Question

In 2017, Leonardo da Vinci's painting Salvator Mundi sold for a record $450.3 million. In 1958, it sold for $125, equivalent in purchasing power to about $1,060 at 2017 prices. The painting was originally commissioned by King Louis XII of France in about 1500. The Wall Street Journal guesstimated that the king may have paid Leonardo the equivalent of $575,000 in 1519.

a. What was the annual rate of appreciation in the price of the painting between 1958 and 2017 adjusted for inflation? (Do not round intermediate calculations. Round percentage answer to 2 decimal places.)

b. What was the annual estimated rate of appreciation in the price of the painting between 1519 and 2017 adjusted for inflation. (Do not round intermediate calculations. Round percentage answer to 2 decimal places.)

Answer 1

a]

future value = present value * (1 + rate)^{number of years}

For present value, we use the nominal price, or the actual price adjusted for inflation, to remove the effects of inflation from the rate of appreciation

$450.3 million = $1060 * (1 + rate)⁵⁹

rate = ($450.3 million / $1060)^1/59 - 1

rate = 0.2456, or 24.56%

b]

future value = present value * (1 + rate)^{number of years}

For present value, we use the nominal price, or the actual price adjusted for inflation, to remove the effects of inflation from the rate of appreciation

$450.3 million = $575,000 * (1 + rate)⁴⁹⁸

rate = ($450.3 million / $575,000)^1/498 - 1

rate = 0.0135, or 1.35%