Consider these long$-$term investment data:

The price of a $10-$year $$100$ par value zero$-$coupon inflation$-$indexed bond is $$81\mathrm{.}44.$

A real$-$estate property is expected to yield $2\%$ per quarter $($nominal$)$ with a SD of the $($effective$)$ quarterly rate of $10\%.$

Compute the annual rate on the real $($i$.$e$.,$ inflation$-$indexed$)$ bond.

Note: Do not round intermediate calculations. Round your answer to $2$ decimal places. $$

Real bond annual rate