Exponential and Logarithm

Question

The Mendes family bought a new house 8 years ago for $126,000. The house is now worth $156,000. Assuming a steady rate of growth, what was the yearly rate of appreciation? Round your answer to the nearest tenth of a percent (1.2% etc)

Answer 1

P = P₀(1+r)^t 

 

Where P represents current principal, P₀ represents original principal, r represents rate, and t represents time. Let's replace all the variables & try to find the rate of growth.

 

156,000 = 126,000(1+r)⁸ 

 

156000/126000 = (1+r)⁸ 

 

26/21 = (1+r)⁸ 

 

(26/21)^1/8 = 1+r

 

r = (26/21)^1/8 - 1 = 1.027 -1 = .027 = 2.7%