Refer to the scenario below to answer the following question.

Melanie is looking for a loan. She is willing to pay no more than an effective rate of 9.955% annually. Which, if any, of the fo

lakkis [162]

Answer:

c) A and B, being r(loan a)= 9.699% annually, r(loan b)=9.862% annual

Step-by-step explanation:

Hi, well, let´s transform all this nominal rates into effective annual rates.

Loan A: 9.265% nominal rate, compounded weekly

In order to find the easiest effective rate, we need to divide this rate by 52 (which are the weeks in a year). Once we do that, we convert this effective weekly rate into an effective annual rate. Let´s walk you through all this.

$r(E.week)=\frac{0.09265}{52} =0.00178173$

Or 0.178173% effective weekly. Now we can transform it into an effective annual rate.

$r(e.a)=(1+r(e.week))^{52} -1$

$r(e.a)=(1+0.00178173)^{52} -1=0.09699$

Or 9.669% annual, which is less than 9.955%, so this one is sellected, let´s check the next.

Loan B: 9.442% nominal rate, compounded monthly

Just like we did with Loan A, we need to divide this rate too, only this time, we will divide by 12, therefore obtaining an effective monthly rate.

$r(E.month)=\frac{0.09442}{12} =0.00786833$

Or 0.786833% effective monthly, let´s turn it into a effective annual rate.

$r(e.a)=(1+r(e.month))^{12} -1$

$r(e.a)=(1+0.00786833)^{12} -1=0.09862$

Or 9.862% annual, so this rate would work for Melanie too. This means that option C) is the answer we are looking for but, let´s walk that extra mile and turn that Loan C rate into an annual rate.

$r(E.quarter)=\frac{0.09719}{4}=0.0242975$

or 2.42975% effective quarterly, now, let´s convert it into an effective annual rate.

$r(e.a)=(1+0.0242975)^{12} -1=0.10079$

That is 10.079% effective annual, therefore, Loan C is not an option for Melanie.

Best of Luck.

5 0

2 years ago

Read 2 more answers

What is 5g6 in verbal expression

AVprozaik [17]

Step-by-step explanation:

I don't know if this is what you mean but 5 multiplied by g multiplied for 6

5 0

2 years ago

Read 2 more answers

Which relation is a function?

DedPeter [7]

It is the third one

3 0

2 years ago

Read 2 more answers

Triangle PQR has vertices P(-3, -1), Q(-1, 7), and R(3, 3), and point A and B are midpoints of PQ and RQ, respectively. Use coor

andrezito [222]

Answer:

Part a) The figure a shows that AB is parallel to PR. Please see attached figure a.

Part b) The length of AB is half the length of PR

Step-by-step explanation:

Part A)

Let M be the midpoint formula between points A(x₁, y₁) and B(x₂, y₂)

$M=({\displaystyle {\frac {x_{1}+x_{2}}{2}}, {\frac {y_{1}+y_{2}}{2})$

Let A be the midpoint of P(-3, -1) and Q(-1, 7)

The coordinates of the midpoint of P(-3, -1) and Q(-1, 7):

$Mpq{} =({\displaystyle {\frac {-3+(-1)}{2}}, {\frac {-1+7}{2})$

$Mpq{} =(-2, 3)$

Let B be the midpoint of Q(-1, 7) and R(3, 3):

$Mqr{} =({\displaystyle {\frac {-1+(3)}{2}}, {\frac {7+3}{2})$

$Mqr{} =(1, 5)$

The figure a shows that AB is parallel to PR. Please see attached figure a.

Part B)

The point A has the coordinates: A(-2, 3)

The point B has the coordinates: B(1, 5)

The distance formula is: $d={\sqrt {(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2}$

So, the length of AB $={\sqrt {(1-(-2))^{2}+(5-3)^{2}$

= $\sqrt{9+4}$

= $\sqrt{13}$

= $3.6056$

And, the length of PR $={\sqrt {(3-(-3))^{2}+(3-(-1)^{2}$

= $\sqrt{36+16}$

= $\sqrt{52}$

= $2\sqrt{13}$

= = $7.2111$

As the length of AB = 3.6056 and the length of PR = 7.2111

So, it is clear that the length of AB is half the length of PR.

Keywords: distance formula, midpoints, triangle, coordinate plane

Learn more about midpoints from brainly.com/question/7560674

#learnwithBrainly

3 0

2 years ago

What is the equation?

mart [117]

Answer:

y=3x+1

Step-by-step explanation:

To figure out equations of tile patterns simply count the initial value and the rate of change, then convert it into (slope intercept form) which is

y = mx+b

In this case in figure 2 we see that there are 4 blocks, in figure 3 we see there are now 7 blocks.

7 - 4 = 3.

If we try again and see figure 3 has 7 blocks and figure 4 has 10 blocks we can do this to double check.

10 - 7 = 3. (This now verifies our rate of change to be 3)

We now see that the rate of change or slope (same thing) is 3 or put into the equation (3x).

Off this information we can also predict the original value of figure 1 (the figure we must calculate ourselves to create the equation).

Simply take figure 2 (4 blocks) and subtract by the rate of change which is (3 blocks) to get figure 1 which will be 1 block.

With all this information we can create the equation with the information we now have.

y = mx+b

y = what you are calculating for

m = 3

x = (the value you fill in when you are calculating for x) [we are not filling this in for this question so you will leave it as simply x]

b = 1 (the constant / y intercept / or simply put as the value we solved when calculating figure 1)

Final Result = [ y = 3x + 1]

4 0

1 year ago