A stock price is worth CHF $229$ on $01\mathrm{.}01\mathrm{.}2022$ and CHF $152$ on $01\mathrm{.}01\mathrm{.}2023.$ The exchange rate between CHF and $ is $1\mathrm{.}0575$ CHF$/$$ and the exchange rate between CHF and british pounds $($GPB$)$ is $0\mathrm{.}972$ CHF$/$GPB$.$ a$)$ If the price growth rate was the same in $2021$ as in $2022,$ what was the price, in CHF$,$ on $01\mathrm{.}01\mathrm{.}2021?($Round your answer to $2$ digits after the decimal point if needed$)$