In $2017,$ Leonardo da Vinci's painting Salvator Mundi sold for a record $$451\mathrm{.}9$ million. In $1958,$ it sold for $$133,$ equivalent in purchasing

power to about $$1,140$ 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 $$375,000$ 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.

a$.$ Annual rate

b$.$ Annual estimated rate

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