Question

In 1923, Mr. Carter bought a brand-new oak desk for $21. Last year (2019), the market value of the same desk, in very good condition, is $1,850. If the average annual rate of inflation in the US during that 1923-2019 period was 2.5%, what has been the annual rate of appreciation of the desk, adjusted for inflation?

Answer 1

To solve for this growth rate, we may use the compounded annual growth rate measure:

Here, the final value is $1850, as of 2019

initial value was $21, in 1923

t = 96 years

Thus,

CAGR = 1.0477 - 1

CAGR = 0.0477 or 4.77%

In nominal terms, the desk has appreciated by 4.77% every year.

Adjusting for inflation,

In real terms, (4.77 - 2.5) = 2.27%

Thus, in real terms, the annual rate of appreciation has been 2.27%.