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Kaylis [27]
3 years ago
14

Sean's house is currently worth $188,900. According to a realtor, house prices in Sean's neighborhood will increase by 4.8% ever

y year. The given function represents the value of Sean's house after t years.
Which statement is true?

A.
The expression (1.0118)4t reveals the approximate quarterly growth rate of the value of Sean's house.
B.
The expression (1.0237)4t reveals the approximate quarterly growth rate of the value of Sean's house.
C.
The expression (1.0237)12t reveals the approximate monthly growth rate of the value of Sean's house.
D.
The expression (1.0118)12t reveals the approximate monthly growth rate of the value of Sean's house.
Mathematics
2 answers:
mrs_skeptik [129]3 years ago
6 0

Answer  

Given

Sean's house is currently worth $188,900.

According to a realtor, house prices in Sean's neighborhood will increase by 4.8% every year.

To prove

Formula

Compound\quaterly\ interest = Principle (1 + \frac{r}{4})^{4t}

Where r is the rate in the decimal form.

As given

Take\ Principle\ = P_{0}

Rate = \frac{4.8}{100}

              = 0.048

Put in the formula

Compound\quaterly\ interest = P_{0}(1 + \frac{0.048}{4})^{4t}

Compound\quaterly\ interest = P_{0} (1 + \frac{0.048}{4})^{4t}

Compound\quaterly\ interest = P_{0} (1 + 0.012)^{4t}       Compound\quaterly\ interest = P_{0} (1.012)^{4t}  

Now also calculated monthly.

Formula

Compound\ monthly = Principle (1 + \frac{r}{12})^{12t}

As given

Take\ Principle\ = P_{0}

Rate = \frac{4.8}{100}

              = 0.048

Put in the formula

Compound\ monthly = P_{0} (1 + \frac{0.048}{12})^{12t}

Compound\ monthly = P_{0} (1 + 0.004)^{12t}

Compound\ monthly = P_{0} (1.004)^{12t}

As the approximation quarterly growth rate of the value of sean's house is near the Compounded quarterly interest .

Thus Option (A) is correct.

i.e

The expression (1.0118)^{4t} reveals the approximate quarterly growth rate of the value of Sean's house.




                                               

                                                       




joja [24]3 years ago
6 0

Answer:

The expression (1.0118)^{4t} reveals the approximate quarterly growth rate of the value of Sean's house.

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