All categories

3 years ago

Patricia got a 5/25 balloon mortgage and her initial payments were $965. She

Mathematics

1 answer:

goldenfox [79]3 years ago

4 0

Answer:

$390,900

Step-by-step explanation:

Given that.

Initial payment = $965

New rapayment = $925

when she decided to refinance her ballon payment with a 30 year mortgage

In this case,

a 5/25 ballon mortgage simply means loan repayment for the first 5 years is at a fixed rate.

Which means the total amount she paid in the first five years was=

12 * 5 * $965

= $57,900

When she refinanced the payment with a 30 year mortgage, her total payment

= $925 * 12 * 30years

= $333,000

Total financed cost Patricia paid =

$57,900 + $333,000

= $390,900

You might be interested in

Determine whether the sequences converge.

Alik [6]

$a_n=\sqrt{\dfrac{(2n-1)!}{(2n+1)!}}$

Notice that

$\dfrac{(2n-1)!}{(2n+1)!}=\dfrac{(2n-1)!}{(2n+1)(2n)(2n-1)!}=\dfrac1{2n(2n+1)}$

So as $n\to\infty$ you have $a_n\to0$ . Clearly $a_n$ must converge.

The second sequence requires a bit more work.

$\begin{cases}a_1=\sqrt2\\a_n=\sqrt{2a_{n-1}}&\text{for }n\ge2\end{cases}$

The monotone convergence theorem will help here; if we can show that the sequence is monotonic and bounded, then $a_n$ will converge.

Monotonicity is often easier to establish IMO. You can do so by induction. When $n=2$ , you have

$a_2=\sqrt{2a_1}=\sqrt{2\sqrt2}=2^{3/4}>2^{1/2}=a_1$

Assume $a_k\ge a_{k-1}$ , i.e. that $a_k=\sqrt{2a_{k-1}}\ge a_{k-1}$ . Then for $n=k+1$ , you have

$a_{k+1}=\sqrt{2a_k}=\sqrt{2\sqrt{2a_{k-1}}\ge\sqrt{2a_{k-1}}=a_k$

which suggests that for all $n$ , you have $a_n\ge a_{n-1}$ , so the sequence is increasing monotonically.

Next, based on the fact that both $a_1=\sqrt2=2^{1/2}$ and $a_2=2^{3/4}$ , a reasonable guess for an upper bound may be 2. Let's convince ourselves that this is the case first by example, then by proof.

We have

$a_3=\sqrt{2\times2^{3/4}}=\sqrt{2^{7/4}}=2^{7/8}$
$a_4=\sqrt{2\times2^{7/8}}=\sqrt{2^{15/8}}=2^{15/16}$

and so on. We're getting an inkling that the explicit closed form for the sequence may be $a_n=2^{(2^n-1)/2^n}$ , but that's not what's asked for here. At any rate, it appears reasonable that the exponent will steadily approach 1. Let's prove this.

Clearly, $a_1=2^{1/2}$ . Let's assume this is the case for $n=k$ , i.e. that $a_k$ . Now for $n=k+1$ , we have

$a_{k+1}=\sqrt{2a_k}$

and so by induction, it follows that $a_n$ for all $n\ge1$ .

Therefore the second sequence must also converge (to 2).

4 0

3 years ago

6) Solve 5x < -10 AX <-2 B) x>-2 CXC-15 D) x < -50

grin007 [14]

Answer:

Step-by-step explanation:

give me brainelest pls

4 0

3 years ago

Read 2 more answers

(4^6)(4^-8) Please write in the form 4^n

stepan [7]

Answer: 4^-2

Step-by-step explanation:

the Bases stays the same the powers changes to negative -2 because you are stubtracting 6-8 which gives you negative -2.

7 0

3 years ago

Convert (-2/sqrt[3] , 2) to polar coordinates

anyanavicka [17]

If you have these conditions:

1. (r ,theta) where r > 0
2. (r, theta) where r < 0

The solution would be:

r = sqrt(x^2 + y^2)

t = arctan(y/x)

r = sqrt(12 + 4) = sqrt(16) = +/- 4

t = arctan(2 / -2sqrt(3)) = arctan(-1 / sqrt(3)) = 5pi/6 , 11pi/6

1)
r > 0
(4 , 11pi/6)

2)
r < 0
(-4 , 5pi/6)


I hope my answer has come to your help. Thank you for posting your question here in Brainly. We hope to answer more of your questions and inquiries soon. Have a nice day ahead!

5 0

3 years ago

How will the volume of a prism change if its height is multiplied by a scale factor of 4?

Fynjy0 [20]

Answer:

It will double in size, as M x M x M x M is simply just 3 changeable values. When we change 4 numbers of a prism (3 changed values ) to all 4 we have a S4 value to the volume, But we didnt do this, applying x 4 to either measurement it can only increase the volume by x 2. We had a one change value SF4 so we have SF 2= double. That means if we have two change value value SF4 we have 3 = 3 x total increase, if we have a three input change by SF4 we can increase size to 4x total increase.

Step-by-step explanation:

5 0

3 years ago