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3 years ago

Find the value of annuity if the periodic deposit is $1500 at 8% compounded semiannually for 22 years

Mathematics

1 answer:

Jet001 [13]3 years ago

8 0

Answer:

The value of annuity is $P_v = \$ 32058$

Step-by-step explanation:

From the question we are told that

The periodic payment is $P = \$ 1500$

The interest rate is $r = 8\% = 0.08$

Frequency at which it occurs in a year is n = 2 (semi-annually )

The number of years is $t = 22 \ years$

The value of the annuity is mathematically represented as

$P_v = P * [1 - (1 + \frac{r}{n} )^{-t * n} ] * [\frac{(1 + \frac{r}{n} )}{ \frac{r}{n} } ]$ (reference EDUCBA website)

substituting values

$P_v = 1500 * [1 - (1 + \frac{0.08}{2} )^{-22 * 2} ] * [\frac{(1 + \frac{0.08}{2} )}{ \frac{0.08}{2} } ]$

$P_v = 1500 * [1 - (1.04 )^{-44} ] * [\frac{(1.04 )}{0.04} ]$

$P_v = 1500 * [1 - 0.178 ] * [\frac{(1.04 )}{0.04} ]$

$P_v = \$ 32058$

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Step-by-step explanation:

Given

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3 years ago

Evaluate P(5, 3). 15 20 60

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Answer:

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Step-by-step explanation:

P(5,3) = 5! / 3!

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3 years ago

A theater has 20 rows of chairs. The first row has 16 chairs, the second has 18, the third has 20, and so on. In total, the thea

Brilliant_brown [7]

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3 years ago

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Now, we create another column with the product of "x" and "y". Like this:

Now, we will add another column with the squares of the values of "x". Like this:

Now, we add another column with the squares of the values of "y":

Now, we sum the values on each of the columns:

Now, to get the correlation factor we use the following formula:

$r=\frac{n\Sigma xy-\Sigma x\Sigma y}{\sqrt{(n\Sigma x^2-(\Sigma x)^2)(n\Sigma y^2-(\Sigma y)^2)}}$

Where:

$\begin{gathered} \Sigma xy=\text{ sum of the column of xy} \\ \Sigma x=\text{ sum of the column x} \\ \Sigma y=\text{ sum of the column y} \\ \Sigma x^2=\text{ sum of the column x\textasciicircum2} \\ \Sigma y^2=\text{ sum of the column y\textasciicircum2} \\ n=\text{ number of rows} \end{gathered}$

Now we substitute the values, we get:

$r=\frac{\left(6)(70.56)-(25.2)(16.4\right)}{\sqrt{((6)(107.12)-(25.2)^2)((6)(47.82)-(16.4)^2)}}$

Solving the operations:

$r=0.858$

Therefore, the correlation factor is 0.858. If the correlation factor approaches the values of +1, this means that there is a strong linear correlation between the variables "x" and "y" and this correlation tends to be with a positive slope.

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1 year ago

Theoretically, if a month is chosen 300 times,

horsena [70]

Answer:

75 times.

Step-by-step explanation:

Well there are 12 months and 3 of them start with the letter J, so theoretically, 25% of the months chosen will start with the letter J because $\frac{3}{12}=\frac{1}{4}$ , which is 25%. 25% of 300 (or $\frac{300}{4}$ , for those who like fractions) is 75, so theoretically, we can expect a month that starts with the letter J 75 times.

Hope this helps!

P.S: Please mark me as brainliest!

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3 years ago