Respuesta :
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
[tex]Compound\quaterly\ interest = Principle (1 + \frac{r}{4})^{4t}[/tex]
Where r is the rate in the decimal form.
As given
[tex]Take\ Principle\ = P_{0}[/tex]
[tex]Rate = \frac{4.8}{100}[/tex]
= 0.048
Put in the formula
[tex]Compound\quaterly\ interest = P_{0}(1 + \frac{0.048}{4})^{4t}[/tex]
[tex]Compound\quaterly\ interest = P_{0} (1 + \frac{0.048}{4})^{4t}[/tex]
[tex]Compound\quaterly\ interest = P_{0} (1 + 0.012)^{4t}[/tex] [tex]Compound\quaterly\ interest = P_{0} (1.012)^{4t}[/tex]
Now also calculated monthly.
Formula
[tex]Compound\ monthly = Principle (1 + \frac{r}{12})^{12t}[/tex]
As given
[tex]Take\ Principle\ = P_{0}[/tex]
[tex]Rate = \frac{4.8}{100}[/tex]
= 0.048
Put in the formula
[tex]Compound\ monthly = P_{0} (1 + \frac{0.048}{12})^{12t}[/tex]
[tex]Compound\ monthly = P_{0} (1 + 0.004)^{12t}[/tex]
[tex]Compound\ monthly = P_{0} (1.004)^{12t}[/tex]
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 [tex](1.0118)^{4t}[/tex] reveals the approximate quarterly growth rate of the value of Sean's house.
Answer:
The expression (1.0118)^{4t} reveals the approximate quarterly growth rate of the value of Sean's house.
