Question

Assume that in 2014, an 1871 $20 double eagle sold for $17,000. what was the rate of return on this investment?

Answer 1

P = $20, the principal in the year 1871.
A = $17,000, the value in the year 2014
t = 2014 - 1871 = 143 years, the duration.

Let r = the yearly return on the investment.
If we assume that the compounding is performed yearly, then
P(1 + r)¹⁴³ = A
That is,
20(1 + r)¹⁴³ = 17000
(1 + r)¹⁴³ = 850

`1+r=850^(1/143)= 1.0483`
r = 0.0483 = 4.83%

Answer: 4.83%