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Vilka [71]
3 years ago
14

Fill in the blank.

Mathematics
1 answer:
natima [27]3 years ago
4 0

The correct answer is: Commutative Property

Further Explanation:

The commutative property states that the order of number doesn't matter and changing the order of numbers or variables will produce the same result.

<u>Commutative Property of Addition:</u>

The Commutative Property of addition means that an expression can be written as a + b = b + a.

<u>Commutative Property of Multiplication:</u>

The Commutative Property of multiplication means that an expression can be written as a • b = b • a

Hence, the correct answer is: Commutative Property

Keywords: Commutative property, addition, multiplication

Learn more about Properties at:

  • brainly.com/question/10081622
  • brainly.com/question/10341324

#LearnwithBrainly

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When the effective interest rate is 9% per annum, what is the present value of a series of 50 annual payments that start at $100
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Answer:

$1,109.62

Step-by-step explanation:

Let's first compute the <em>future value FV.</em>  

In order to see the rule of formation, let's see the value (in $) for the first few years

<u>End of year 0</u>

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<u>End of year 1(capital + interest + new deposit)</u>

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<u>End of year 2 (capital + interest + new deposit)</u>

(1,000*(1.09)+10)*1.09 +10 =

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<u>End of year 3 (capital + interest + new deposit)</u>

\bf (1,000*(1.09)^2+10(1+1.09))(1.09)+10=\\1,000*(1.09)^3+10(1+1.09+1.09^2)

and we can see that at the end of year 50, the future value is

\bf FV=1,000*(1.09)^{50}+10(1+1.09+(1.09)^2+...+(1.09)^{49}

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\bf 1+1.09+(1.09)^2+...+(1.09)^{49}

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\bf \frac{(1.09)^{50}-1}{1.09-1}=815.08356

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\bf FV=1,000*(1.09)^{50}+10*815.08356=82,508.35564

The <em>present value PV</em> is

\bf PV=\frac{FV}{(1.09)^{50}}=\frac{82508.35564}{74.35572}=1,109.616829\approx \$1,109.62

rounded to the nearest hundredth.

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