Today is $1$ July, $2022,$ Georg plans to purchase a corporate

bond with a coupon rate of j$2=5\mathrm{.}46\%$ p$.$a$.$ and a face value

of $$100.$ This corporate bond matures at par. Its maturity date is $1$ January, $2025.$ The yield rate is assumed to bej$2=14\mathrm{.}9\%$ p$.$a$.$ Assume that this corporate bond has a $14\%$ chance of default in any six$-$month period during its term.

Assume, also, that, if default occurs, Georg will receive no further payments at all. Calculate Georg's purchase price.

Round your answer to three decimal places.