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Sergio [31]
1 year ago
6

Explain the error a student is asked to find when the value of an investment of $5200 is an account that earns 4.2% annual inter

est compounded quarterly reaches $16,500. The student uses the model V(t)=5200(1.014)^3t and finds that the investment reaches a value of $16,500 after approximately 27.7 years. Fine and correct the students error.
Mathematics
1 answer:
zloy xaker [14]1 year ago
5 0

We are given the following information

Investment = $5200

Annual interest rate = 4.2% = 0.042

Final amount = $16,500

Number of years = 27.7 years

Number of compoudings = quartely = 4

The student uses the following model

V(t)=5200(1.014)^{3t}

The general formula for compound interest is given by

V(t)=P(1+\frac{r}{n})^{nt}

As you can see, the number of compoundings is incorrect (3 vs 4)

The interest rate is also incorrect.

Let us substitute the given values into the above formula

\begin{gathered} V(t)=P(1+\frac{r}{n})^{nt} \\ V(t)=5200(1+\frac{0.042}{4})^{4\cdot27.7} \\ V(t)=5200(1+0.0105)^{110.8} \\ V(t)=5200(1.0105)^{110.8} \\ V(t)=\$16543.5^{} \end{gathered}

Therefore, the final amount is approximately $16,543.5

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Given data:

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Answer:

A 90% confidence interval to estimate the mean DRP score in Henrico County Schools  is =32±2.7280

i.e. C.I.  [29.3,34.7]

Hence the results are not significant.

Step-by-step explanation:

Given:

Total no of students =44

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Standard deviation=11

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90 % confidence interval and conclusion on it.

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Here for C.I. we required mean, standard deviation and no of students.

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Now Here to commit on calculated interval we should check  value of Z-score

So we need to calculate the sample mean.

Sample mean =Sum of all values /Total no of values.

=[40+ 26 +39+ 14+ 42+ 18 +25+ 43+ 46 +27 +19+ 47+ 19 +26+ 35 +34+ 15+ 44 40+ 38+ 31+ 46 +52 +25+ 35 +35+ 33 +29 +34 +41 +49+ 28+ 42+ 47 +35 +48 +22 33+ 41 +51 +27 +14+ 54 +45]/44

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=(34.86-32)/[11/Sqrt(44)]

Z=1.72465

For ,

P(Z≥1.72465)=0.08544

For 0.05 significance level  the results are not significant at  p<0.01.

Researcher claimed mean is not correct upto 0.05 significant level

i.e calculated mean and Sample mean are different.

Hence the results are not significant.

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