MATHEMATICS HIGH SCHOOL

Connor is a prospective student who has been accepted for a $50,000 student loan from two different loan providers. He wants to select the student loan with the lowest total cost. The first loan is a 10-year loan at 4% and the second loan is a 20-year loan at 3%. Both loans compound the interest monthly. Which student loan should Connor select?

Answers

Answer 1
Answer:

Answer:

To figure out which loan has the lower total cost, we need to calculate the total repayment amount for both loans.

The formula to calculate the monthly payment for a loan is:

P = [r*PV] / [1 - (1 + r)^-n]

where:

P is the monthly payment

r is the monthly interest rate (annual rate / 12)

PV is the present value, i.e., the loan amount

n is the number of payments (months)

For the first loan:

r = 4% / 12 = 0.00333 (approximately)

n = 10 years * 12 = 120 months

PV = $50,000

Plugging these numbers into the formula, we get the monthly payment for the first loan.

For the second loan, we do the same calculation, but with r = 3% / 12 and n = 20 * 12.

After we have the monthly payments, we multiply each by the total number of payments (n) to get the total repayment amount for each loan. The loan with the lower total repayment amount is the one Connor should select.

I hope that helps
Answer 2
Answer:

Answer:

Connor should select the 10-year loan because it has a lower total cost than the 20-year loan.

Step-by-step explanation: To calculate the total cost of each loan, first find the monthly payment of the loans. Use the formula below to find the monthly payments, where P is the monthly payment, L is the principal amount of the loan, i is the interest rate, and n is the duration of the loan.

P=L×i1−(1+i)−n

The loan amount needed, L, is $50,000 for both loans. Since the interest rate is compounded monthly, the interest rate offered is 4% per year or 0.0412 per month. The time period is 10 years or 120 months. Substituting the values into the formula and converting the interest rate to the monthly rate yields the following.

PP=50,000×0.04121−(1+0.0412)−120≈$506.23

Multiply the monthly payment by the number of months in the loan, 120, to determine the total cost of the loan.

$506.23×120=$60,747.60

Now calculate the monthly cost of the 20-year loan.

PP=50,000×0.03121−(1+0.0312)−240≈$277.30

$277.30×240=$66,552

Since the total cost of the 10-year loan, $60,747.60, is less than the total cost of the 20-year loan, $66,552, Connor should select the 10-year loan.

Your answer:

Connor should select the 20-year loan because it costs less than the 10-year loan.

The 20-year loan has a total cost of $66,552 while the 10-year loan has a total cost of $60,747.60.

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Quadrilateral ABCD is inscribed in a circle. m A is 64°, m B is (6x + 4)°, and m C is (9x - 1)°. What is m D?A. 64°
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E. 116°

Answers

Answer: Choice D) 98 degrees

============================================================

Explanation:

The quadrilateral is inscribed in the circle which means every corner point (A,B,C,D) is on the circle. No part of the quadrilateral is outside the circle. 

One property of inscribed quadrilaterals is that the opposite angles add to 180 degrees. So,
A+C = 180
B+D = 180

We know that
A = 64
B = 6x+4
C = 9x-1

Let's use angles A and C to find x
A+C = 180
64+9x-1= 180
9x+63 = 180
9x+63-63 = 180-63
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Which helps us find angle B
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Then we can finally find angle D
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Answer:

choiced c 98

Step-by-step explanation:

Which is smaller, -5 or -17 and show your work

Answers

On a number line it seen as this

.... -10, -9, -8,-7,-6,-5,-4,-3,-2,-1,0,1,2,3,4,5...

The farther left the number, the smaller it is. So -17 < -5

Which of the following is the solution to the equation 25^(z - 4) = 125 ? Select one: A. z = 5.5. B. z = 3.5. C. z = -2.5. D. z = -0.5.

Answers


given
25^(z - 4) = 125
ln(25^(z - 4)) = ln (125)
(z-4)ln(25) = ln(125)
z = ln(125)/ln(25) + 4
z = 5.5

which means that the answer is A. 

The solution of 25^(z - 4) = 125 is equal to a. Z = 5.5

How to solve this equation

25^(z - 4) = 125

From here we have to the ln  of the equation

z-4 ln25 = ln125

z-4 (3.219)= 4.828

From here we have to multiply the equation

3.219z - 12.876 = 4.828

3.219z = 4.828 + 12.876

When we divide this equation by 3.219

We have z = 5.499

Hence z = 5.5

Therefore the solution to the equation is given as 5.5

Read more on solutions to equations here:

brainly.com/question/2972832

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For f(x) = 3x +1 and g(x) = x2 – 6, find (f- g)(x).

Answers

Answer:

\boxed{\sf (f-g)(x) = -{x}^(2) + 3x + 7}

Given:

\sf f(x) = 3x + 1 \n \sf g(x) = {x}^(2) - 6

To find:

\sf (f - g)(x) = f(x) - g(x)

Step-by-step explanation:

\sf \implies(f - g)x = f(x) - g(x) \n \n \sf \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = (3x + 1) - ( {x}^(2) - 6) \n \n \sf \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = (3x + 1) + (- {x}^(2) + 6) \n \n \sf \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 3x + 1 - {x}^(2) + 6 \n \n \sf \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = - {x}^(2) + 3x + 1 + 6 \n \n \sf \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = -{x}^(2) + 3x + 7

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Variables are: d (for dimes) and q (for quarters)

Answers

There's two actually.
0.25q + 0.10d = 3.85
q + d = 25

Kalon has $175 and needs to save at least $700 for a new computer. If he can save $35 per week, what is the minimum number of weeks Kalon will need to save to reach his goal?

Answers

The minimum would be 15. I'm sorry if I'm wrong, but I'm pretty sure that's the answer.

Answer:

15 weeks

Step-by-step explanation:

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