A house is purchased for $150,000.

Question

A house is purchased for $150,000. If the value of the house will appreciate 3.8% each year, how much will the house be worth in 5 years to the nearest dollar?

 

 

a. $155,775

b. $181,387

c. $123,585

d. $180,750

Answer 1

Hey Honey,

This math problem involves knowledge of the concept of appreciation and how to apply it to an asset's worth.

So let's look at what this involves >

In this particular case, we're dealing with real estate, one house to be precise. The house in question currently costs $150,000 on the market. Using the information we're given, this house is expected to appreciate (or increase in value) 3.8% each year, and the "each year" part is key to solving this problem... which we'll see below. If/when you need to appreciate a certain asset, like a house in this case, make sure to pay attention to the language used in the question. Okay! This gives us a fundamental understanding of what we're dealing with.

Now let's apply this knowledge to the problem at hand >

Our given information, along with beginning variables, is as follows:

 

P = 150000 [this is the initial price of our asset - the starting price of the house as measured in unit dollars]

r = .038 [this is the rate of appreciation - the rate of increasing value as converted to decimal form]

... and we know that we are looking ahead 5 years from now ...

 

So let's solve step by step >

 

• Step 1: Solve for the house's value 1 year from today where variable "a" represents the house's 1-year value.

P + P*r = a ... (150000) + (150000)*(.038) = a ... a = 155700

• Step 2: Solve for the house's value 2 years from today where variable "b" represents the house's 2-year value.

*** BE SURE TO NOW USE VARIABLE "a" AS YOUR NEW CURRENT PRICE OF THE HOUSE ***

a + a*r = b ... (155700) + (155700)*(.038) = b ... b = 161616.6

• Step 3: Solve for the house's value 3 years from today where variable "c" represents the house's 3-year value.

*** BE SURE TO NOW USE VARIABLE "b" AS YOUR NEW CURRENT PRICE OF THE HOUSE ***

b + b*r = c ... (161616.6) + (161616.6)*(.038) = c ... c = 167758.0308

• Step 4: Solve for the house's value 4 years from today where variable "d" represents the house's 4-year value.

*** BE SURE TO NOW USE VARIABLE "c" AS YOUR NEW CURRENT PRICE OF THE HOUSE ***
c + c*r = d ... (167758.0308) + (167758.0308)*(.038) = d ... d = 174132.8359704

• Step 5: Solve for the house's value 5 years from today where variable "e" represents the house's 5-year value.

*** BE SURE TO NOW USE VARIABLE "d" AS YOUR NEW CURRENT PRICE OF THE HOUSE ***
d + d*r = e ... (174132.8359704) + (174132.8359704)*(.038) = e ... e = 180749.8837372752

• Step 6: Round to the nearest dollar.

180749.8837372752 rounded yields 180750... which = $180,750 when expressed in unit dollars.

 

The answer is therefore choice d. $180,750... notice that throughout this process variable "r", the rate of appreciation, remained constant while the price of the house changed from year to year given the effect of appreciation.

I hope you found this answer to be both helpful and thorough. Best of luck with your studies!