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3 years ago

How much would $500 invested at 6% interest compounded monthly be worth after 5 years? round your answer to the nearest cent.

2 answers:

8 0

Use this formula: A = P(1 + r/n)^nt, where A is the amount after interest (what you are solving for), P is the amount you invested originally, r is the rate at which it was invested in decimal form, n is the number of times the compounding occurs each year, t is the time in years it is invested. It would look like this: A = 500(1 + [.06/12])^12*5. Do inside the parenthesis first to get 1 + .005 = 1.005. Now raise that to the 60th power (12 times 5 is 60) to get 1.34558. Now multiply that by the 500 out front to get a total amount of $674.43

GenaCL600 [577]3 years ago

5 0

Answer- $674.43

Step-by-step explanation:

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The 95% confidence interval would be given by (5.139;5.861)

Step-by-step explanation:

1) Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

$\bar X$ represent the sample mean for the sample

$\mu$ population mean (variable of interest)

s represent the sample standard deviation

n represent the sample size

2) Confidence interval

Assuming that $\bar X =5.5$ and the ranfom sample n=1086.

The confidence interval for the mean is given by the following formula:

$\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}$ (1)

In order to calculate the critical value $t_{\alpha/2}$ we need to find first the degrees of freedom, given by:

$df=n-1=1086-1=1085$

Since the Confidence is 0.98 or 98%, the value of $\alpha=0.02$ and $\alpha/2 =0.01$ , and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-T.INV(0.01,1085)".And we see that $t_{\alpha/2}=2.33$

Now we have everything in order to replace into formula (1):

$5.5-2.33\frac{5.1}{\sqrt{1086}}=5.139$

$5.5+2.333\frac{5.1}{\sqrt{1086}}=5.861$

So on this case the 95% confidence interval would be given by (5.139;5.861) We are 98% confident that the mean time spent volunteering for the population of parents of school-aged children is between these two values.

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Explanation:89% of 10,000 is 8900 subtract 8900 from 10,000 bam you got 1100

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