Question

A woman sold a painting at auction in 1990 for $71 Million. Her family had originally purchased the work for $165,000 in 1929. What was her rate of return on investment (put your answer in percent units, example 12.5 for 12.5%)?

Show the exact steps! Thank you.

Answer 1

Originally purchased in 1929 = 165,000

Sold in 1990 = 71,000,000

Time period (1929 - 1990) = 62 years

Calculate the rate of return.

165,000 (1 + i) N = 71,000,000

In the above equation "i" is the unkmown rate of return.

165,000 (1 + i) 62 = 71,000,000

(1 + i) 62 = 71,000,000 165,000

(1 + i) 62 = 430.3030

(1 + i) =

1 + i = 1.102758

i = 1.102758 - 1

i = 0.102758 or 10.2758% or rounding to two decimal 10.28%

As per the instructions, the rate of return will be 10.28 (ignoring the percentage sign)