The Mendes family bought a new house 11 years ago for $100,000. The house is now worth $196,000. Assuming a steady rate of growth, what was the yearly rate of appreciation?
I'm not sure how to set this problem up at all. Please help :(
100000(1+i)^11 = 196000
(1+i)^11 = 1.96
take 11th root of both sides
1+i = 1.96^(1/11) = 1.06309
i = .06309
or
appr 6.3%
check:
100000(1.06309)^11 = 196006 , not bad
To find the yearly rate of appreciation, you need to calculate the average annual growth rate over the 11-year period. Here's how you can set up the problem:
1. Calculate the total appreciation over the 11 years:
Total Appreciation = Current Value - Original Value
= $196,000 - $100,000
= $96,000
2. Calculate the average annual growth rate:
Average Annual Growth Rate = Total Appreciation / Number of Years
= $96,000 / 11
≈ $8,727.27
3. Lastly, convert the average annual growth rate to a percentage by dividing it by the original value and multiplying by 100:
Yearly Rate of Appreciation = (Average Annual Growth Rate / Original Value) * 100
= ($8,727.27 / $100,000) * 100
≈ 8.73%
Therefore, the yearly rate of appreciation for the Mendes family's house is approximately 8.73%.