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Sydney invested $440 in an account paying an interest rate of 5.6% compounded daily. Assuming no deposits or withdrawals are mad

stealth61 [152]

Answer:

The time required to get a total amount of $ 640.00 from compound interest on a principal of $ 440.00 at an interest rate of 5.6% per year and compounded 365 times per year is approximately 7 years.

Step-by-step explanation:

Given

Principle Amount P = $440

Accrued Amount A = $640

Interest rate r = 5.6% = 0.056

Compounded daily n = 365

To determine:

Time period t = ?

Using the formula

$A\:=\:P\left(1\:+\:\frac{r}{n}\right)^{nt}$

solving for t

t = ln(A/P) / n[ln(1 + r/n)]

substituting the values A = 640, P = 440, n = 365 and r = 0.056

t = ln(640/440) / ( 365 × [ln(1 + 0.00015342465753425/365)] )

t = 6.691

t ≈ 7 (nearest year)

Therefore, the time required to get a total amount of $ 640.00 from compound interest on a principal of $ 440.00 at an interest rate of 5.6% per year and compounded 365 times per year is approximately 7 years.

4 0

3 years ago

Explain how to find the distance between two integers using the difference

maksim [4K]

Answer:

Step-by-step explanation:

When we want to find the distance between two integers using the difference, the best way is to plot them on number line. And then count distance between them.

For example -3 and -1.

When we want to find difference we have:

-3-(-1)=-2

But distance can not be negative.

Now, we need to count distance between numbers -3 and -1 on the number line.

So we have from -3 to -2, one place and from -2 to -1 one place it is 2 places.

So distance is 2.

6 0

3 years ago

Read 2 more answers

How do you divide 2.16 by 3

lozanna [386]

Answer:

by moving the decimal in both numbers twice to the right and doing normal long division (the decimal in 3 is at the end) to get the answer of 0.72

3 0

3 years ago

Read 2 more answers

Item 10 At 1:00 P.M., you have 24 megabytes of a movie. At 1:15 P.M., you have 96 megabytes. What is the download rate in megaby

alex41 [277]

Answer:

4.8 megabytes / minute.

Step-by-step explanation:

At the beginning of recording the download you have 24 megabytes.

15 minutes later, you have 96 megabytes.

In 15 minutes you have downloaded 96 - 24 = 72 megabytes

So the question turns out to be a proportion of

x megabytes / 1 minute = 72 megabytes / 15 minutes.

x = 72/15

x = 4.8 megabytes / minute

3 0

3 years ago

A laboratory scale is known to have a standard deviation (sigma) or 0.001 g in repeated weighings. Scale readings in repeated we

weqwewe [10]

Answer:

99% confidence interval for the given specimen is [3.4125 , 3.4155].

Step-by-step explanation:

We are given that a laboratory scale is known to have a standard deviation (sigma) or 0.001 g in repeated weighing. Scale readings in repeated weighing are Normally distributed with mean equal to the true weight of the specimen.

Three weighing of a specimen on this scale give 3.412, 3.416, and 3.414 g.

Firstly, the pivotal quantity for 99% confidence interval for the true mean specimen is given by;

P.Q. = $\frac{\bar X - \mu}{\frac{\sigma}{\sqrt{n} } }$ ~ N(0,1)

where, $\bar X$ = sample mean weighing of specimen = $\frac{3.412+3.416+3.414}{3}$ = 3.414 g

$\sigma$ = population standard deviation = 0.001 g

n = sample of specimen = 3

$\mu$ = population mean

<em>Here for constructing 99% confidence interval we have used z statistics because we know about population standard deviation (sigma).</em>

So, 99% confidence interval for the population mean, $\mu$ is ;

P(-2.5758 < N(0,1) < 2.5758) = 0.99 {As the critical value of z at 0.5% level

of significance are -2.5758 & 2.5758}

P(-2.5758 < $\frac{\bar X - \mu}{\frac{\sigma}{\sqrt{n} } }$ < 2.5758) = 0.99

P( $-2.5758 \times {\frac{\sigma}{\sqrt{n} } }$ < ${\bar X - \mu}$ < $2.5758 \times {\frac{\sigma}{\sqrt{n} } }$ ) = 0.99

P( $\bar X-2.5758 \times {\frac{\sigma}{\sqrt{n} } }$ < $\mu$ < $\bar X+2.5758 \times {\frac{\sigma}{\sqrt{n} } }$ ) = 0.99

<u>99% confidence interval for</u> $\mu$ = [ $\bar X-2.5758 \times {\frac{\sigma}{\sqrt{n} } }$ , $\bar X+2.5758 \times {\frac{\sigma}{\sqrt{n} } }$ ]

= [ $3.414-2.5758 \times {\frac{0.001}{\sqrt{3} } }$ , $3.414+2.5758 \times {\frac{0.001}{\sqrt{3} } }$ ]

= [3.4125 , 3.4155]

Therefore, 99% confidence interval for this specimen is [3.4125 , 3.4155].

6 0

3 years ago