MATH SOLVE

2 months ago

Q:
# TON OF FREE POINTS FOR THE SMARTEST FINANCE PERSON! EASY PEASY, JUST NEED HELP TO DO IT THE RIGHT WAY ASAP!!! WHO SHALL WIN? Do not answer incorrectly or to get free points please, or you will be reported, and not smart.David buys a home for $278,640. His home is predicted to increase in value 4% each year. What is the predicted value of David's home in 18 years? Round your answer to the nearest dollar.Options:$542,638$564,474$576,284$580,122Thanks in advance, you guys truly rock.

Accepted Solution

A:

The problem can be represented by the the exponential growth formula which is :

[tex]P(t) = A * r^{t} [/tex]

Where: t ⇒ time , A ⇒ initial amount , r ⇒ rate of increase

P(t) ⇒ predicted amount at the end of t.

For the given problem:

initial amount = A = $278,640

predicted increase in value per year = 4% =0.04

∴ r = 1 + 0.04 = 1.04

for t = 18 years

∴ [tex]P(t) = A * r^{t} =278,640 * 1.04^{18}=\framebox{564,473.5}[/tex]

Rounding to the nearest dollar ⇒ ∴ P(t) = 564,474

So, the predicted value of David's home in 18 years = $564,474

So, The correct option is $564,474

[tex]P(t) = A * r^{t} [/tex]

Where: t ⇒ time , A ⇒ initial amount , r ⇒ rate of increase

P(t) ⇒ predicted amount at the end of t.

For the given problem:

initial amount = A = $278,640

predicted increase in value per year = 4% =0.04

∴ r = 1 + 0.04 = 1.04

for t = 18 years

∴ [tex]P(t) = A * r^{t} =278,640 * 1.04^{18}=\framebox{564,473.5}[/tex]

Rounding to the nearest dollar ⇒ ∴ P(t) = 564,474

So, the predicted value of David's home in 18 years = $564,474

So, The correct option is $564,474