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Aleksandr-060686 [28]
3 years ago
12

Pamela deposits $4,000 in an account that earns interest at 5% APR compounded weekly. What is her ending balance after 2 years?

Round to the nearest cent.
Mathematics
2 answers:
Triss [41]3 years ago
6 0
The answer is $4419.76

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

Therefore,

A = 4000 (1 + 0.05/52)^52 x 2
A = 4000 (1.00096)^104
A = 4000 (1.1049)
A= 4419.76

Hope that helps!
(I'll take brainliest thank you ;))
Anarel [89]3 years ago
3 0
Hi there :-)

A=p (1+r/k)^kt
A future value
P present value 4000
R interest rate 0.05
K compounded weekly 52
T time 2 years

A=4,000×(1+0.05÷52)^(52×2)
A=4,420.47

Hope it helps
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Answer:

a) The 99% confidence interval would be given by (24.409;24.979)  

b) n=464

Step-by-step explanation:

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.  

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

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

df=n-1=47-1=46  

Since the Confidence is 0.95 or 95%, the value of \alpha=0.05 and \alpha/2 =0.025, and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-T.INV(0.025,46)".And we see that t_{\alpha/2}=2.01  

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

525-2.01\frac{75}{\sqrt{47}}=503.01  

525+2.01\frac{75}{\sqrt{47}}=546.99  

So on this case the 95% confidence interval would be given by (503.01;546.99)

Part b

The margin of error is given by this formula:  

ME=t_{\alpha/2}\frac{s}{\sqrt{n}} (1)  

And on this case we have that ME =7 msec, we are interested in order to find the value of n, if we solve n from equation (1) we got:  

n=(\frac{t_{\alpha/2} s}{ME})^2 (2)  

The critical value for 95% of confidence interval is provided, t_{\alpha/2}=2.01 from part a, replacing into formula (2) we got:  

n=(\frac{2.01(75)}{7})^2 =463.79 \approx 464  

So the answer for this case would be n=464 rounded up to the nearest integer  

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Answer:

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