Exponential Growth or Decay

Question

You buys a house for $130,000. It appreciates 6% per year. How much is it worth in 10 years?

Answer 1

Hi Halo S

There are Exponential Growth Formulas that you can look up and use such as

Formula

	=	exponential growth function
	=	initial amount
	=	growth rate
	=	number of time intervals

If

a = $130,000

r = 6%

x = number of time intervals ( you have 10 years listed above and an appreciation per year)

Is 130,000 your initial amount?

Can you substitute in your data and do the calculation?

Answer 2

Use the formula A = P(1+r)^t

To solve this, use formula for exponential growth:

A=P(1+r)^t

A=future value (what the house will be worth), so we need to find future worth of the house in 10 years from now.

P (initial price) your present value= 130,000

r (annual appreciation rate)= 0.06 (6%)= well it's increasing by 6%

t (time)= 10 years

Now solve for A

A=130,000(1+.06)⁽¹⁰⁾

A=130,000(1.06)¹⁰

A=$232,810.11

The house will be worth $232,810.11 in 10 years from now.

Answer 3

the underlying formula that you want to use here for compound growth is

A = P(1 + r)^t

for this set of parameters that becomes

A = $130,000(1 + 0.06)^10

A = $130,00(1.7908)

A = $232,810.20

meaning that the house will be worth approximately $232,810.20 in 10 years

Answer 4

This is a classic exponential growth problem because the value of the house is increasing over time.

Formula for Exponential Growth:

A = P(1 + r)^t

Where:

1. A is the amount (future value)
2. P is the principal (initial amount) = $130,000
3. r is the annual growth rate (as a decimal) = 6% = 0.06
4. t is the time in years = 10

Plug in the values:

A=130,000(1+0.06)¹⁰

=130,000(1.06)¹⁰

𝐴 ≈130,000 × 1.790847

𝐴 ≈ 232,810.11

Final Answer:

The house will be worth approximately $232,810.11 in 10 years.

Answer 5

a(1 + r)¹⁰ where a = amount, r = rate, and 10 = years

130,000(1.06)¹⁰ using PEMDAS order of operations

130,000 x 1.790847697 = 232,810

Answer 6

To solve this, you can use the formula for exponential growth:

A=P(1+r)^t

A=future value (what the house will be worth)

P (initial price)= 130,000

r (annual appreciation rate)= 0.06 (6%)

t (time)= 10 years

A=130,000(1+0.06)¹⁰=232,810.11

If a house is purchased for $130,000 and appreciates at a rate of 6% per year, after 10 years it will be worth approximately $232,810.11.

Answer 7

A = P(1+r)^t = 130,000(1+0.06)¹⁰ = $232,810.20