Question

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. 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.

Answer 1

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

Answer 2

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 + (r)/(4))^(4t)`

Where r is the rate in the decimal form.

As given

`Take\ Principle\ = P_(0)`

`Rate = (4.8)/(100)`

= 0.048

Put in the formula

`Compound\quaterly\ interest = P_(0)(1 + (0.048)/(4))^(4t)`

`Compound\quaterly\ interest = P_(0) (1 + (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 + (r)/(12))^(12t)`

As given

`Take\ Principle\ = P_(0)`

`Rate = (4.8)/(100)`

= 0.048

Put in the formula

`Compound\ monthly = P_(0) (1 + (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.