 14

a + b + c = 4

4a + 2b + c = 5

Using the two upper equations, if we add them together (you can do that as it doesn't change the values of the variables) you get:

2a + 2c = 18

Note: the ' b ' variables cancelled out in the addition [ b +  (-b) ]

If you further simplify the equation:

a + c = 9

Awesome. Now we already know that <u>c = 7</u>, so if you plug that into the equation:

a + 7 = 9

Solve for a. So then a = 2

Now that we know the following:

a = 2

c = 7

We can then use the equation:

a + b + c = 4

And solve for b!

2 + b + 7 = 4

Simplify.

b + 9 = 4

Simplify.

b = -5

Now at this point, since you know what a, b and c are, you can write the equation!

f(x) = 2x² - 5x + 7

You can confirm your work by putting any of the x values in the table through!

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3 years ago
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