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)

Rate of appreciation is based on an exponential function, i. e.

if r=rate of appreciation, after n years, the new value is

F=P (1+r) ^n.

P=present worth

F=future worth.

Here,

P=126000

F=156000

n=8

so

156000=126000 (1+r) ^8

=>

(1+r) ^8 = (156000/126000) = 26/21

=>

(1+r) = (26/21) ^ (1/8) = 1.02706 (approx.)

=>

r=1.02706-1=0.02706, or

rate of appreciation is approximately 2.7%