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Feliz [49]
2 years ago
10

Carlos deposited $7,924 into a savings account 30 years ago. The account has an interest rate of 4.6% and the balance is current

ly $30,541.83. How often does the interest compound?
Mathematics
1 answer:
exis [7]2 years ago
6 0

Answer:

n = 1, this means the interest compounds ANNUALLY.

Step-by-step explanation:

Carlos deposited $7,924 into a savings account 30 years ago. The account has an interest rate of 4.6% and the balance is currently $30,541.83. How often does the interest compound?

Compound Interest Formula

: A = P(1 + r/n)^nt

A = Amount after time t

P = Principal (Initial Amount Invested)

r = Interest rate

n = Number of times the interest is compounded

t = time in years

A = $30,541.83

r = 4.6% = 0.046

t = 30

P = $7,924

Hence,

$30,541.83 = $7924(1 + 0.046/n)^30n

Divide both sides by 7924

$30,541.93/$7924 = (1 + 0.046/n)^30n

$30,541.93/$7924 = (n + 0.046/n)^30n

3.8543576477 = (n + 0.046/n)^30n

We take the logarithm of both sides

log 3.8543576477 = log (n + 0.046/n)^30n

Solving for n,

n = 1

Therefore, from the calculation above, since n = 1, this means the interest compounds ANNUALLY.

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Answer:

=1600

Step-by-step explanation:

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4 0
2 years ago
Write an equation in slope intercept form for the line that passes through (-1, -2) and (3, 4)
LenaWriter [7]

Answer:

The slope-intercept form of the line equation  is:

  • y=\:\frac{3}{2}x\:-\frac{1}{2}

Step-by-step explanation:

The slope-intercept form of the line equation

y = mx+b

where

  • m is the slope
  • b is the y-intercept

Given the points

  • (-1, -2)
  • (3, 4)

Determining the slope between (-1, -2) and (3, 4)

\mathrm{Slope}=\frac{y_2-y_1}{x_2-x_1}

\left(x_1,\:y_1\right)=\left(-1,\:-2\right),\:\left(x_2,\:y_2\right)=\left(3,\:4\right)

m=\frac{4-\left(-2\right)}{3-\left(-1\right)}

m=\frac{3}{2}

Thus, the slope of the line is:

m = 3/2

substituting m = 3/2 and the point (3, 4) in the slope-intercept form of the line equation

y = mx+b

4=\frac{3}{2}\left(3\right)+b

switch sides

\frac{3}{2}\left(3\right)+b=4

\frac{9}{2}+b=4

subtract 9/2 from both sides

\frac{9}{2}+b-\frac{9}{2}=4-\frac{9}{2}

b=-\frac{1}{2}

now substituting m = 3/2 and b = -1/2 in the slope-intercept form of the line equation

y = mx+b

y=\:\frac{3}{2}x\:+\:\left(-\frac{1}{2}\right)

y=\:\frac{3}{2}x\:-\frac{1}{2}

Therefore, the slope-intercept form of the line equation  is:

  • y=\:\frac{3}{2}x\:-\frac{1}{2}
8 0
2 years ago
Lin solved the equation 8(x-3)+7=2x(4-17) incorrectly. Find the errors in her solution. What should her answer have been?
Irina-Kira [14]

Answer: The correr solution is x=\frac{17}{34}

Step-by-step explanation:

Since the steps in Lin's solution are not shown, we are not able to find her erros. However, we can solve it step by step and find the correct result:

8(x-3)+7=2x(4-17)

Firstly, in the left part of the equation we have to multiply 8 by the numbers inside the parenthesis; and in the right side we have to solve first what is inside the parenthesis:

8x-24+7=2x(-13)

Adding similar terms in the left side and multiplying 2x by the number inside the parenthesis in the right side:

8x-17=-26 x

Isolating x:

x=\frac{17}{34} This is the correct solution

4 0
3 years ago
It says Evaluate but i need help! 6 + (5 × 2) − 10 ÷ 6 − 4 + 1
Elanso [62]

Answer:

11.3

Step-by-step explanation:

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6+10-10/6-4+1

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16-1.6-4+1

14.3-4+1

10.3+1

11.3

5 0
2 years ago
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