$($Real interest$$ rates: approximation method$)$ The CFO of your firm has asked you for an approximate answer to this$$ question: What was the increase in real purchasing power associated with both$3-$month Treasury bills and$30-$year Treasury$$ bonds? Assume that the current$3-$month Treasury bill rate is $4\mathrm{.}34\%,$ the$30-$year Treasury bond rate is $7\mathrm{.}33\%,$ and the inflation rate is $2\mathrm{.}78\%.$Also$,$ the chief financial officer wants a short explanation should the$3-$month real rate turn out to be less than the$30-$year real rate.

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Part $1$

The inferred real interest rate of Treasury bills is