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2 years ago

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Nicole took out a 30-year mortgage for $90,000 at 7.5%. How much is her monthly mortgage payment? I assume $675,000?

1 answer:

V125BC [204]2 years ago

7 0

Answer:

Nicole pays $629.29 per month
Zack pays $563.24 per month

Step-by-step explanation:

We're not quite sure why you estimated the monthly payment at several times the value of the entire loan.

The applicable formula is the amortization formula. It computes the monthly payment A on loan principal value P at annual rate r for t years to be ...

A = P(r/12)/(1 -(1 +r/12)^(-12t))

The value of r used in this formula is the decimal equivalent of the percentage rate. 7.5% = 0.075; 9% = 0.09

__

<h3>a)</h3>

The formula with Nicole's numbers filled in looks like ...

A = $90,000(0.075/12)/(1 -(1 +0.075/12)^(-12·30))

= $90,000(0.00625)/(1 -(1.00625^-360)) = $562.50/(1 -0.1051398)

A ≈ $629.293 ≈ $629.29 . . . . Nicole's monthly payment

__

<h3>b)</h3>

Using the same formula with P=$70,000, r=0.09, t=30, we find Zack's monthly payment to be $563.24.

_____

<em>Additional comment</em>

If you're doing a number of problems of this type, it can be helpful to use a tool that will do the calculation for you without error. A graphing calculator or spreadsheet can do that. One example is shown in the attachment.

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Answer:

C

Step-by-step explanation:

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3 years ago

One sample has Aa Aa One sample has n 10 scores and a variance of s2 20, and a second sample has n 15 scores and a variance of s

siniylev [52]

Answer:

option (a) It will be closer to 30 than to 20

Step-by-step explanation:

Data provided in the question:

For sample 1:

n₁ = 10

variance, s₁² = 20

For sample 2:

n₂ = 15

variance, s₂² = 30

Now,

The pooled variance is calculated using the formula,

$S^{2}_{p} = \frac{(n_{1}-1)\times s^{2}_{1} +(n_{2}-1)\times s^{2}_{2}}{n_{1}+n_{2}-2}$

on substituting the given respective values, we get

$S^{2}_{p} = \frac{(10-1)\times 20 +(15-1)\times 30}{10+15-2}$

or

$S^{2}_{p}$ = 26.0869

Hence,

the pooled variance will be closer to 30 than to 20

Therefore,

The correct answer is option (a) It will be closer to 30 than to 20

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3 years ago

If you are making a scale drawing of a girrafe that is 6m tall, and the height of the girrafe in your drawing is 3cm, what is th

k0ka [10]

Answer:

1cm to 200cm

Step-by-step explanation:

l of giraffe = 6m = 600cm

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scale = drawing : real = 3 : 600 = 1 : 200

Therefore the scale is 1cm to 200cm

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3 years ago

Toni had 5 1/2 kilograms of sugar.how many cakes can he bake if he ise 1/4 hilogram of sugar per cake?

allochka39001 [22]

Answer:

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Step-by-step explanation:

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3 years ago

Read 2 more answers

Verify that P = Ce^t /1 + Ce^t is a one-parameter family of solutions to the differential equation dP dt = P(1 − P).

NemiM [27]

Answer:

See verification below

Step-by-step explanation:

We can differentiate P(t) respect to t with usual rules (quotient, exponential, and sum) and rearrange the result. First, note that

$1-P=1-\frac{ce^t}{1+ce^t}=\frac{1+ce^t-ce^t}{1+ce^t}=\frac{1}{1+ce^t}$

Now, differentiate to obtain

$\frac{dP}{dt}=(\frac{ce^t}{1+ce^t})'=\frac{(ce^t)'(1+ce^t)-(ce^t)(1+ce^t)'}{(1+ce^t)^2}$

$=\frac{(ce^t)(1+ce^t)-(ce^t)(ce^t)}{(1+ce^t)^2}=\frac{ce^t+ce^{2t}-ce^{2t}}{(1+ce^t)^2}=\frac{ce^t}{(1+ce^t)^2}$

To obtain the required form, extract a factor in both the numerator and denominator:

$\frac{dP}{dt}=\frac{ce^t}{1+ce^t}\frac{1}{1+ce^t}=P(1-P)$

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4 years ago