Question

The Freeman family bought a new apartment five years ago for $80,000. The house is now worth $199,200. Assuming a steady rate of growth, what was the yearly rate of appreciation?

Answer 1

199200=80000(1+r)^5
Solve for r
r=((199,200÷80,000)^(1÷5)−1)×100
r=20 %

Answer 2

Rate of yearly appreciation of the house is 20%

Explanation:

The Freeman family bought a new apartment 5 years ago for $80000.

The house worth now $199200.

We have to calculate the yearly rate of appreciation.

To get the rate of appreciation we will use the formula

P =
`P_(0)(1+r)^(t)`

P = current worth

`P_(0)` = Worth before time t years

r = rate of appreciation

t = duration

Now we put the values in the formula

`199200=80000(1+r)^(5)`

`(1+r)^(5)=(199200)/(80000)=2.49`

`(1+r)=2.49^{(1)/(5)}`

(1 + r) = 1.20

r = 1.20 - 1

r = 0.20

Or rate of yearly appreciation of the house is 20%