In $2017,$ Leonardo da Vinci's painting Salvator Mundi sold for a record $$451\mathrm{.}5$ million. In $1958,$ it sold for $$131,$ equivalent in purchasing power to about $$1,120$ at $2017$ prices. The painting was originally commissioned by King Louis XII of France in about $1500.$ The Wall Street Journal guesstimated that the king may have paid Leonardo the equivalent in purchasing power of $$425,000$ in $1519.$

What was the annual rate of appreciation in the price of the painting between $1958$ and $2017$ adjusted for inflation?

Note: Do not round intermediate calculations. Enter your answer as a percent rounded to $2$ decimal places.

What was the annual estimated rate of appreciation in the price of the painting between $1519$ and $2017$ adjusted for inflatio

In $2017,$ Leonardo da Vinci's painting Salvator Mundi sold for a record $$450\mathrm{.}5$ million. In $1958,$ it sold for $$126,$ equivalent in purchasing

power to about $$1,070$ 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 in purchasing power of $$550,000$ in $1519.$

a$.$ What was the annual rate of appreciation in the price of the painting between $1958$ and $2017$ adjusted for inflation?

Note: Do not round intermediate calculations. Enter your answer as a percent rounded 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.

Note: Do not round intermediate calculations. Enter your answer as a percent rounded to $2$ decimal places.