Assume that the inflation rate in $2022$ was about $16\mathrm{.}00\%,$ while the $1-$yr Treasury bills issued at the start of that year offered a nominal rate of $10\mathrm{.}00\%.$ Which of the following statements is correct?

Purchasing power of money stayed the same over time.

The true increase in purchasing power that resulted from investing in these bonds was $10\mathrm{.}00\%$

The real is $-5\mathrm{.}17\%,$ thus investors in these bonds decreased their purchasing power over time.

The real rate is $16\mathrm{.}00\%,$ thus investors in these bonds increased their purchasing power over time.