An investor earned a $5$ percent nominal risk free rate over the year. However, over the year, prices increased by $2$ percent. The investor's real risk free rate was less than his nominal rate of return. T or F$?$ My work: Real $=$ nominal $-$ inflation, so Real $=5\%-2\%=3\%.$Because $3\%($real$)$ is less than $5\%($nominal$),$ the answer is true. Is my reasoning correct?$$