Mathematics, 20.01.2022 14:00 bm42400

If $500 were to compound continuously at a yearly interest
rate of 7%, what would the total
amount be after 10 years?
$[?]
Round your answer to the nearest hundredth.

Answers: 1

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Answer from: bettymj3071

Total amount: $1,006.88

Step-by-step explanation:

Given the principal amount of $500 that is compounded continuously for 10 years at an annual interest rate of 7%:

We can use the following Continuous Compound Interest Formula to determine the future value of the total amount of investment:

$\displaystyle\mathsf{\Bigg\ Continuous\:Compound\:Interest:\quad\ A\:=\:Pe^{(r\times\\ t)}}$

where:

A = The future value of the total amount in the account at the end of "t" number of years

P = Present value of the principal amount invested = $500

e = constant (base of the exponential function) ≈ 2.71828

r = Annual interest rate = 7% or 0.07

t = time (in years) = 10 years

Solution:

Substitute the given values into the Continuous Compound Interest Formula:

$\displaystyle\mathsf{\Bigg\ Continuous\:Compound\:Interest:\quad\ A\:=\:Pe^{(r\times\\ t)}}$

$\displaystyle\mathsf{A\:=\:$500\:\times\ 2.71828 ^{(0.07\times\\ 10)}}$

$\displaystyle\mathsf{A\:=\:$500\:\times\ [2.71828 ^{(0.70)}]}$

$\displaystyle\mathsf{A\:=\:$500\:\times\ 2.013752707}$

$\displaystyle\mathsf{A\:=\$1,006.88}}$

Therefore, the total amount accumulated after continuously compounding the principal investment for 10 years is $1,006.88. This includes the principal amount invested, $500, plus the interest accrued of $506.88.

Answer from: Quest

for the friend request.

when a figure, such as triangle (xyz) is reflected over the line y = x to create x'y'z' the x-coordinates and y-coordinates of the original image (pre-image) will be reversed for the image. (e.g., (x, y) > (y, x)) this means that the pre-image position of the x- and y-coordinates switch places which in turn provides a mirror like image of the original xyz.

i notice that when i draw a line segment from x to x', that the points are parallel from each other -- they are exactly across from each other and do not intersect with any other points.

yes, think i would see the same characteristic if you drew the line segment connecting y with the reflecting line and then y' with the reflecting line because of the essence of reflections. because it is a mirror image, each point was effected the same way which leads me to conclude that they same would apply to y and y'.

Answer from: Quest

answer: yes i agree that you should not put it on/p>

step-by-step explanation: the reason for this is that it wastes other peoples time and also make them fail as well and that is never good.

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