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Long-term Appreciation

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THE SCENARIO When they moved to Southern California in the early 1960s, a couple of my relatives bought a nice house in the hills overlooking the ocean in a tiny artist community called Laguna Beach. Fast forward to 2018, and everything has filled in around them, including a Ferrari dealership and the kinds of folks with the kind of money that allow such an establishment to remain open year after year. Changing the dates and values a bit to protect their privacy, they bought their house in February 1962, for 32,000. Today, in February 2018, that same house is worth 1.5 million (most of which is the ground on which the house sits - it's far more modest a building than the neighbors have). That is, it's now worth nearly 47 times what they bought it for. The Question: What's the average annualized appreciation of my relatives' house over the past 5 ½ decades?
THE SOLUTION My relatives bought the house in 1962, which is 2018 - 1962 = 56 years ago. 56 years is 56 x 12 = 672 months. First things first, make sure the calculator is using 12 Payments per Year. N: 672 (My relatives bought their house 56 years ago) I/YR: (This is what I'm trying to find) PV: -32,000 (They bought their house for $32,000) PMT: 0 FV: 1,500,000 (The house is worth $1.5 million today)

My relatives' house has appreciated an average of 6.89% per year over the past 56 years.

The house's value is now nearly 47 times what it was when they bought it, and yet the annualized appreciation isn't even 7%. Does that number surprise you? Did you think it would be higher than that? Lower? Why? Let us know in the comments!